/** Micro Mezzo Macro Flation -- Overheated Economy ., Last Update: Feb. 12th
 * 2013 **/ //{

/** Header .. **/  //{
#define LOCAL

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <ctime>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>

using namespace std;

#define REP(i, n) for (int i = 0; i < int(n); ++i)
#define FOR(i, a, b) for (int i = int(a); i < int(b); ++i)
#define DWN(i, b, a) for (int i = int(b - 1); i >= int(a); --i)
#define REP_1(i, n) for (int i = 1; i <= int(n); ++i)
#define FOR_1(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define DWN_1(i, b, a) for (int i = int(b); i >= int(a); --i)
#define REP_C(i, n) for (int n____ = int(n), i = 0; i < n____; ++i)
#define FOR_C(i, a, b) for (int b____ = int(b), i = a; i < b____; ++i)
#define DWN_C(i, b, a) for (int a____ = int(a), i = b - 1; i >= a____; --i)
#define REP_N(i, n) for (i = 0; i < int(n); ++i)
#define FOR_N(i, a, b) for (i = int(a); i < int(b); ++i)
#define DWN_N(i, b, a) for (i = int(b - 1); i >= int(a); --i)
#define REP_1_C(i, n) for (int n____ = int(n), i = 1; i <= n____; ++i)
#define FOR_1_C(i, a, b) for (int b____ = int(b), i = a; i <= b____; ++i)
#define DWN_1_C(i, b, a) for (int a____ = int(a), i = b; i >= a____; --i)
#define REP_1_N(i, n) for (i = 1; i <= int(n); ++i)
#define FOR_1_N(i, a, b) for (i = int(a); i <= int(b); ++i)
#define DWN_1_N(i, b, a) for (i = int(b); i >= int(a); --i)
#define REP_C_N(i, n) for (int n____ = (i = 0, int(n)); i < n____; ++i)
#define FOR_C_N(i, a, b) for (int b____=(i=0,int(b);i<b____;++i)
#define DWN_C_N(i, b, a) for (int a____ = (i = b - 1, int(a)); i >= a____; --i)
#define REP_1_C_N(i, n) for (int n____ = (i = 1, int(n)); i <= n____; ++i)
#define FOR_1_C_N(i, a, b) for (int b____=(i=1,int(b);i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (int a____ = (i = b, int(a)); i >= a____; --i)

#define ECH(it, A) for (__typeof(A.begin()) it = A.begin(); it != A.end(); ++it)
#define REP_S(i, str) for (char *i = str; *i; ++i)
#define REP_L(i, hd, nxt) for (int i = hd; i; i = nxt[i])
#define REP_G(i, u) REP_L(i, hd[u], suc)
#define DO(n) for (int ____n##__line__ = n; ____n##__line__--;)
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)
#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)
#define REP_4(i, j, k, ii, n, m, l, nn) \
  REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)
#define REP_4_1(i, j, k, ii, n, m, l, nn) \
  REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)

#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define BSC(A, x) (lower_bound(ALL(A), x) - A.begin())
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int(A.size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define PTT pair<T, T>
#define fi first
#define se second

#define Rush for (int ____T = RD(); ____T--;)

#define Display(A, n, m)                \
  {                                     \
    REP(i, n) {                         \
      REP(j, m) cout << A[i][j] << " "; \
      cout << endl;                     \
    }                                   \
  }

#define Display_1(A, n, m)                \
  {                                       \
    REP_1(i, n) {                         \
      REP_1(j, m) cout << A[i][j] << " "; \
      cout << endl;                       \
    }                                     \
  }

#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define Ruby system("ruby main.rb")
#define Haskell system("runghc main.hs")
#define Python system("python main.py")
#define Pascal system("fpc main.pas")

typedef long long LL;
// typedef long double DB;
typedef double DB;
typedef unsigned UINT;
typedef unsigned long long ULL;

typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VF;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;

template <class T>
inline T &RD(T &);
template <class T>
inline void OT(const T &);
inline LL RD() {
  LL x;
  return RD(x);
}
inline DB &RF(DB &);
inline DB RF() {
  DB x;
  return RF(x);
}
inline char *RS(char *s);
inline char &RC(char &c);
inline char RC();
inline char &RC(char &c) {
  scanf(" %c", &c);
  return c;
}
inline char RC() {
  char c;
  return RC(c);
}
// inline char& RC(char &c){c = getchar(); return c;}
// inline char RC(){return getchar();}

template <class T>
inline T &RDD(T &x) {
  char c;
  for (c = getchar(); c < '-'; c = getchar())
    ;
  if (c == '-') {
    x = '0' - getchar();
    for (c = getchar(); '0' <= c && c <= '9'; c = getchar())
      x = x * 10 + '0' - c;
  } else {
    x = c - '0';
    for (c = getchar(); '0' <= c && c <= '9'; c = getchar())
      x = x * 10 + c - '0';
  }
  return x;
}

inline LL RDD() {
  LL x;
  return RDD(x);
}

template <class T0, class T1>
inline T0 &RD(T0 &x0, T1 &x1) {
  RD(x0), RD(x1);
  return x0;
}
template <class T0, class T1, class T2>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2) {
  RD(x0), RD(x1), RD(x2);
  return x0;
}
template <class T0, class T1, class T2, class T3>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3) {
  RD(x0), RD(x1), RD(x2), RD(x3);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6);
  return x0;
}
template <class T0, class T1>
inline void OT(const T0 &x0, const T1 &x1) {
  OT(x0), OT(x1);
}
template <class T0, class T1, class T2>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2) {
  OT(x0), OT(x1), OT(x2);
}
template <class T0, class T1, class T2, class T3>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3) {
  OT(x0), OT(x1), OT(x2), OT(x3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4, const T5 &x5) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4, const T5 &x5, const T6 &x6) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);
}
inline char &RC(char &a, char &b) {
  RC(a), RC(b);
  return a;
}
inline char &RC(char &a, char &b, char &c) {
  RC(a), RC(b), RC(c);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d) {
  RC(a), RC(b), RC(c), RC(d);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e) {
  RC(a), RC(b), RC(c), RC(d), RC(e);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e, char &f) {
  RC(a), RC(b), RC(c), RC(d), RC(e), RC(f);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g) {
  RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g);
  return a;
}
inline DB &RF(DB &a, DB &b) {
  RF(a), RF(b);
  return a;
}
inline DB &RF(DB &a, DB &b, DB &c) {
  RF(a), RF(b), RF(c);
  return a;
}
inline DB &RF(DB &a, DB &b, DB &c, DB &d) {
  RF(a), RF(b), RF(c), RF(d);
  return a;
}
inline DB &RF(DB &a, DB &b, DB &c, DB &d, DB &e) {
  RF(a), RF(b), RF(c), RF(d), RF(e);
  return a;
}
inline DB &RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f) {
  RF(a), RF(b), RF(c), RF(d), RF(e), RF(f);
  return a;
}
inline DB &RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g) {
  RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g);
  return a;
}
inline void RS(char *s1, char *s2) { RS(s1), RS(s2); }
inline void RS(char *s1, char *s2, char *s3) { RS(s1), RS(s2), RS(s3); }
template <class T0, class T1>
inline void RDD(const T0 &a, const T1 &b) {
  RDD(a), RDD(b);
}
template <class T0, class T1, class T2>
inline void RDD(const T0 &a, const T1 &b, const T2 &c) {
  RDD(a), RDD(b), RDD(c);
}

template <class T>
inline void RST(T &A) {
  memset(A, 0, sizeof(A));
}
template <class T>
inline void FLC(T &A, int x) {
  memset(A, x, sizeof(A));
}
template <class T>
inline void CLR(T &A) {
  A.clear();
}

template <class T0, class T1>
inline void RST(T0 &A0, T1 &A1) {
  RST(A0), RST(A1);
}
template <class T0, class T1, class T2>
inline void RST(T0 &A0, T1 &A1, T2 &A2) {
  RST(A0), RST(A1), RST(A2);
}
template <class T0, class T1, class T2, class T3>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  RST(A0), RST(A1), RST(A2), RST(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);
}
template <class T0, class T1>
inline void FLC(T0 &A0, T1 &A1, int x) {
  FLC(A0, x), FLC(A1, x);
}
template <class T0, class T1, class T2>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x);
}
template <class T0, class T1, class T2, class T3>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x),
      FLC(A6, x);
}
template <class T>
inline void CLR(priority_queue<T, vector<T>, less<T> > &Q) {
  while (!Q.empty()) Q.pop();
}
template <class T>
inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q) {
  while (!Q.empty()) Q.pop();
}
template <class T0, class T1>
inline void CLR(T0 &A0, T1 &A1) {
  CLR(A0), CLR(A1);
}
template <class T0, class T1, class T2>
inline void CLR(T0 &A0, T1 &A1, T2 &A2) {
  CLR(A0), CLR(A1), CLR(A2);
}
template <class T0, class T1, class T2, class T3>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);
}
template <class T>
inline void CLR(T &A, int n) {
  REP(i, n) CLR(A[i]);
}

template <class T>
inline T &SRT(T &A) {
  sort(ALL(A));
  return A;
}
template <class T, class C>
inline T &SRT(T &A, C B) {
  sort(ALL(A), B);
  return A;
}
template <class T>
inline T &UNQ(T &A) {
  A.resize(unique(ALL(SRT(A))) - A.begin());
  return A;
}

//}

/** Constant List .. **/  //{

const int dx4[] = {-1, 0, 1, 0};
const int dy4[] = {0, 1, 0, -1};

const int dx8[] = {-1, 0, 1, 0, -1, -1, 1, 1};
const int dy8[] = {0, 1, 0, -1, -1, 1, -1, 1};

const int dxhorse[] = {-2, -2, -1, -1, 1, 1, 2, 2};
const int dyhorse[] = {1, -1, 2, -2, 2, -2, 1, -1};

const LL MOD = 1000000007;
// int MOD = 99990001;
const int INF = 0x3f3f3f3f;
const LL INFF = 1LL << 60;
const DB EPS = 1e-9;
const DB OO = 1e15;
const DB PI = acos(-1.0);  // M_PI;

//}

/** Add On .. **/  //{
// <<= '0. Nichi Joo ., //{
template <class T>
inline void checkMin(T &a, const T b) {
  if (b < a) a = b;
}
template <class T>
inline void checkMax(T &a, const T b) {
  if (a < b) a = b;
}
template <class T>
inline void checkMin(T &a, T &b, const T x) {
  checkMin(a, x), checkMin(b, x);
}
template <class T>
inline void checkMax(T &a, T &b, const T x) {
  checkMax(a, x), checkMax(b, x);
}
template <class T, class C>
inline void checkMin(T &a, const T b, C c) {
  if (c(b, a)) a = b;
}
template <class T, class C>
inline void checkMax(T &a, const T b, C c) {
  if (c(a, b)) a = b;
}
template <class T>
inline T min(T a, T b, T c) {
  return min(min(a, b), c);
}
template <class T>
inline T max(T a, T b, T c) {
  return max(max(a, b), c);
}
template <class T>
inline T min(T a, T b, T c, T d) {
  return min(min(a, b), min(c, d));
}
template <class T>
inline T max(T a, T b, T c, T d) {
  return max(max(a, b), max(c, d));
}
template <class T>
inline T sqr(T a) {
  return a * a;
}
template <class T>
inline T cub(T a) {
  return a * a * a;
}
inline int ceil(int x, int y) { return (x - 1) / y + 1; }
inline int sgn(DB x) { return x < -EPS ? -1 : x > EPS; }
inline int sgn(DB x, DB y) { return sgn(x - y); }
//}
// <<= '1. Bitwise Operation ., //{
namespace BO {

inline bool _1(int x, int i) { return bool(x & 1 << i); }
inline bool _1(LL x, int i) { return bool(x & 1LL << i); }
inline LL _1(int i) { return 1LL << i; }
inline LL _U(int i) { return _1(i) - 1; };

inline int reverse_bits(int x) {
  x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
  x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
  x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
  x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
  x = ((x >> 16) & 0x0000ffff) | ((x << 16) & 0xffff0000);
  return x;
}

inline LL reverse_bits(LL x) {
  x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);
  x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);
  x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);
  x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);
  x = ((x >> 16) & 0x0000ffff0000ffffLL) | ((x << 16) & 0xffff0000ffff0000LL);
  x = ((x >> 32) & 0x00000000ffffffffLL) | ((x << 32) & 0xffffffff00000000LL);
  return x;
}

template <class T>
inline bool odd(T x) {
  return x & 1;
}
template <class T>
inline bool even(T x) {
  return !odd(x);
}
template <class T>
inline T low_bit(T x) {
  return x & -x;
}
template <class T>
inline T high_bit(T x) {
  T p = low_bit(x);
  while (p != x) x -= p, p = low_bit(x);
  return p;
}
template <class T>
inline T cover_bit(T x) {
  T p = 1;
  while (p < x) p <<= 1;
  return p;
}

inline int low_idx(int x) { return __builtin_ffs(x); }
inline int low_idx(LL x) { return __builtin_ffsll(x); }
inline int high_idx(int x) { return low_idx(reverse_bits(x)); }
inline int high_idx(LL x) { return low_idx(reverse_bits(x)); }
inline int clz(int x) { return __builtin_clz(x); }
inline int clz(LL x) { return __builtin_clzll(x); }
inline int ctz(int x) { return __builtin_ctz(x); }
inline int ctz(LL x) { return __builtin_ctzll(x); }
inline int parity(int x) { return __builtin_parity(x); }
inline int parity(LL x) { return __builtin_parityll(x); }
inline int lg2(int a) { return 31 - clz(a); }
inline int lg2(LL a) { return 63 - clz(a); }
inline int count_bits(int x) { return __builtin_popcount(x); }
inline int count_bits(LL x) { return __builtin_popcountll(x); }

}  // namespace BO
using namespace BO;  //}
// <<= '2. Number Theory .,//{
namespace NT {
inline LL __lcm(LL a, LL b) { return a * b / __gcd(a, b); }
inline void INC(int &a, int b) {
  a += b;
  if (a >= MOD) a -= MOD;
}
inline int sum(int a, int b) {
  a += b;
  if (a >= MOD) a -= MOD;
  return a;
}
inline void DEC(int &a, int b) {
  a -= b;
  if (a < 0) a += MOD;
}
inline int dff(int a, int b) {
  a -= b;
  if (a < 0) a += MOD;
  return a;
}
inline void MUL(int &a, int b) { a = (LL)a * b % MOD; }
inline int pdt(int a, int b) { return (LL)a * b % MOD; }

inline int sum(int a, int b, int c) { return sum(sum(a, b), c); }
inline int sum(int a, int b, int c, int d) { return sum(sum(a, b), sum(c, d)); }
inline int pdt(int a, int b, int c) { return pdt(pdt(a, b), c); }
inline int pdt(int a, int b, int c, int d) { return pdt(pdt(pdt(a, b), c), d); }

inline int pow(int a, int b) {
  int c(1);
  while (b) {
    if (b & 1) MUL(c, a);
    MUL(a, a), b >>= 1;
  }
  return c;
}

inline int pow(int a, LL b) {
  int c(1);
  while (b) {
    if (b & 1) MUL(c, a);
    MUL(a, a), b >>= 1;
  }
  return c;
}

template <class T>
inline T pow(T a, LL b) {
  T c(1);
  while (b) {
    if (b & 1) c *= a;
    a *= a, b >>= 1;
  }
  return c;
}

inline int _I(int b) {
  int a = MOD, x1 = 0, x2 = 1, q;
  while (true) {
    q = a / b, a %= b;
    if (!a) return (x2 + MOD) % MOD;
    DEC(x1, pdt(q, x2));

    q = b / a, b %= a;
    if (!b) return (x1 + MOD) % MOD;
    DEC(x2, pdt(q, x1));
  }
}

inline void DIV(int &a, int b) { MUL(a, _I(b)); }
inline int qtt(int a, int b) { return pdt(a, _I(b)); }

inline int phi(int n) {
  int res = n;
  for (int i = 2; sqr(i) <= n; ++i)
    if (!(n % i)) {
      DEC(res, qtt(res, i));
      do {
        n /= i;
      } while (!(n % i));
    }
  if (n != 1) DEC(res, qtt(res, n));
  return res;
}

};  // namespace NT
//}

/** Miscellaneous .. **/  //{
// <<= 'Random Event .. . //{
namespace RNG {
// srand((unsigned)time(NULL));
inline unsigned int rand16() { return ((rand()) << 15) ^ rand(); }
inline unsigned int rand32() { return (rand16() << 16) | rand16(); }
inline ULL rand64() { return ((LL)rand32() << 32) | rand32(); }
inline ULL random(LL l, LL r) { return l == r ? l : rand64() % (r - l) + l; }
int dice() { return rand() % 6; }
bool coin() { return bool(rand() % 2); }
}  // namespace RNG
using namespace RNG;
//}
// <<= 'Clock .. . //{
namespace CLOCK {
DB s0, s1, rd, k, T;
inline DB getTime() {
#ifdef LOCAL
  return 1.0 * clock() / CLOCKS_PER_SEC;
#else
  timeval tv;
  gettimeofday(&tv, 0);
  return tv.tv_sec + tv.tv_usec * 1e-6;
#endif
}

inline void st0(DB _T = 0.98) { T = _T, s0 = getTime(); }
inline void st1(DB _k = 1.618) { k = _k, s1 = getTime(); }
inline void ed1() { rd = getTime() - s1; }
inline DB elapsed() { return getTime() - s0; }
inline bool safe() { return elapsed() + rd * k < T; }
}  // namespace CLOCK
//}
// <<= 'Temp .. . //{
namespace TMP {
template <class T>
PTT operator+(const PTT &p1, const PTT &p2) {
  return PTT(p1.fi + p2.fi, p1.se + p2.se);
}

template <class T>
PTT operator-(const PTT &p1, const PTT &p2) {
  return PTT(p1.fi - p2.fi, p1.se - p2.se);
}

template <class T>
PTT operator*(const PTT &lhs, T k) {
  return PTT(lhs.fi * k, lhs.se * k);
}
}  // namespace TMP
using namespace TMP;
//}
//}

/** Algorithm    .. */  //{
// <<= '-. Math .,//{
namespace Math {
typedef long long typec;
/// Lib functions
typec GCD(typec a, typec b) { return b ? GCD(b, a % b) : a; }
typec extendGCD(typec a, typec b, typec &x, typec &y) {
  if (!b) return x = 1, y = 0, a;
  typec res = extendGCD(b, a % b, x, y), tmp = x;
  x = y, y = tmp - (a / b) * y;
  return res;
}
/// for x^k
typec power(typec x, typec k) {
  typec res = 1;
  while (k) {
    if (k & 1) res *= x;
    x *= x, k >>= 1;
  }
  return res;
}
/// for x^k mod m
typec powerMod(typec x, typec k, typec m) {
  typec res = 1;
  while (x %= m, k) {
    if (k & 1) res *= x, res %= m;
    x *= x, k >>= 1;
  }
  return res;
}
/***************************************
Inverse in mod p^t system
***************************************/
typec inverse(typec a, typec p, typec t = 1) {
  typec pt = power(p, t);
  typec x, y;
  y = extendGCD(a, pt, x, y);
  return x < 0 ? x += pt : x;
}
/***************************************
Linear congruence theorem
x = a (mod p)
x = b (mod q)
for gcd(p, q) = 1, 0 <= x < pq
***************************************/
typec linearCongruence(typec a, typec b, typec p, typec q) {
  typec x, y;
  y = extendGCD(p, q, x, y);
  while (b < a) b += q / y;
  x *= b - a, x = p * x + a, x %= p * q;
  if (x < 0) x += p * q;
  return x;
}
/***************************************
prime table
O(n)
***************************************/
const int PRIMERANGE = 1000000;
int prime[PRIMERANGE + 1];
int getPrime() {
  memset(prime, 0, sizeof(int) * (PRIMERANGE + 1));
  for (int i = 2; i <= PRIMERANGE; i++) {
    if (!prime[i]) prime[++prime[0]] = i;
    for (int j = 1; j <= prime[0] && prime[j] <= PRIMERANGE / i; j++) {
      prime[prime[j] * i] = 1;
      if (i % prime[j] == 0) break;
    }
  }
  return prime[0];
}
/***************************************
get factor of n
O(sqrt(n))
factor[][0] is prime factor
factor[][1] is factor generated by this prime
factor[][2] is factor counter

need: Prime Table
***************************************/
/// you should init the prime table before
int factor[100][3], facCnt;
int getFactors(int x) {
  facCnt = 0;
  int tmp = x;
  for (int i = 1; prime[i] <= tmp / prime[i]; i++) {
    factor[facCnt][1] = 1, factor[facCnt][2] = 0;
    if (tmp % prime[i] == 0) factor[facCnt][0] = prime[i];
    while (tmp % prime[i] == 0)
      factor[facCnt][2]++, factor[facCnt][1] *= prime[i], tmp /= prime[i];
    if (factor[facCnt][1] > 1) facCnt++;
  }
  if (tmp != 1)
    factor[facCnt][0] = tmp, factor[facCnt][1] = tmp, factor[facCnt++][2] = 1;
  return facCnt;
}
typec combinationModP(typec n, typec k, typec p) {
  if (k > n) return 0;
  if (n - k < k) k = n - k;
  typec a = 1, b = 1, x, y;
  int pcnt = 0;
  for (int i = 1; i <= k; i++) {
    x = n - i + 1, y = i;
    while (x % p == 0) x /= p, pcnt++;
    while (y % p == 0) y /= p, pcnt--;
    x %= p, y %= p, a *= x, b *= y;
    b %= p, a %= p;
  }
  if (pcnt) return 0;
  extendGCD(b, p, x, y);
  if (x < 0) x += p;
  a *= x, a %= p;
  return a;
}
};  // namespace Math
//}
// <<= '-. Geo ,.//{
namespace Geo {
#define typec double
const typec eps = 1e-8;
int dblcmp(double d) {
  if (fabs(d) < eps) return 0;
  return d > eps ? 1 : -1;
}
int sgn(double a) { return a < -eps ? -1 : a > eps; }
inline double sqr(double x) { return x * x; }
struct Point2D {
  typec x, y;
  Point2D() {}
  Point2D(typec _x, typec _y) : x(_x), y(_y){};
  void input() { scanf("%lf%lf", &x, &y); }
  void output() { printf("%.2f %.2f\n", x, y); }
  bool operator==(Point2D a) const {
    return dblcmp(a.x - x) == 0 && dblcmp(a.y - y) == 0;
  }
  bool operator<(Point2D a) const {
    return dblcmp(a.x - x) == 0 ? dblcmp(y - a.y) < 0 : x < a.x;
  }
  typec len() { return hypot(x, y); }
  typec len2() { return x * x + y * y; }
  Point2D operator+(const Point2D &A) const {
    return Point2D(x + A.x, y + A.y);
  }
  Point2D operator-(const Point2D &A) const {
    return Point2D(x - A.x, y - A.y);
  }
  Point2D operator*(const typec _x) const { return Point2D(x * _x, y * _x); }
  typec operator*(const Point2D &A) const { return x * A.x + y * A.y; }
  typec operator^(const Point2D &A) const { return x * A.y - y * A.x; }
  Point2D operator/(const typec _p) const { return Point2D(x / _p, y / _p); }
  typec distance(Point2D p) { return hypot(x - p.x, y - p.y); }
  Point2D add(Point2D p) { return Point2D(x + p.x, y + p.y); }
  Point2D sub(Point2D p) { return Point2D(x - p.x, y - p.y); }
  Point2D mul(typec b) { return Point2D(x * b, y * b); }
  Point2D div(typec b) { return Point2D(x / b, y / b); }
  typec dot(Point2D p) { return x * p.x + y * p.y; }
  typec det(Point2D p) { return x * p.y - y * p.x; }
  typec rad(Point2D a, Point2D b) {
    Point2D p = *this;
    return fabs(atan2(fabs(a.sub(p).det(b.sub(p))), a.sub(p).dot(b.sub(p))));
  }
  Point2D trunc(typec r) {
    typec l = len();
    if (!dblcmp(l)) return *this;
    r /= l;
    return Point2D(x * r, y * r);
  }
  Point2D rotleft() { return Point2D(-y, x); }
  Point2D rotright() { return Point2D(y, -x); }
  Point2D rotate(Point2D p, typec angle)  //ÈƵãpÄæʱÕëÐýתangle½Ç¶È
  {
    Point2D v = this->sub(p);
    typec c = cos(angle), s = sin(angle);
    return Point2D(p.x + v.x * c - v.y * s, p.y + v.x * s + v.y * c);
  }
};

typec cross(Point2D a, Point2D b, Point2D c) {
  return (b.sub(a)).det(c.sub(a));
}
}  // namespace Geo
using namespace Geo;
//}
//}

/** I/O Accelerator Interface .. **/  //{
template <class T>
inline T &RD(T &x) {
  // cin >> x;
  // scanf("%d", &x);
  char c;
  for (c = getchar(); c < '0'; c = getchar())
    ;
  x = c - '0';
  for (c = getchar(); '0' <= c && c <= '9'; c = getchar()) x = x * 10 + c - '0';
  // char c; c = getchar(); x = c - '0'; for (c = getchar(); c >= '0'; c =
  // getchar()) x = x * 10 + c - '0';
  return x;
}

inline DB &RF(DB &x) {
  // cin >> x;
  scanf("%lf", &x);
  /*char t; while ((t=getchar())==' '||t=='\n'); x = t - '0';
  while ((t=getchar())!=' '&&t!='\n'&&t!='.')x*=10,x+=t-'0';
  if (t=='.'){DB l=1; while ((t=getchar())!=' '&&t!='\n')l*=0.1,x +=
  (t-'0')*l;}*/
  return x;
}

inline char *RS(char *s) {
  // gets(s);
  scanf("%s", s);
  return s;
}

int Case;
template <class T>
inline void OT(const T &x) {
  // printf("Case %d: %d\n", ++Case, x);
  // printf("%.2lf\n", x);
  // printf("%d\n", x);
  cout << x << endl;
}
//}
/* ..................................................................................................................................
 */
LL cnt[20][2][7][7], dp[20][2][7][7], dpsum[20][2][7][7];
LL ten[20];
LL num[20];
void init() {
  ten[0] = 1;
  REP_1(i, 19) ten[i] = (ten[i - 1] * 10) % MOD;
}
LL dfscnt(int i, bool seven, int numbersum, int sum, bool e) {
  if (i == -1) return (seven || numbersum % 7 == 0 || sum % 7 == 0) ? 1 : 0;
  if (!e && ~cnt[i][seven][numbersum][sum])
    return cnt[i][seven][numbersum][sum];
  LL res = 0;
  int u = e ? num[i] : 9;
  for (int d = 0; d <= u; ++d)
    res = (res + dfscnt(i - 1, (seven || d == 7), (numbersum + d) % 7,
                        (sum * 10 + d) % 7, e && d == u)) %
          MOD;
  return e ? res : cnt[i][seven][numbersum][sum] = res;
}
LL mul(LL x, LL y) {
  x %= MOD;
  y %= MOD;
  return (x * y) % MOD;
}
LL dfssum(int i, int seven, int numbersum, int sum, bool e) {
  if (i == -1) return 0;
  if (!e && ~dpsum[i][seven][numbersum][sum])
    return dpsum[i][seven][numbersum][sum];
  LL res = 0;
  int u = e ? num[i] : 9;
  for (int d = 0; d <= u; ++d) {
    LL has = dfscnt(i - 1, (seven || d == 7), (numbersum + d) % 7,
                    (sum * 10 + d) % 7, e && d == u);
    LL tmp = mul(d, ten[i]);
    tmp = mul(has, tmp);
    res = (res + dfssum(i - 1, (seven || d == 7), (numbersum + d) % 7,
                        (sum * 10 + d) % 7, e && d == u)) %
          MOD;
    res = (res + tmp) % MOD;
  }
  return e ? res : dpsum[i][seven][numbersum][sum] = res;
}
LL dfs(int i, int seven, int numbersum, int sum, bool e) {
  if (i == -1) return 0;
  if (!e && ~dp[i][seven][numbersum][sum]) return dp[i][seven][numbersum][sum];
  LL res = 0;
  int u = e ? num[i] : 9;
  for (int d = 0; d <= u; ++d) {
    LL has = dfscnt(i - 1, (seven || d == 7), (numbersum + d) % 7,
                    (sum * 10 + d) % 7, e && d == u);
    LL sum1 = dfssum(i - 1, (seven || d == 7), (numbersum + d) % 7,
                     (sum * 10 + d) % 7, e && d == u);
    LL tmp = mul(d, ten[i]);
    LL nownow = mul(tmp, tmp);
    LL hasnow = mul(nownow, has);
    nownow = mul(2, mul(tmp, sum1));
    res = (res + dfs(i - 1, (seven || d == 7), (numbersum + d) % 7,
                     (sum * 10 + d) % 7, e && d == u)) %
          MOD;
    res = (res + hasnow) % MOD;
    res = (res + nownow) % MOD;
  }
  return e ? res : dp[i][seven][numbersum][sum] = res;
}
LL l, r;
LL gao(LL x) {
  LL a = x, b = x + 1, c = 2 * x + 1;
  LL p = 2;
  if (a % p == 0)
    a /= p;
  else if (b % p == 0)
    b /= p;
  else if (c % p == 0)
    c /= p;
  p = 3;
  if (a % p == 0)
    a /= p;
  else if (b % p == 0)
    b /= p;
  else if (c % p == 0)
    c /= p;
  return mul(mul(a, b), c);
}
LL getans(LL x) {
  if (x == 0) return 0;
  int s = 0;
  LL y = x;
  while (x) {
    num[s++] = x % 10;
    x /= 10;
  }
  x = y;
  LL res = gao(x);  // return res;
  res -= dfs(s - 1, 0, 0, 0, 1);
  res %= MOD;
  res += MOD;
  res %= MOD;
  return res;
}
void solve() {
  RD(l, r);
  LL ans = getans(r) - getans(l - 1);
  ans %= MOD;
  ans += MOD;
  ans %= MOD;
  printf("%I64d\n", ans);
}
int main() {
#ifndef ONLINE_JUDGE
  freopen("in.txt", "r", stdin);
  // freopen("out.txt", "w", stdout);
#endif

  FLC(dp, -1);
  FLC(cnt, -1);
  FLC(dpsum, -1);
  init();
  Rush solve();
}