We have a rectangular parallelepiped of dimensions A×B×C, divided into 1×1×1 small cubes. The small cubes have coordinates from (0, 0, 0) through (A-1, B-1, C-1).

Let p, q and r be integers. Consider the following set of abc small cubes:

\\{(\ (p + i) mod A, (q + j) mod B, (r + k) mod C\ ) | i, j and k are integers satisfying 0 ≤ i < a, 0 ≤ j < b, 0 ≤ k < c \\}

A set of small cubes that can be expressed in the above format using some integers p, q and r, is called a torus cuboid of size a×b×c.

Find the number of the sets of torus cuboids of size a×b×c that satisfy the following condition, modulo 10^9+7:

* No two torus cuboids in the set have intersection.
* The union of all torus cuboids in the set is the whole rectangular parallelepiped of dimensions A×B×C.

Constraints

* 1 ≤ a < A ≤ 100
* 1 ≤ b < B ≤ 100
* 1 ≤ c < C ≤ 100
* All input values are integers.

Input

Input is given from Standard Input in the following format:


a b c A B C


Output

Print the number of the sets of torus cuboids of size a×b×c that satisfy the condition, modulo 10^9+7.

Examples

Input

1 1 1 2 2 2


Output

1


Input

2 2 2 4 4 4


Output

744


Input

2 3 4 6 7 8


Output

0


Input

2 3 4 98 99 100


Output

471975164
#include <bits/stdc++.h>
#define MP make_pair
#define PB push_back
#define int long long
#define st first
#define nd second
#define rd third
#define FOR(i, a, b) for(int i =(a); i <=(b); ++i)
#define RE(i, n) FOR(i, 1, n)
#define FORD(i, a, b) for(int i = (a); i >= (b); --i)
#define REP(i, n) for(int i = 0;i <(n); ++i)
#define VAR(v, i) __typeof(i) v=(i)
#define FORE(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i)
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())
#define __builtin_ctz __builtin_ctzll
#define __builtin_clz __builtin_clzll
#define __builtin_popcount __builtin_popcountll
using namespace std;
template<typename TH> void _dbg(const char* sdbg, TH h) { cerr<<sdbg<<"="<<h<<"\n"; }
template<typename TH, typename... TA> void _dbg(const char* sdbg, TH h, TA... t) {
  while(*sdbg != ',') { cerr<<*sdbg++; } cerr<<"="<<h<<","; _dbg(sdbg+1, t...);
}
#ifdef LOCAL
#define debug(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
#define debugv(x) {{cerr <<#x <<" = "; FORE(itt, (x)) cerr <<*itt <<", "; cerr <<"\n"; }}
#else
#define debug(...) (__VA_ARGS__)
#define debugv(x)
#define cerr if(0)cout
#endif
#define next ____next
#define prev ____prev
#define left ____left
#define hash ____hash
typedef long long ll;
typedef long double LD;
typedef pair<int, int> PII;
typedef pair<ll, ll> PLL;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<ll> VLL;
typedef vector<pair<int, int> > VPII;
typedef vector<pair<ll, ll> > VPLL;

template<class C> void mini(C&a4, C b4){a4=min(a4, b4); }
template<class C> void maxi(C&a4, C b4){a4=max(a4, b4); }
template<class T1, class T2>
ostream& operator<< (ostream &out, pair<T1, T2> pair) { return out << "(" << pair.first << ", " << pair.second << ")";}
template<class A, class B, class C> struct Triple { A first; B second; C third;
  bool operator<(const Triple& t) const { if (st != t.st) return st < t.st; if (nd != t.nd) return nd < t.nd; return rd < t.rd; } };
template<class T> void ResizeVec(T&, vector<int>) {}
template<class T> void ResizeVec(vector<T>& vec, vector<int> sz) {
  vec.resize(sz[0]); sz.erase(sz.begin()); if (sz.empty()) { return; }
  for (T& v : vec) { ResizeVec(v, sz); }
}
typedef Triple<int, int, int> TIII;
template<class A, class B, class C>
ostream& operator<< (ostream &out, Triple<A, B, C> t) { return out << "(" << t.st << ", " << t.nd << ", " << t.rd << ")"; }
template<class T> ostream& operator<<(ostream& out, vector<T> vec) { out<<"("; for (auto& v: vec) out<<v<<", "; return out<<")"; }
template<class T> ostream& operator<<(ostream& out, set<T> vec) { out<<"("; for (auto& v: vec) out<<v<<", "; return out<<")"; }
template<class L, class R> ostream& operator<<(ostream& out, map<L, R> vec) { out<<"("; for (auto& v: vec) out<<v<<", "; return out<<")"; }

const int P = 1e9 + 7;
int spow(int a, int b) {
  int r = 1;
  while (b) {
    if (b % 2) {
      r = r * a % P;
    }
    a = a * a % P;
    b /= 2;
  }
  return r;
}
int Cut1(int a, int b, int c, int A, int B, int C) {
  return c * spow((a * spow(b, A / a) + b * spow(a, B / b) - a * b) % P, C / c) % P;
}
int Cut2(int a, int b, int c, int A, int B, int C) {
  return a * b * spow(c, A / a * B / b) % P;
}
int Cut3(int a, int b, int c, int A, int B, int C) {
  return a * b * c;
}
const int N = 111;
int dp[N][N][N];
int newt[N][N];
void AddSelf(int& a, int b) {
  //debug(a, b);
  assert(b >= 0 && b < P);
  a += b;
  if (a >= P) {
    a -= P;
  }
}
int32_t main() {

  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(10);
  cerr << fixed << setprecision(10);
  cin.tie(0);
  //double beg_clock = 1.0 * clock() / CLOCKS_PER_SEC;
  
  REP (i, N) {
    newt[i][0] = newt[i][i] = 1;
    RE (j, i - 1) {
      newt[i][j] = (newt[i - 1][j] + newt[i - 1][j - 1]) % P;
    }
  }
  
  int a, b, c, A, B, C;
  cin>>a>>b>>c>>A>>B>>C;
  if (A % a || B % b || C % c) { cout<<0<<endl; return 0; }
  int with_cut = Cut1(a, b, c, A, B, C) + Cut1(b, c, a, B, C, A) + Cut1(c, a, b, C, A, B) -
                (Cut2(a, b, c, A, B, C) + Cut2(b, c, a, B, C, A) + Cut2(c, a, b, C, A, B)) + Cut3(a, b, c, A, B, C);
  with_cut = ((with_cut % P) + P) % P;
  debug(with_cut);
  
  int without_cut = 0;
  VI powsc1(N);
  VI powsc0(N);
  powsc1[0] = powsc0[0] = 1;
  RE (i, N - 1) {
    powsc1[i] = powsc1[i - 1] * (c - 1) % P;
    powsc0[i] = powsc0[i - 1] * c % P;
  }
  RE (Y, N - 1) {
    dp[Y][0][Y] = 1;
    RE (X, N - 1) {
      FOR (prv_moving, 0, Y) {
        FOR (new_moving, 0, prv_moving) {
          if (prv_moving == new_moving) {
            AddSelf(dp[Y][X][new_moving], dp[Y][X - 1][prv_moving] * (powsc0[Y - new_moving] - 1) % P);
          } else {
            if (Y == 1 && X == 1) {
              debug(prv_moving, new_moving);
              debug(dp[Y][X - 1][prv_moving], powsc0[Y - prv_moving], newt[prv_moving][new_moving], powsc1[prv_moving - new_moving]);
            }
            AddSelf(dp[Y][X][new_moving], dp[Y][X - 1][prv_moving] * powsc0[Y - prv_moving] % P * newt[prv_moving][new_moving] % P * powsc1[prv_moving - new_moving] % P);
          }
        }
      }
    }
  }
  debug(dp[1][1][0], dp[1][1][1]);
  RE (rigid_hor, B / b - 1) {
    RE (rigid_ver, A / a - 1) {
      int moving_hor = B / b - rigid_hor;
      int moving_ver = A / a - rigid_ver;
      int posses_at_layer = (spow(a, moving_hor) + spow(b, moving_ver) - 1) % P;
      int bad = (spow(spow(a, moving_hor), C / c) + spow(spow(b, moving_ver), C / c) + P - 1) % P;
      without_cut = (without_cut + (spow(posses_at_layer, C / c) - bad + P) % P * dp[rigid_hor][rigid_ver][0] % P * newt[B / b][moving_hor] % P * newt[A / a][moving_ver]) % P;
    }
  }
  without_cut *= a * b * c;
  cout<<(with_cut + without_cut) % P<<endl;
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  return 0;
}
