AOJ2751.cpp

#include <bits/stdc++.h>

#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()

using namespace std;

using ll = long long;

const int mod = 1000000007;

struct Mod {
  int n;
  Mod () : n(0) {;}
  Mod (int m) : n(m) {
    if (n >= mod) n %= mod;
    else if (n < 0) n = (n % mod + mod) % mod;
  }
  operator int() { return n; }
};

bool operator==(Mod a, Mod b) { return a.n == b.n; }
Mod operator+=(Mod &a, Mod b) { a.n += b.n; if (a.n >= mod) a.n -= mod; return a; }
Mod operator-=(Mod &a, Mod b) { a.n -= b.n; if (a.n < 0) a.n += mod; return a; }
Mod operator*=(Mod &a, Mod b) { a.n = ((long long)a.n * b.n) % mod; return a; }
Mod operator+(Mod a, Mod b) { return a += b; }
Mod operator-(Mod a, Mod b) { return a -= b; }
Mod operator*(Mod a, Mod b) { return a *= b; }
Mod operator^(Mod a, int n) {
  if (n == 0) return Mod(1);
  Mod res = (a * a) ^ (n / 2);
  if (n % 2) res = res * a;
  return res;
}

ll inv(ll a, ll p) {
  return (a == 1 ? 1 : (1 - p * inv(p%a, a)) / a + p);
}
Mod operator/(Mod a, Mod b) { return a * Mod(inv(b, mod)); }

#define MAX_N 4096000

Mod fact[MAX_N], factinv[MAX_N];
void init() {
  fact[0] = Mod(1); factinv[0] = 1;
  REP(i,MAX_N-1) {
    fact[i+1] = fact[i] * Mod(i+1);
    factinv[i+1] = factinv[i] / Mod(i+1);
  }
}
Mod comb(int a, int b) { return fact[a] * factinv[b] * factinv[a-b]; }

Mod hyper_comb(int a, int b) {
  if (b == 0) return Mod(a == 0);
  return comb(a + b - 1, b - 1);
}

int main() {
  init();
  int A, B, C, Sx, Sy;
  while (cin >> A >> B >> C >> Sx >> Sy, A + B + C) {
    Mod res = 0;
    Mod base = fact[A + B + C] * factinv[A] * factinv[B] * factinv[C];
    REP(com, min(Sx, Sy) + 1) {
      int Awin = Sx - com, Bwin = Sy - com;
      if (Awin < A || Bwin < B) continue;
      Mod x = hyper_comb(Awin - A, A);
      Mod y = hyper_comb(Bwin - B, B);
      Mod z = hyper_comb(com, A + B + C);
      res += x * y * z;
    }
    cout << res * base << endl;
  }
  return 0;
}