/* -*- coding: utf-8 -*- * * 1683.cc: No.1683 Robot Guidance - yukicoder */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; /* constant */ const int MAX_N = 2000000; const int MOD = 1000000007; enum { XP, YP, XM, YM }; /* typedef */ typedef long long ll; /* typedef */ typedef long long ll; template struct MI { int v; MI(): v() {} MI(int _v): v(_v % MOD) {} MI(ll _v): v(_v % MOD) {} MI operator+(const MI m) const { return MI((v + m.v) % MOD); } MI operator-(const MI m) const { return MI((v + MOD - m.v) % MOD); } MI operator*(const MI m) const { return MI((ll)v * m.v % MOD); } MI &operator+=(const MI m) { return (*this = *this + m); } MI &operator-=(const MI m) { return (*this = *this - m); } MI &operator*=(const MI m) { return (*this = *this * m); } MI pow(int n) const { // a^n % MOD MI pm = 1, a = *this; while (n > 0) { if (n & 1) pm *= a; a *= a; n >>= 1; } return pm; } MI inv() const { return pow(MOD - 2); } MI operator/(const MI m) const { return *this * m.inv(); } MI &operator/=(const MI m) { return (*this = *this / m); } }; typedef MI mi; /* global variables */ mi fs[MAX_N + 1], invfs[MAX_N + 1]; int rcs[4], dcs[4]; /* subroutines */ inline mi nck(int n, int k) { if (n < k || k < 0) return 0; return fs[n] * invfs[n - k] * invfs[k]; } inline mi nhk(int n, int k) { mi c = nck(n + k - 1, k); //printf("nhk(%d, %d) = %d\n", n, k, c.v); return c; } void prepare_fracs(int n) { fs[0] = invfs[0] = 1; for (int i = 1; i <= n; i++) { fs[i] = fs[i - 1] * i; invfs[i] = fs[i].inv(); } } /* main */ int main() { int a, b, x, y; scanf("%d%d%d%d", &a, &b, &x, &y); int r = a - (abs(x) + abs(y)); if (r < 0 || (r & 1)) { puts("0"); return 0; } r /= 2; //printf("r=%d\n", r); if (x > 0) rcs[XP] = x; else if (x < 0) rcs[XM] = -x; if (y > 0) rcs[YP] = y; else if (y < 0) rcs[YM] = -y; int bq = (b + 1) / 4, br = (b + 1) % 4; for (int di = 0; di < 4; di++) { dcs[di] = bq + (di < br ? 1 : 0); if (dcs[di] == 0 && rcs[di] > 0) { puts("0"); return 0; } } //for (int di = 0; di < 4; di++) printf("%d ", dcs[di]); putchar('\n'); prepare_fracs(a + b); mi sum = 0; for (int xc = 0; xc <= r; xc++) { rcs[XP] += xc, rcs[XM] += xc; rcs[YP] += r - xc, rcs[YM] += r - xc; mi p = 1; for (int di = 0; di < 4; di++) { if (dcs[di] == 0) { if (rcs[di] > 0) p = 0; } else p *= nhk(dcs[di], rcs[di]); } sum += p; rcs[XP] -= xc, rcs[XM] -= xc; rcs[YP] -= r - xc, rcs[YM] -= r - xc; } printf("%d\n", sum.v); return 0; }