#include #include using namespace std; using int64 = long long; const int MOD = 1000000007; struct mint { int64 x; mint(const int64 x1=0) { x = x1%MOD; }; mint& operator++(int n) { x+=1; return *this; }; mint& operator--(int n) { x-=1; return *this; }; mint& operator=(int64 n) { x=n%MOD; return *this; }; mint& operator--() {x-=1; return *this; }; mint& operator+=(const mint a) { if ( (x+=a.x) >= MOD) x-=MOD; return *this; } mint& operator-=(const mint a) { if ( (x+= MOD-a.x) >= MOD) x-= MOD; return *this; } mint& operator*=(const mint a) { (x*=a.x) %= MOD; return *this; } mint& operator/=(const mint a) { return (*this) *= a.inv();} mint operator+(const mint a) const { mint res(*this); return res+=a; } mint operator-(const mint a) const { mint res(*this); return res-=a; } mint operator*(const mint a) const { mint res(*this); return res*=a; } mint operator/(const mint a) const { mint res(*this); return res/=a; } mint inv() const { return pow(MOD-2);} friend ostream& operator<<(ostream &os, const mint a) noexcept { return os << a.x; } constexpr bool operator == (const mint& r) const noexcept { return this->x == r.x; } constexpr bool operator != (const mint& r) const noexcept { return this->x != r.x; } mint pow(long long t) const { if (!t) return mint(1); mint a = pow(t>>1); a*=a; if(t&1) a*= *this; return a; } }; long long pow(long long a, long long n, long long p) { long long res = 1; while(n!=0) { if (n%2) { res *= a; res %= p; } a *= a; a %= p; n >>= 1; } return res % p; } long long inv(long long a) { return pow(a, MOD-2, MOD); } int main() { int h,w; cin >> h >> w; vector> a(h, vector(w,0)); for (int i=0; i> a[i][j]; } } vector> cpro(h+1, vector(w+1, 1)); for (int i=1; i<=h; i++) { for (int j=1; j<=w; j++) { cpro[i][j] = (cpro[i-1][j] * cpro[i][j-1])%MOD; (cpro[i][j] *= pow(cpro[i-1][j-1],MOD-2,MOD)) %= MOD; (cpro[i][j] *= a[i-1][j-1]) %= MOD; } } for (int i=0; i<=h; i++) { for (int j=0; j<=w; j++) { cerr << cpro[i][j] << " "; } cerr<> q; for (int i=0; i> r >> c; mint ans = cpro[r-1][c-1]; // 左上 // 右上 ans *= cpro[r-1][w]; ans *= inv(cpro[r-1][c]); // 左下 ans *= cpro[h][c-1]; ans *= inv(cpro[r][c-1]); // 右下 ans *= cpro[h][w]; ans *= inv(cpro[h][c]); ans *= inv(cpro[r][w]); ans *= cpro[r][c]; cout << ans << endl; } } /* * 1 2 3 * 4 5 6 * 7 8 9 * * 000001 000001 000001 000001 * 000001 000001 000002 000006 * 000001 000004 000040 000720 * 000001 000028 002240 362880 * 5*6*8*9 = 2160 * (3612880 / 6) / 28 = 2160 * * * 累積積 * 01 02 03 04 * 05 06 07 08 * 09 10 11 12 * 13 14 15 16 * * x^p ≡ x * x^{p-1} ≡ 1 mod p * x^{p-2} ≡ 1/x mod p */