#include #define rep(i,n) for (int i = 0; i < (n); ++i) #define rrep(i,n) for (int i = (n)-1; i >= 0; --i) #define chmax(a, b) a = max(a, b) #define chmin(a, b) a = min(a, b) #define all(x) (x).begin(), (x).end() using namespace std; using ll = long long; using P = pair; using VI = vector; using VVI = vector; #define MOD 1000000007 //#define MOD 998244353 struct mint { int i; mint() : i(0) {} mint(int x) { i = int(x % MOD); if (i < 0) i += MOD; } template mint(T x) { i = int(x % MOD); if (i < 0) i += MOD; } mint operator+(const mint x) const {return i + x.i;} mint operator-(const mint x) const {return i - x.i;} mint operator*(const mint x) const {return (long long)i * x.i;} mint operator/(const mint x) const {return (long long)i * x.pow(MOD - 2).i;} mint inv() {return pow(MOD - 2);} template mint pow(T p) const { long long r = 1; long long t = i; for(; p > 0; p >>= 1) { if (p & 1) r = r * t % MOD; t = t * t % MOD; } return r; } template static mint pow(T1 a, T2 b) { long long r = 1; long long t = (long long)(a % MOD); for(; b > 0; b >>= 1) { if (b & 1) r = r * t % MOD; t = t * t % MOD; } return r; } mint& operator+=(const mint x) { i = (i + x.i) % MOD; return *this; } mint& operator-=(const mint x) { i = i - x.i; if (i < 0) i += MOD; return *this; } mint& operator*=(const mint x) { i = (int)((long long)i * x.i % MOD); return *this; } mint& operator/=(const mint x) { i = (long long)i * x.pow(MOD - 2).i % MOD; return *this; } }; std::ostream& operator<<(std::ostream& os, const mint& m) { return os << m.i; } struct combination { vector fact, ifact; combination(int n):fact(n+1),ifact(n+1) { assert(n < MOD); fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i; } mint operator()(int n, int k) { if (k < 0 || k > n) return 0; return fact[n]*ifact[k]*ifact[n-k]; } } comb(5e6); int main() { int n, m; cin >> n >> m; VVI s(n, VI(m)); rep(i, n) rep(j, m) cin >> s[i][j]; mint ans = 0; VVI blockmax = s; rrep(i, n) rrep(j, m) { if (i + 1 < n) chmax(blockmax[i][j], blockmax[i+1][j]); if (j + 1 < m) chmax(blockmax[i][j], blockmax[i][j+1]); } rep(i, n) rep(j, m) { if (i == n - 1) { ans += comb(i + j, i) * comb(i + j + s[i][j], i + j + 1); } else { ans += comb(i + j, i) * (comb(i + j + s[i][j], i + j + 1) - comb(i + j + blockmax[i + 1][j], i + j + 1)); } if (j == m - 1) { ans += comb(i + j, i) * comb(i + j + s[i][j], i + j + 1); } else { ans += comb(i + j, i) * (comb(i + j + s[i][j], i + j + 1) - comb(i + j + blockmax[i][j + 1], i + j + 1)); } ans += comb(i + j, i) * comb(i + j + s[i][j] - 1, i + j); } cout << ans << endl; }