#include using namespace std; using lint = long long int; using P = pair; using PL = pair; #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) #define ALL(a) (a).begin(),(a).end() constexpr int MOD = 1000000007; constexpr lint B1 = 1532834020; constexpr lint M1 = 2147482409; constexpr lint B2 = 1388622299; constexpr lint M2 = 2147478017; constexpr int INF = 2147483647; void yes(bool expr) {cout << (expr ? "Yes" : "No") << "\n";} constexpr int MAX = 2000000; lint fact[MAX], finv[MAX], inv[MAX]; void cominit() { fact[0] = fact[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; FOR(i, 2, MAX){ fact[i] = fact[i-1] * i % MOD; inv[i] = MOD - inv[MOD%i] * (MOD/i) % MOD; finv[i] = finv[i-1] * inv[i] % MOD; } } lint power(lint x, lint n, lint mod) { lint ret = 1; while(n > 0) { if(n & 1) (ret *= x) %= mod; (x *= x) %= mod; n >>= 1; } return ret; } lint ncr(lint n, lint r, lint mod) { if(n < 0 || r < 0 || n-r < 0) return 0; return fact[n]*finv[r]%mod*finv[n-r]%mod; } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); lint N, M; cin >> N >> M; vector> S(N+1, vector(M+1)); REP(i, N) REP(j, M) cin >> S[i][j]; lint ans = 0; cominit(); REP(i, N) REP(j, M) { ans = (ans + ncr(S[i][j]-1+i+j, i+j, MOD) * ncr(i+j, j, MOD) % MOD) % MOD; ans = (ans + ((S[i][j] * ncr(S[i][j]+i+j, i+j, MOD) % MOD - S[i+1][j] * ncr(S[i+1][j]+i+j, i+j, MOD) % MOD + MOD ) * power(i+j+1, MOD-2, MOD) % MOD * ncr(i+j, j, MOD) % MOD)) % MOD; ans = (ans + ((S[i][j] * ncr(S[i][j]+i+j, i+j, MOD) % MOD - S[i][j+1] * ncr(S[i][j+1]+i+j, i+j, MOD) % MOD + MOD ) * power(i+j+1, MOD-2, MOD) % MOD * ncr(i+j, j, MOD) % MOD)) % MOD; } cout << ans << endl; }