#include #include template std::vector vec(int len, T elem) { return std::vector(len, elem); } template struct ModInt { using lint = long long; int val; // constructor ModInt(lint v = 0) : val(v % MOD) { if (val < 0) val += MOD; }; // unary operator ModInt operator+() const { return ModInt(val); } ModInt operator-() const { return ModInt(MOD - val); } ModInt inv() const { return this->pow(MOD - 2); } // arithmetic ModInt operator+(const ModInt& x) const { return ModInt(*this) += x; } ModInt operator-(const ModInt& x) const { return ModInt(*this) -= x; } ModInt operator*(const ModInt& x) const { return ModInt(*this) *= x; } ModInt operator/(const ModInt& x) const { return ModInt(*this) /= x; } ModInt pow(lint n) const { auto x = ModInt(1); auto b = *this; while (n > 0) { if (n & 1) x *= b; n >>= 1; b *= b; } return x; } // compound assignment ModInt& operator+=(const ModInt& x) { if ((val += x.val) >= MOD) val -= MOD; return *this; } ModInt& operator-=(const ModInt& x) { if ((val -= x.val) < 0) val += MOD; return *this; } ModInt& operator*=(const ModInt& x) { val = lint(val) * x.val % MOD; return *this; } ModInt& operator/=(const ModInt& x) { return *this *= x.inv(); } // compare bool operator==(const ModInt& b) const { return val == b.val; } bool operator!=(const ModInt& b) const { return val != b.val; } bool operator<(const ModInt& b) const { return val < b.val; } bool operator<=(const ModInt& b) const { return val <= b.val; } bool operator>(const ModInt& b) const { return val > b.val; } bool operator>=(const ModInt& b) const { return val >= b.val; } // I/O friend std::istream& operator>>(std::istream& is, ModInt& x) noexcept { lint v; is >> v; x = v; return is; } friend std::ostream& operator<<(std::ostream& os, const ModInt& x) noexcept { return os << x.val; } }; template struct Combination { int max_n; std::vector f, invf; explicit Combination(int n) : max_n(n), f(n + 1), invf(n + 1) { f[0] = 1; for (int i = 1; i <= n; ++i) { f[i] = f[i - 1] * i; } invf[max_n] = f[max_n].inv(); for (int i = max_n - 1; i >= 0; --i) { invf[i] = invf[i + 1] * (i + 1); } } T fact(int n) const { return n < 0 ? T(0) : f[n]; } T invfact(int n) const { return n < 0 ? T(0) : invf[n]; } T perm(int a, int b) const { return a < b || b < 0 ? T(0) : f[a] * invf[a - b]; } T binom(int a, int b) const { return a < b || b < 0 ? T(0) : f[a] * invf[a - b] * invf[b]; } }; constexpr int MOD = 1000000007; using mint = ModInt; const Combination C(2000000); void solve() { int n, m; std::cin >> n >> m; auto xss = vec(n + 1, vec(m + 1, 0)); for (int x = 0; x < n; ++x) { for (int y = 0; y < m; ++y) { std::cin >> xss[x][y]; } } mint ans = 0; for (int x = 0; x < n; ++x) { for (int y = 0; y < m; ++y) { int s = xss[x][y]; ans += C.binom(x + y + s - 1, x) * C.binom(y + s - 1, y); { int t = xss[x + 1][y]; ans += C.binom(x + y, x) * (C.binom(x + y + s, s - 1) - C.binom(x + y + t, t - 1)); } { int t = xss[x][y + 1]; ans += C.binom(x + y, x) * (C.binom(x + y + s, s - 1) - C.binom(x + y + t, t - 1)); } } } std::cout << ans << "\n"; } int main() { std::cin.tie(nullptr); std::ios::sync_with_stdio(false); solve(); return 0; }