#pragma GCC optimize ("Ofast") #include using namespace std; #define MD (1000000007U) void *wmem; char memarr[96000000]; template inline void walloc1d(T **arr, int x, void **mem = &wmem){ static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] ); (*arr)=(T*)(*mem); (*mem)=((*arr)+x); } struct Modint{ unsigned val; Modint(){ val=0; } Modint(int a){ val = ord(a); } Modint(unsigned a){ val = ord(a); } Modint(long long a){ val = ord(a); } Modint(unsigned long long a){ val = ord(a); } inline unsigned ord(unsigned a){ return a%MD; } inline unsigned ord(int a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned ord(unsigned long long a){ return a%MD; } inline unsigned ord(long long a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned get(){ return val; } inline Modint &operator+=(Modint a){ val += a.val; if(val >= MD){ val -= MD; } return *this; } inline Modint &operator-=(Modint a){ if(val < a.val){ val = val + MD - a.val; } else{ val -= a.val; } return *this; } inline Modint &operator*=(Modint a){ val = ((unsigned long long)val*a.val)%MD; return *this; } inline Modint &operator/=(Modint a){ return *this *= a.inverse(); } inline Modint operator+(Modint a){ return Modint(*this)+=a; } inline Modint operator-(Modint a){ return Modint(*this)-=a; } inline Modint operator*(Modint a){ return Modint(*this)*=a; } inline Modint operator/(Modint a){ return Modint(*this)/=a; } inline Modint operator+(int a){ return Modint(*this)+=Modint(a); } inline Modint operator-(int a){ return Modint(*this)-=Modint(a); } inline Modint operator*(int a){ return Modint(*this)*=Modint(a); } inline Modint operator/(int a){ return Modint(*this)/=Modint(a); } inline Modint operator+(long long a){ return Modint(*this)+=Modint(a); } inline Modint operator-(long long a){ return Modint(*this)-=Modint(a); } inline Modint operator*(long long a){ return Modint(*this)*=Modint(a); } inline Modint operator/(long long a){ return Modint(*this)/=Modint(a); } inline Modint operator-(void){ Modint res; if(val){ res.val=MD-val; } else{ res.val=0; } return res; } inline operator bool(void){ return val!=0; } inline operator int(void){ return get(); } inline operator long long(void){ return get(); } inline Modint inverse(){ int a = val; int b = MD; int u = 1; int v = 0; int t; Modint res; while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0){ u += MD; } res.val = u; return res; } inline Modint pw(unsigned long long b){ Modint a(*this); Modint res; res.val = 1; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } inline bool operator==(int a){ return ord(a)==val; } inline bool operator!=(int a){ return ord(a)!=val; } } ; inline Modint operator+(int a, Modint b){ return Modint(a)+=b; } inline Modint operator-(int a, Modint b){ return Modint(a)-=b; } inline Modint operator*(int a, Modint b){ return Modint(a)*=b; } inline Modint operator/(int a, Modint b){ return Modint(a)/=b; } inline Modint operator+(long long a, Modint b){ return Modint(a)+=b; } inline Modint operator-(long long a, Modint b){ return Modint(a)-=b; } inline Modint operator*(long long a, Modint b){ return Modint(a)*=b; } inline Modint operator/(long long a, Modint b){ return Modint(a)/=b; } inline int my_getchar_unlocked(){ static char buf[1048576]; static int s = 1048576; static int e = 1048576; if(s == e && e == 1048576){ e = fread_unlocked(buf, 1, 1048576, stdin); s = 0; } if(s == e){ return EOF; } return buf[s++]; } inline void rd(int &x){ int k; int m=0; x=0; for(;;){ k = my_getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = my_getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } struct MY_WRITER{ char buf[1048576]; int s; int e; MY_WRITER(){ s = 0; e = 1048576; } ~MY_WRITER(){ if(s){ fwrite_unlocked(buf, 1, s, stdout); } } } ; MY_WRITER MY_WRITER_VAR; void my_putchar_unlocked(int a){ if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){ fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout); MY_WRITER_VAR.s = 0; } MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a; } inline void wt_L(char a){ my_putchar_unlocked(a); } inline void wt_L(int x){ int s=0; int m=0; char f[10]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ my_putchar_unlocked('-'); } while(s--){ my_putchar_unlocked(f[s]+'0'); } } inline void wt_L(Modint x){ int i; i = (int)x; wt_L(i); } template inline S chmax(S &a, T b){ if(a struct Comb{ int mem_fact; T *factri; T *ifactri; Comb(){ mem_fact = 0; } inline void expand_fact(int k){ if(k <= mem_fact){ return; } chmax(k, 2* mem_fact); if(mem_fact == 0){ int i; factri = (T*)malloc(k * sizeof(T)); ifactri = (T*)malloc(k * sizeof(T)); factri[0] = 1; for(i=(1);i<(k);i++){ factri[i] = i * factri[i-1]; } ifactri[k-1] = 1 / factri[k-1]; for(i=(k-1)-1;i>=(0);i--){ ifactri[i] = (i+1) * ifactri[i+1]; } } else{ int i; factri = (T*)realloc(factri, k * sizeof(T)); ifactri = (T*)realloc(ifactri, k * sizeof(T)); for(i=(mem_fact);i<(k);i++){ factri[i] = i * factri[i-1]; } ifactri[k-1] = 1 / factri[k-1]; for(i=(k-1)-1;i>=(mem_fact);i--){ ifactri[i] = (i+1) * ifactri[i+1]; } } mem_fact = k; } inline T fac(int k){ if(mem_fact < k+1){ expand_fact(k+1); } return factri[k]; } inline T ifac(int k){ if(mem_fact < k+1){ expand_fact(k+1); } return ifactri[k]; } inline T C(int a, int b){ if(b < 0 || b > a){ return 0; } if(mem_fact < a+1){ expand_fact(a+1); } return factri[a] * ifactri[b] * ifactri[a-b]; } inline T P(int a, int b){ if(b < 0 || b > a){ return 0; } if(mem_fact < a+1){ expand_fact(a+1); } return factri[a] * ifactri[a-b]; } inline T H(int a, int b){ if(a==0 && b==0){ return 1; } if(a <= 0 || b < 0){ return 0; } if(mem_fact < a+b){ expand_fact(a+b); } return C(a+b-1, b); } inline T Multinomial(int sz, int a[]){ int i; int s = 0; T res; for(i=(0);i<(sz);i++){ s += a[i]; } if(mem_fact < s+1){ expand_fact(s+1); } res = factri[s]; for(i=(0);i<(sz);i++){ res *= ifactri[a[i]]; } return 1; } inline T Multinomial(int a){ return 1; } inline T Multinomial(int a, int b){ if(mem_fact < a+b+1){ expand_fact(a+b+1); } return factri[a+b] * ifactri[a] * ifactri[b]; } inline T Multinomial(int a, int b, int c){ if(mem_fact < a+b+c+1){ expand_fact(a+b+c+1); } return factri[a+b+c] * ifactri[a] * ifactri[b] * ifactri[c]; } inline T Multinomial(int a, int b, int c, int d){ if(mem_fact < a+b+c+d+1){ expand_fact(a+b+c+d+1); } return factri[a+b+c+d] * ifactri[a] * ifactri[b] * ifactri[c] * ifactri[d]; } inline T Catalan(int n){ if(n < 0){ return 0; } if(mem_fact < 2*n+1){ expand_fact(2*n+1); } return factri[2*n] * ifactri[n] * ifactri[n+1]; } inline T C_s(long long a, long long b){ long long i; T res; if(b < 0 || b > a){ return 0; } if(b > a - b){ b = a - b; } res = 1; for(i=(0);i<(b);i++){ res *= a - i; res /= i + 1; } return res; } inline T P_s(long long a, long long b){ long long i; T res; if(b < 0 || b > a){ return 0; } res = 1; for(i=(0);i<(b);i++){ res *= a - i; } return res; } inline T per_s(long long n, long long k){ T d; int m; if(n < 0 || k < 0){ return 0; } if(n == k && k == 0){ return 1; } if(n == 0 || k == 0){ return 0; } if(k==1){ return 1; } if(k==2){ d = n / 2; return d; } if(k==3){ d = (n-1) / 6; m = (n-1) % 6; if(m==0){ return 3 * d * d + d; } if(m==1){ return 3 * d * d + 2 * d; } if(m==2){ return 3 * d * d + 3 * d + 1; } if(m==3){ return 3 * d * d + 4 * d + 1; } if(m==4){ return 3 * d * d + 5 * d + 2; } if(m==5){ return 3 * d * d + 6 * d + 3; } } assert(0 && "per_s should be k <= 3"); return -1; } } ; int N; int M; int A[1000][1000]; int main(){ wmem = memarr; int i; int j; int k; int x; Modint res = 0; Modint tmp; Comb c; rd(N); rd(M); { int Lj4PdHRW; int KL2GvlyY; for(Lj4PdHRW=(0);Lj4PdHRW<(N);Lj4PdHRW++){ for(KL2GvlyY=(0);KL2GvlyY<(M);KL2GvlyY++){ rd(A[Lj4PdHRW][KL2GvlyY]); } } } for(i=(0);i<(N);i++){ for(j=(0);j<(M);j++){ tmp = c.C(i+j, i) * c.H(i+j+1, A[i][j]-1); res += tmp; if(i==N-1){ k =0; } else{ k =A[i+1][j]; } tmp = c.C(i+j, i) * (c.H(i+j+2, A[i][j]-1) - c.H(i+j+2, k-1)); res += tmp; if(j==M-1){ k =0; } else{ k =A[i][j+1]; } tmp = c.C(i+j, i) * (c.H(i+j+2, A[i][j]-1) - c.H(i+j+2, k-1)); res += tmp; } } wt_L(res); wt_L('\n'); return 0; } // cLay varsion 20200813-1 [beta] // --- original code --- // int N, M, A[1000][1000]; // { // int i, j, k, x; // Modint res = 0, tmp; // Comb c; // // rd(N,M,A(N,M)); // rep(i,N) rep(j,M){ // tmp = c.C(i+j, i) * c.H(i+j+1, A[i][j]-1); // res += tmp; // // k = if[i==N-1, 0, A[i+1][j]]; // tmp = c.C(i+j, i) * (c.H(i+j+2, A[i][j]-1) - c.H(i+j+2, k-1)); // res += tmp; // // k = if[j==M-1, 0, A[i][j+1]]; // tmp = c.C(i+j, i) * (c.H(i+j+2, A[i][j]-1) - c.H(i+j+2, k-1)); // res += tmp; // } // wt(res); // }