#yukicoder 2792 Security Cameras on Young Diagram #MODnCr計算機(行数削減版) class MODnCr: def __init__(self,fact_N,MOD,invN=1000): self._N=fact_N; self._invN=invN; self._MOD=MOD; self._fact=[1]*(self._N+1); self._inv=[1]*(self._invN+1); self._finv=[1]*(self._N+1) for i in range(2,self._N+1): self._fact[i]=self._fact[i-1]*i%self._MOD for i in range(2,self._invN+1): self._inv[i]=-self._inv[self._MOD%i]*(self._MOD//i)%self._MOD for i in range(2,min(self._invN,self._N)+1): self._finv[i]=self._finv[i-1]*self._inv[i]%self._MOD self._finv[self._N]=pow(self._fact[self._N],self._MOD-2,self._MOD) for i in range(self._N-1,self._invN,-1): self._finv[i]=self._finv[i+1]*(i+1)%self._MOD def _update(self,N): if N<=self._N: return 0 dist=N-self._N; self._fact.extend([1]*dist); self._finv.extend([1]*dist) for i in range(self._N+1,N+1): self._fact[i]=self._fact[i-1]*i%self._MOD self._finv[N]=self.modinv(self._fact[N]) for i in range(N-1,self._N,-1): self._finv[i]=self._finv[i+1]*(i+1)%self._MOD self._N=N; return 1 def fact(self,x): self._update(x) if x>self._N else None; return self._fact[x] def finv(self,x): self._update(x) if x>self._N else None; return self._finv[x] def modinv(self,x): return self._inv[x] if x<=self._invN else (-self._inv[self._MOD%x]*(self._MOD//x))%self._MOD if x> self._invN>=self._MOD%x else pow(x,self._MOD-2,self._MOD) def nCr(self,n,r): self._update(n); return 0 if any([n 0 else 1, 0, 0, ・・・ #DP = [[1] + [0] * A[0]] + [[nCr.nCr(i + j - 1, j) for j in range(A[0] + 1)] for i in range(1, N + 1)] #ans = sum(DP[N][j] for j in range(A[-1] + 1)) % MOD ans = sum(nCr.nCr(N + j - 1, j) for j in range(A[-1] + 1)) % MOD for i in range(N): for j in range(A[i] + 1, A[i - 1] + 1): #ans += DP[i][j] ans += nCr.nCr(i + j - 1, j) ans %= MOD print(ans % MOD)