80 lines
1.8 KiB
C++
80 lines
1.8 KiB
C++
#include<stdio.h>
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#include<string.h>
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#define MAXD 33
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#define MOD 1000000007
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typedef __int64 LL;
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int N, M, K;
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LL C[MAXD][MAXD][MAXD], f[MAXD][MAXD], X[MAXD], S[MAXD];
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LL fac(LL a, int n)
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{
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int i;
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LL ans = 1;
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for(i = 0; i < n; i ++) ans = ans * a % MOD;
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return ans;
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}
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void exgcd(LL a, LL b, LL &x, LL &y)
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{
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if(b == 0) x = 1, y = 0;
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else exgcd(b, a % b, y, x), y -= x * (a / b);
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}
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LL getinv(LL a)
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{
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LL x, y;
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exgcd(a, MOD, x, y);
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x %= MOD;
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if(x < 0) x += MOD;
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return x;
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}
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void prepare()
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{
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int i, j, t;
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memset(C, 0, sizeof(C));
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C[1][0][0] = 1;
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for(i = 1; i <= 32; i ++)
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{
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C[1][i][0] = 1;
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for(j = 1; j <= i; j ++)
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C[1][i][j] = (C[1][i - 1][j] + C[1][i - 1][j - 1]) % MOD;
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}
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for(t = 2; t <= 32; t ++)
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for(i = 0; i <= 32; i ++)
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for(j = 0; j <= 32; j ++)
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C[t][i][j] = fac(C[1][i][j], t);
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}
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void solve()
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{
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int i, j, k, t;
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LL ans;
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for(t = 1; t <= N; t ++)
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{
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memset(f, 0, sizeof(f)), f[0][0] = 1;
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for(i = 1; i <= K; i ++)
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for(j = 0; j <= M; j ++)
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for(k = 0; k <= j; k ++)
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f[i][j] = (f[i][j] + f[i - 1][k] * C[t][M - k][j - k]) % MOD;
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X[t] = f[K][M];
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}
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S[0] = 1, S[1] = X[1];
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for(i = 2; i <= N; i ++)
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{
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S[i] = 0;
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for(j = 1; j <= i; j ++)
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{
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if(j & 1) S[i] = (S[i] + S[i - j] * X[j] + MOD) % MOD;
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else S[i] = (S[i] - S[i - j] * X[j] + MOD) % MOD;
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}
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S[i] = S[i] * getinv(i) % MOD;
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}
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ans = S[N];
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for(i = 2; i <= N; i ++) ans = ans * i % MOD;
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if(ans < 0) ans += MOD;
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printf("%I64d\n", ans);
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}
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int main()
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{
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prepare();
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while(scanf("%d%d%d", &N, &M, &K) == 3)
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solve();
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return 0;
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}
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