mirror of
https://github.com/Kiritow/OJ-Problems-Source.git
synced 2024-03-22 13:11:29 +08:00
80 lines
1.8 KiB
C++
80 lines
1.8 KiB
C++
|
#include<stdio.h>
|
||
|
|
#include<string.h>
|
||
|
|
#define MAXD 33
|
||
|
|
#define MOD 1000000007
|
||
|
|
typedef __int64 LL;
|
||
|
|
int N, M, K;
|
||
|
|
LL C[MAXD][MAXD][MAXD], f[MAXD][MAXD], X[MAXD], S[MAXD];
|
||
|
|
LL fac(LL a, int n)
|
||
|
|
{
|
||
|
|
int i;
|
||
|
|
LL ans = 1;
|
||
|
|
for(i = 0; i < n; i ++) ans = ans * a % MOD;
|
||
|
|
return ans;
|
||
|
|
}
|
||
|
|
void exgcd(LL a, LL b, LL &x, LL &y)
|
||
|
|
{
|
||
|
|
if(b == 0) x = 1, y = 0;
|
||
|
|
else exgcd(b, a % b, y, x), y -= x * (a / b);
|
||
|
|
}
|
||
|
|
LL getinv(LL a)
|
||
|
|
{
|
||
|
|
LL x, y;
|
||
|
|
exgcd(a, MOD, x, y);
|
||
|
|
x %= MOD;
|
||
|
|
if(x < 0) x += MOD;
|
||
|
|
return x;
|
||
|
|
}
|
||
|
|
void prepare()
|
||
|
|
{
|
||
|
|
int i, j, t;
|
||
|
|
memset(C, 0, sizeof(C));
|
||
|
|
C[1][0][0] = 1;
|
||
|
|
for(i = 1; i <= 32; i ++)
|
||
|
|
{
|
||
|
|
C[1][i][0] = 1;
|
||
|
|
for(j = 1; j <= i; j ++)
|
||
|
|
C[1][i][j] = (C[1][i - 1][j] + C[1][i - 1][j - 1]) % MOD;
|
||
|
|
}
|
||
|
|
for(t = 2; t <= 32; t ++)
|
||
|
|
for(i = 0; i <= 32; i ++)
|
||
|
|
for(j = 0; j <= 32; j ++)
|
||
|
|
C[t][i][j] = fac(C[1][i][j], t);
|
||
|
|
}
|
||
|
|
void solve()
|
||
|
|
{
|
||
|
|
int i, j, k, t;
|
||
|
|
LL ans;
|
||
|
|
for(t = 1; t <= N; t ++)
|
||
|
|
{
|
||
|
|
memset(f, 0, sizeof(f)), f[0][0] = 1;
|
||
|
|
for(i = 1; i <= K; i ++)
|
||
|
|
for(j = 0; j <= M; j ++)
|
||
|
|
for(k = 0; k <= j; k ++)
|
||
|
|
f[i][j] = (f[i][j] + f[i - 1][k] * C[t][M - k][j - k]) % MOD;
|
||
|
|
X[t] = f[K][M];
|
||
|
|
}
|
||
|
|
S[0] = 1, S[1] = X[1];
|
||
|
|
for(i = 2; i <= N; i ++)
|
||
|
|
{
|
||
|
|
S[i] = 0;
|
||
|
|
for(j = 1; j <= i; j ++)
|
||
|
|
{
|
||
|
|
if(j & 1) S[i] = (S[i] + S[i - j] * X[j] + MOD) % MOD;
|
||
|
|
else S[i] = (S[i] - S[i - j] * X[j] + MOD) % MOD;
|
||
|
|
}
|
||
|
|
S[i] = S[i] * getinv(i) % MOD;
|
||
|
|
}
|
||
|
|
ans = S[N];
|
||
|
|
for(i = 2; i <= N; i ++) ans = ans * i % MOD;
|
||
|
|
if(ans < 0) ans += MOD;
|
||
|
|
printf("%I64d\n", ans);
|
||
|
|
}
|
||
|
|
int main()
|
||
|
|
{
|
||
|
|
prepare();
|
||
|
|
while(scanf("%d%d%d", &N, &M, &K) == 3)
|
||
|
|
solve();
|
||
|
|
return 0;
|
||
|
|
}
|