2017-10-湖南套题3

# include<iostream>
# include<cstdio>
# include<cstring>
# include<cstdlib>
using namespace std;
const int pp=1000000007;
int c[2008][2008],f[2008],p[2008],ni[2008];
int n,m,k,nn;
inline int power(int x,int n)
{
int ans=1,tmp=x;
while (n)
{
if (n&1) ans=(long long)ans*tmp%pp;
tmp=(long long)tmp*tmp%pp;n>>=1;
}
return ans;
}
void Count_c()
{
for (int i=0;i<=nn;i++) c[i][0]=1;
for (int i=1;i<=nn;i++)
for (int j=1;j<=i;j++)
{
c[i][j]=c[i-1][j-1]+c[i-1][j];
if (c[i][j]>=pp) c[i][j]-=pp;
}
}
void Count_p()
{
int mm=(m-2)*n;
for (int i=0;i<=nn;i++)
p[i]=power(i,mm);
}
void Count_f()
{
f[0]=0;f[1]=1;
for (int i=2;i<=nn;i++)
{
f[i]=power(i,n);
for (int j=1;j<i;j++)
{
f[i]-=(long long)f[j]*c[i][j]%pp;
if (f[i]<=-pp) f[i]+=pp;
}
if (f[i]<0) f[i]+=pp;
}
}
void Count_ni()
{
ni[1]=1;
for (int i=2;i<=nn;i++)
ni[i]=power(i,pp-2);
}
int main()
{
freopen("photo.in","r",stdin);
freopen("photo.out","w",stdout);
scanf("%d%d%d",&n,&m,&k);
nn=min(n,k);
if (m==1)
printf("%d\n",power(k,n));
else
{
Count_c();
Count_p();
Count_f();
Count_ni();
long long tmp=1,tmp1=1,sum=0,sum1;
for (int s=1;s<=nn;s++)
{
tmp=tmp*ni[s]%pp;
tmp=tmp*(k-s+1)%pp;
tmp1=1;sum1=0;
for (int j=0;j<=s;j++)
{
sum1+=tmp1*c[s][s-j]%pp*p[s-j]%pp;
if (sum1>=pp) sum1-=pp;
tmp1=tmp1*ni[j+1]%pp;
if (k-s<j+1) break;
tmp1=tmp1*(k-s-j)%pp;
}
sum+=tmp*f[s]%pp*f[s]%pp*sum1%pp;
if (sum>=pp) sum-=pp;
}
printf("%d\n",sum);
}
fclose(stdin);
fclose(stdout);
return 0;
}