推公式就不推了,学个这个公式就够了
#include<bits/stdc++.h>
#define PI acos(-1.0)
#define pb push_back
#define F first
#define S second
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int N=2000;
const int MOD=1e9+7;
template <class T>
bool sf(T &ret){ //Faster Input
char c; int sgn; T bit=0.1;
if(c=getchar(),c==EOF) return 0;
while(c!='-'&&c!='.'&&(c<'0'||c>'9')) c=getchar();
sgn=(c=='-')?-1:1;
ret=(c=='-')?0:(c-'0');
while(c=getchar(),c>='0'&&c<='9') ret=ret*10+(c-'0');
if(c==' '||c=='\n'){ ret*=sgn; return 1; }
while(c=getchar(),c>='0'&&c<='9') ret+=(c-'0')*bit,bit/=10;
ret*=sgn;
return 1;
}
ll F[N],inv[N],Finv[N];
ll B[N];
ll comb(ll n,ll m){
if(m<0||m>n) return 0;
return F[n]*1ll*Finv[n-m]%MOD*Finv[m]%MOD;
}
void init(){
inv[1]=1;
for(int i=2;i<N;i++)
inv[i]=(MOD-MOD/i)*1ll*inv[MOD%i]%MOD;
F[0]=Finv[0]=1;
for(int i=1;i<N;i++){
F[i]=F[i-1]*1ll*i%MOD;
Finv[i]=Finv[i-1]*1ll*inv[i]%MOD;
}
B[0] = 1; /// 伯努利数
for(int i=1; i<N; i++)
{
ll ans = 0;
if(i == N - 1) break;
for(int j=0; j<i; j++)
{
ans += comb(i+1,j) * B[j];
ans %= MOD;
}
ans *= -inv[i+1];
ans = (ans % MOD + MOD) % MOD;
B[i] = ans;
}
}
ll qm(ll a,ll b){
ll ans=1%MOD;
while(b){
if(b&1) ans=ans*a%MOD;
b>>=1;
a=a*a%MOD;
}
return ans%MOD;
}
ll n,a[N];
ll gao(ll n,ll k){
ll ans=0;
for(int i=1;i<=k+1;i++){
ans=(ans+ comb(k+1,i)%MOD*B[k+1-i]%MOD*qm(n+1,i)%MOD)%MOD;
}
ans=ans*inv[k+1]%MOD;
return ans;
}
int main(void){
init();
while((scanf("%lld",&n))==1){
for(int i=1;i<=n;++i) sf(a[i]);
sort(a+1,a+1+n);
ll mul=1,ans=0;
ans=a[n];
for(int i=1;i<=n;i++) ans*=a[i],ans%=MOD;
for(int i=1;i<=n;i++){
ll det;
if(i!=n) det=mul*(gao(a[i],n-i+1)-gao(a[i-1],n-i+1))%MOD;
else det=mul*(gao(a[i]-1,n-i+1)-gao(a[i-1],n-i+1))%MOD;
det+=MOD;
det%=MOD;
ans= ((ans-det)%MOD+MOD)%MOD;
mul*=a[i];
mul%=MOD;
}
printf("%lld\n",ans);
}
return 0;
}