bzoj3601

题解：gi(pq=pqi-pqi+di

至于为什么，可以看看往上的题解

代码：

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll N=1005,D=105,q=1e9+7;
ll p[N],s[N],a[D][D],as[N];
ll read()
{
    ll x=0;char c;
    for (;c<'0'||c>'9';c=getchar());
    for (;c>='0'&&c<='9';c=getchar())x=x*10+c-48;
    return x;
}
ll ksm(ll x,ll y) 
{
    ll ret=1;
    for (;y;y/=2,(x*=x)%=q)
     if (y&1)(ret*=x)%=q;
    return ret;
}
void elm(ll n) 
{
    for (ll i=1;i<n;i++) 
     {
        if (!a[i][i]) 
         for (ll j=i+1;j<=n;j++) 
          if (a[j][i]) 
           {
            for (ll k=1;k<=n+1;k++) swap(a[j][k],a[i][k]);
            break;
           }     
        ll inv=ksm(a[i][i],q-2);
        for (ll j=i+1;j<=n;j++)
         if (a[j][i])
          {
            ll tmp=(a[j][i]*inv)%q;
            for (ll k=1;k<=n+1;k++) 
             a[j][k]=((a[j][k]-a[i][k]*tmp+q)%q+q)%q;
          }
     }
    for (ll i=n;i;i--)
     {
        if (!a[i][i])
        for (ll j=i-1;j;j--)
         if (a[j][i])
          {
            for (ll k=1;k<=n+1;k++) swap(a[j][k],a[i][k]);
            break;
          }   
        ll inv=ksm(a[i][i],q-2);
        for (ll j=i-1;j;j--)
         if (a[j][i])
          {
            ll tmp=(a[j][i]*inv)%q;
            for (ll k=1;k<=n+1;++k) 
             a[j][k]=((a[j][k]-a[i][k]*tmp+q)%q+q)%q; 
          }
     }
}
int main() 
{
    ll d=read(),w=read();
    for (ll i=1;i<=w;i++) p[i]=read(),s[i]=read();
    ll sum=0;d++;
    for (ll i=1;i<=d;i++)
     {
        (sum+=ksm(i,d-1))%=q;
        ll tmp=1;
        for (ll j=1;j<=d;j++) (tmp*=i)%=q,a[i][j]=tmp;
        a[i][d+1]=sum;
     }
    elm(d); 
    for (ll i=1;i<=d;i++) as[i]=(a[i][d+1]*ksm(a[i][i],q-2))%q;
    ll ans=0;
    for (ll i=1;i<=d;i++)
     {
        ll g=1;
        for (ll j=1;j<=w;j++)
         {
            ll tmp=(ksm(p[j],s[j]*i)-ksm(p[j],s[j]*i+d-i-1)+q)%q;
            (g*=tmp)%=q;
         }
        (ans+=(as[i]*g))%=q;
     }
    printf("%lld",ans);
}