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=,D=,q=1e9+;
ll p[N],s[N],a[D][D],as[N];
ll read()
{
    ll x=;char c;
    for (;c<''||c>'';c=getchar());
    for (;c>=''&&c<='';c=getchar())x=x*+c-;
    return x;
}
ll ksm(ll x,ll y)
{
    ll ret=;
    for (;y;y/=,(x*=x)%=q)
     if (y&)(ret*=x)%=q;
    return ret;
}
void elm(ll n)
{
    for (ll i=;i<n;i++)
     {
        if (!a[i][i])
         for (ll j=i+;j<=n;j++)
          if (a[j][i])
           {
            for (ll k=;k<=n+;k++) swap(a[j][k],a[i][k]);
            break;
           }
        ll inv=ksm(a[i][i],q-);
        for (ll j=i+;j<=n;j++)
         if (a[j][i])
          {
            ll tmp=(a[j][i]*inv)%q;
            for (ll k=;k<=n+;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-;j;j--)
         if (a[j][i])
          {
            for (ll k=;k<=n+;k++) swap(a[j][k],a[i][k]);
            break;
          }
        ll inv=ksm(a[i][i],q-);
        for (ll j=i-;j;j--)
         if (a[j][i])
          {
            ll tmp=(a[j][i]*inv)%q;
            for (ll k=;k<=n+;++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=;i<=w;i++) p[i]=read(),s[i]=read();
    ll sum=;d++;
    for (ll i=;i<=d;i++)
     {
        (sum+=ksm(i,d-))%=q;
        ll tmp=;
        for (ll j=;j<=d;j++) (tmp*=i)%=q,a[i][j]=tmp;
        a[i][d+]=sum;
     }
    elm(d);
    for (ll i=;i<=d;i++) as[i]=(a[i][d+]*ksm(a[i][i],q-))%q;
    ll ans=;
    for (ll i=;i<=d;i++)
     {
        ll g=;
        for (ll j=;j<=w;j++)
         {
            ll tmp=(ksm(p[j],s[j]*i)-ksm(p[j],s[j]*i+d-i-)+q)%q;
            (g*=tmp)%=q;
         }
        (ans+=(as[i]*g))%=q;
     }
    printf("%lld",ans);
}