BZOJ5323 JXOI2018游戏（线性筛+组合数学）

#include<iostream> 
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
#define ll long long
#define N 10000010
#define P 1000000007
char getc(){char c=getchar();while ((c<‘A‘||c>‘Z‘)&&(c<‘a‘||c>‘z‘)&&(c<‘0‘||c>‘9‘)) c=getchar();return c;}
int gcd(int n,int m){return m==0?n:gcd(m,n%m);}
int read()
{
    int x=0,f=1;char c=getchar();
    while (c<‘0‘||c>‘9‘) {if (c==‘-‘) f=-1;c=getchar();}
    while (c>=‘0‘&&c<=‘9‘) x=(x<<1)+(x<<3)+(c^48),c=getchar();
    return x*f;
}
int n,l,r,prime[N],fac[N],inv[N],cnt,sum,ans;
bool flag[N];
int C(int n,int m){return 1ll*fac[n]*inv[n-m]%P*inv[m]%P;}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("bzoj5323.in","r",stdin);
    freopen("bzoj5323.out","w",stdout);
    const char LL[]="%I64d\n";
#else
    const char LL[]="%lld\n";
#endif
    l=read(),r=read();n=r-l+1;
    fac[0]=1;for (int i=1;i<=n;i++) fac[i]=1ll*i*fac[i-1]%P;
    inv[0]=inv[1]=1;for (int i=2;i<=n;i++) inv[i]=P-1ll*(P/i)*inv[P%i]%P;
    for (int i=2;i<=n;i++) inv[i]=1ll*inv[i]*inv[i-1]%P;
    if (l==1) sum=1;
    else
    {
        for (int i=2;i<l;i++)
        {
            if (!flag[i]) prime[++cnt]=i;
            for (int j=1;j<=cnt&&prime[j]*i<l;j++)
            {
                flag[prime[j]*i]=1;
                if (i%prime[j]==0) break;
            }
        }
        sum=-cnt;
        for (int i=l;i<=r;i++)
        {
            if (!flag[i]) prime[++cnt]=i;
            for (int j=1;j<=cnt&&prime[j]*i<=r;j++)
            {
                flag[prime[j]*i]=1;
                if (i%prime[j]==0) break;
            }
        }
        sum+=cnt;
    }
    for (int i=sum;i<=n;i++) ans=(ans+1ll*fac[n-sum]*C(i-1,sum-1)%P*i)%P;
    cout<<1ll*ans*fac[sum]%P;
    return 0;
}