codeforces396A

Posted 2022-06-18 gaojunonly1

sol：很显然就是找出所有质因数，然后分别塞进去就行了，怎么塞就是组合数。感觉就是道小学奥数题

 

#include <bits/stdc++.h>
using namespace std;
typedef int ll;
inline ll read()

    ll s=0; bool f=0; char ch=‘ ‘;
    while(!isdigit(ch))    f|=(ch==‘-‘); ch=getchar();
    while(isdigit(ch)) s=(s<<3)+(s<<1)+(ch^48); ch=getchar();
    return (f)?(-s):(s);

#define R(x) x=read()
inline void write(ll x)

    if(x<0) putchar(‘-‘); x=-x;
    if(x<10) putchar(x+‘0‘); return;
    write(x/10); putchar((x%10)+‘0‘);

#define W(x) write(x),putchar(‘ ‘)
#define Wl(x) write(x),putchar(‘\\n‘)
const int Mod=1000000007;
int n;
map<int,int>Map;
int num[1000005],cnt[1000005];
int fac[15505],invf[15505];
inline int ksm(int x,int y)

    int ans=1;
    while(y)
    
        if(y&1) ans=1LL*ans*x%Mod;
        x=1LL*x*x%Mod;
        y>>=1;
    return ans;

inline int C(int n,int m)

    int oo;
    oo=1LL*fac[n]*invf[m]%Mod*invf[n-m]%Mod;
    return oo;

int main()

    freopen("codeforces396A_data.in","r",stdin);
    int i,j,k,x;
    R(n);
    fac[0]=invf[0]=1;
    for(i=1;i<=15500;i++) fac[i]=1LL*fac[i-1]*i%Mod;
    invf[15500]=ksm(fac[15500],Mod-2);
    for(i=15499;i>=1;i--) invf[i]=1LL*invf[i+1]*(i+1)%Mod;
    for(i=1;i<=n;i++)
    
        R(x);
        for(j=2;j<=sqrt(x);j++) if(x%j==0)
        
            int oo=0;
            while(x%j==0) x/=j; oo++;
            if(!Map[j])
            
                Map[j]=++(*num); num[*num]=j; cnt[*num]=oo;
            else cnt[Map[j]]+=oo;
        
        if(x>1)
        
            if(!Map[x])
            
                Map[x]=++(*num); num[*num]=x; cnt[*num]=1;
            else cnt[Map[x]]++;
        
    
    int ans=1;
    for(i=1;i<=*num;i++)
    
        ans=1LL*ans*C(cnt[i]+n-1,n-1)%Mod;
    Wl(ans);
    return 0;

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