BestCoder Round #72 (div.2) Clarke and math

表示题解给的卷积没看懂，不能理解。。

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <vector>
#include <cstring>
#include <queue>
#include <climits>
#include <cmath>
#include <map>
#include <set>

#define LL long long

#define pr pair < int, int >

using namespace std;

vector <LL> v[110005],w[110005];

LL MOD=1000000007;

int n,k;LL a[110005];

LL f[110005],fac[200005],inv[200005];

LL pow_mod(LL a,LL b,LL m){
    LL ans=1LL;
    a%=m;
    while(b){
        if(b&1)ans=ans*a%m;
        a=a*a%m;
        b>>=1;
    }
    return ans;
}

LL c(LL n,LL m){
    if(n<m||n<0||m<0)return 0;
    return fac[n]*inv[m]%MOD*inv[n-m]%MOD;
}

int main()
{
    //freopen("in.txt","r",stdin);
    fac[0]=1LL;
    for(LL i=1;i<=101000;++i){
        fac[i]=i*fac[i-1]%MOD;
    }
    inv[101000]=pow_mod(fac[101000],MOD-2,MOD);
    for(LL i=101000-1;i>=0;--i){
        inv[i]=inv[i+1]*(i+1)%MOD;
    }
    for(LL i=1;i<=101000;++i){
        for(LL j=1;j*j<=i;++j){
            if(i%j==0){
                if(i!=j*j){
                    v[i].push_back(j);
                    v[i].push_back(i/j);
                }
                else v[i].push_back(j);
            }
        }
    }
    for(LL i=1;i<=101000;++i){
        LL now=i,cnt=0LL;
        for(LL j=2;j*j<=i;++j){
            if(now%j==0){
                while(now%j==0){
                    ++cnt;
                    now/=j;
                }
                w[i].push_back(cnt);
                cnt=0LL;
            }
        }
        if(now!=1LL)w[i].push_back(1LL);
    }
    int T;
    scanf("%d", &T);
    while(T--)
    {
        scanf("%d%d",&n,&k);
        for(int i=1;i<=n;++i)scanf("%I64d",a+i);
        int len;k--;
        for(int i=1;i<=n;++i){
            len=w[i].size();
            f[i]=1LL;
            for(int j=0;j<len;++j){
                f[i]*=c(k+w[i][j],k);
                f[i]%=MOD;
            }
        }
        LL ans;
        for(int i=1;i<=n;++i){
            ans=0LL;len=v[i].size();
            for(int j=0;j<len;++j){
                ans+=(LL)a[v[i][j]]*f[i/v[i][j]];
                if(ans>=MOD)ans%=MOD;
            }
            if(i!=1)putchar(' ');
            printf("%I64d",ans);
        }
        puts("");
    }
    return 0;
}