https://oj.neu.edu.cn/problem/1460
Thinking: If n = (p1 ^ a1) * (p2 ^ a2) ... (pn ^ an), then f (n, 0) = a1 * a2 * ... * an, obviously f (n, 0) it is a multiplicative function for f (x, y) we can see that he is f (x, y-1) Dirichlet convolution results obtained with itself, so that f (x, y) is also a multiplicative function. Thus, as long as the quality of factoring n, then the value of dp can be pre-sort and power. Note concepts multiplicative function of a, b must be coprime!
#include<bits/stdc++.h>
#define int long long
using namespace std;
const int mod = 1000000007;
maxn const int = 1000000 + 5, MaxM = 10000 + 5;
int dp[30][maxm];
vector<int> g[maxn];
inline void solve(int n){
int nn = n;
for(int i=2;i*i<=n;i++){
if(n%i==0){
int num = 0;
while(n%i==0) n/=i,num++;
g[nn].push_back(num);
}
}
if(n>1) g[nn].push_back(1);
}
void init(int n=30,int m=maxm){
for(int i=1;i<n;i++) dp[i][0] = i;
for(int i=1;i<n;i++){
for(int j=1;j<m;j++){
if(i==1){
dp[i][j] = dp[i][j-1]*2%mod;
}
else {
dp[i][j] = dp[i][j-1]*2%mod;
for(int k=1;k<i;k++){
dp[i][j] = (dp[i][j] + dp[k][j - 1] * dp[i - k][j - 1] % mod) % mod;
}
}
}
}
}
signed main(){
ios::sync_with_stdio(0);
cin.tie (0);
cout.tie (0);
init();
int t;
cin>>t;
while(t--){
int n,m;
cin>>n>>m;
if(n==1) cout<<1<<endl;
else{
if(g[n].size()==0) solve(n);
int year = 1;
for(int i=0;i<g[n].size();i++){
ans = ans*dp[g[n][i]][m]%mod;
}
cout<<ans<<endl;
}
}
return 0;
}