#include <bits/stdc++.h>
using namespace std;
#define int              long long int
#define double           long double
#define print(a)         for(auto x : a) cout << x << " "; cout << endl


const int M = 1000000007;
const int INF = 2e9+1;
const int LINF = 2000000000000000001;

inline int power(int a, int b, int mod=M) {
    int x = 1;
    a %= mod;
    while (b) {
        if (b & 1) x = (x * a) % mod; 
        a = (a * a) % mod;
        b >>= 1;
    }
    return x;
}


//_ ***************************** START Below *******************************


const int N = 10000007;


vector<int> spf;
vector<int> primes;

void seive(){
    spf.assign(N+1, 0);
    for(int i=2; i<=N; i++) spf[i] = i;

    for(int i=2; i*i<=N; i++){
        if(spf[i] != i) continue;
        for(int j=i*i; j<=N; j+=i){
            spf[j] = min(spf[j], i);
        }
    }
    for(int i=2; i<=N; i++){
        if(spf[i] == i) primes.push_back(i);
    }
}


vector<int> a;

vector<int> consistency(int n, int m){

    unordered_map<int,int> mp;
    int d = 1;
    for(auto& q : primes){
        int p = q;
        int e = 0;

        while(m/p>0){
            e += m/p;
            p *= q;
        }
        mp[q] = e;
        d = (d * (e+1))%M;
    }


    vector<int> ans;
    for(auto& it : a){
        int x = it;

        int val = d;

        while(x>1){
            
            int p = spf[x];
            int e = 0;

            while(x % p == 0){
                e++;
                x /= p;
            }

            int de = mp[p];

            int nmr = (e+de+1)%M;
            int dnr = power(de+1, M-2);
    
            val = (val * ( (nmr * dnr)%M)  ) % M;
            
        }

        ans.push_back(val);
    }

    return ans;

}
















vector<int> practice(int n, int m){


}





void solve() {
    static int _ = (seive(), 0);
    
    int n, m;
    cin>> n >> m;
    
    a.resize(n);
    for(int i=0; i<n; i++) cin >> a[i];
    
    auto ans = consistency(n, m);
    
    for(auto& it : ans) cout << it << " "; cout << endl;


}





int32_t main() {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);

    int t = 1;
    // cin >> t;
    while (t--) {
        solve();
    }

    return 0;
}