#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 N = 3e5+9;
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 *******************************
 
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& p : primes){
        int q = p;
        while(m/q>0){
            mp[p] += m/q;
            q *= p;
        }
    }
    for(auto& p : mp){
        int e = p.second;
        d = (d * (e+1))%M;
    }
 
    vector<int> ans;
    for(auto& it : a){
        int x = it;
        unordered_map<int,int> xmp;
 
        while(x>1){
            xmp[spf[x]]++;
            x /= spf[x];
        }
 
        int val = 1;
        for(auto& x : xmp){
            int p = x.first;
            int e = x.second;
 
            int oldE = mp[p];
 
            int nmr = (e+oldE+1)%M;
            int dnr = power( (oldE+1)%M, 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;
}

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