#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <atcoder/modint>
using namespace std;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
#define rep(i,n) for(int i=0; i<(n); i++)


using m32 = atcoder::modint1000000007;

vector<pair<u64,u64>> factorize(u64 n){
  vector<pair<u64,u64>> res;
  for(u64 i=2; i*i<=n; i++){
    if(n%i) continue;
    res.push_back({i,0});
    while(n%i==0){ n/=i; res.back().second++; }
  }
  if(n!=1) res.push_back({n,1});
  return res;
}

vector<pair<u64,u64>> gcd_frequency(u64 n){
  vector<pair<u64,u64>> ans;
  ans.push_back(make_pair((u64)1, (u64)1));
  for(auto f : factorize(n)){
    vector<pair<u64,u64>> buf;
    u64 multiplier = 1;
    u64 inv_multiplier = 1;
    for(u64 p_idx=0; p_idx<f.second; p_idx++) inv_multiplier *= f.first;
    for(u64 p_idx=0; p_idx<=f.second; p_idx++){
      if(p_idx != 0){
        multiplier *= f.first;
        inv_multiplier /= f.first;
      }
      u64 freq = inv_multiplier;
      if(p_idx != f.second) freq = freq / f.first * (f.first - 1);
      for(auto a : ans) buf.push_back(make_pair(a.first*multiplier, freq));
    }
    swap(ans, buf);
  }
  return ans;
}


void testcase(){
  u64 num_vertices; cin >> num_vertices;
  i64 num_colors; cin >> num_colors;

  m32 ans = 0;
  for(auto g : gcd_frequency(num_vertices)){
    m32 simple_count = m32(num_colors).pow(g.first * 2);
    ans += simple_count * g.second;
  }
  ans /= num_vertices;
  ans += m32(num_colors).pow(num_vertices);
  ans /= 2;
  cout << ans.val() << "\n";
}


int main(){
  int testcase_count; cin >> testcase_count;
  for(int testcase_idx = 0; testcase_idx < testcase_count; testcase_idx++){
    testcase();
  }
  return 0;
}




struct ios_do_not_sync {
    ios_do_not_sync() {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
    }
} ios_do_not_sync_instance;