Problem: Bash got tired on his journey to become the greatest Pokemon master. So he decides to take a break and play with functions.

Bash defines a function f0(n), which denotes the number of ways of factoring n into two factors p and q such that gcd(p, q) = 1. In other words, f0(n) is the number of ordered pairs of positive integers (p, q) such that p·q = n and gcd(p, q) = 1.

But Bash felt that it was too easy to calculate this function. So he defined a series of functions, where fr + 1 is defined as:

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Where (u, v) is any ordered pair of positive integers, they need not to be co-prime.

Now Bash wants to know the value of fr(n) for different r and n. Since the value could be huge, he would like to know the value modulo 109 + 7. Help him!

Input

The first line contains an integer q (1 ≤ q ≤ 106) — the number of values Bash wants to know.

Each of the next q lines contain two integers r and n (0 ≤ r ≤ 106, 1 ≤ n ≤ 106), which denote Bash wants to know the value fr(n).

Output

Print q integers. For each pair of r and n given, print fr(n) modulo 109 + 7 on a separate line.

Example

Input

5
0 30
1 25
3 65
2 5
4 48


Output

8
5
25
4
630

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 5, mod = 1e9 + 7, LOG = 22;
int jm(int a, int b) { return ((a + b + 2LL * mod) % mod); }
int zrb(int a, int b) {
  return (((a * 1LL * b + 2LL * mod) % mod + 2LL * mod) % mod);
}
int dp[N][LOG], q, n, r, ans, AH[N];
int main() {
  AH[1] = 1;
  for (int i = 2; i < N; i++)
    if (!AH[i])
      for (int j = i; j < N; j += i) AH[j] = i;
  for (int i = 0; i < N; i++) dp[i][0] = 1LL;
  for (int i = 1; i < LOG; i++) dp[0][i] = 2LL;
  for (int i = 1; i < N; i++)
    for (int j = 1; j < LOG; j++) dp[i][j] = jm(dp[i][j - 1], dp[i - 1][j]);
  scanf("%d", &q);
  for (int Q = 0; Q < q; Q++) {
    scanf("%d %d", &r, &n);
    ans = 1LL;
    while (n > 1) {
      int cnt = 0, p = AH[n];
      while (n % p == 0) n /= p, cnt++;
      ans = zrb(ans, dp[r][cnt]);
    }
    printf("%d\n", ans);
  }
}