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 JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Problem5 {
    static int MAX = (int)1e6 + 10;
    static int MOD = (int)1e9 + 7;

    static int last_prime [];

    static void fill_last_prime () {
        last_prime = new int[MAX];
        last_prime[1] = 1;
        for (int i = 2; i < MAX; i++)
            if (last_prime[i] == 0) {
                for (int j = i; j < MAX; j += i)
                    last_prime[j] = i;
            }
    }
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        fill_last_prime();
        int f [][] = new int[MAX][21];
        for (int i = 0; i < 21; i++)
            f[0][i] = i == 0 ? 1 : 2;

        for (int i = 1; i < MAX; i++)
            for (int j = 0; j < 21; j++)
                for (int k = 0; k <= j; k++) {
                    f[i][j] = (f[i][j] + f[i - 1][k]);
                    if (f[i][j] >= MOD) f[i][j] -= MOD;
                }

        int q = sc.nextInt();
        while (q -- > 0) {
            int r = sc.nextInt() , n = sc.nextInt();
            long res = 1;
            while (n != 1) {
                int cnt = 0;
                int last = last_prime[n];
                while (n != 1 && n % last == 0) {
                    cnt ++ ;
                    n /= last;
                }
                res = res * f[r][cnt] % MOD;
            }
            out.println(res);
        }


        out.flush();
        out.close();
    }

























    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }
}