Let's introduce some definitions that will be needed later.

Let prime(x) be the set of prime divisors of x. For example, prime(140) = \{ 2, 5, 7 \}, prime(169) = \{ 13 \}.

Let g(x, p) be the maximum possible integer p^k where k is an integer such that x is divisible by p^k. For example:

  * g(45, 3) = 9 (45 is divisible by 3^2=9 but not divisible by 3^3=27), 
  * g(63, 7) = 7 (63 is divisible by 7^1=7 but not divisible by 7^2=49). 



Let f(x, y) be the product of g(y, p) for all p in prime(x). For example:

  * f(30, 70) = g(70, 2) ⋅ g(70, 3) ⋅ g(70, 5) = 2^1 ⋅ 3^0 ⋅ 5^1 = 10, 
  * f(525, 63) = g(63, 3) ⋅ g(63, 5) ⋅ g(63, 7) = 3^2 ⋅ 5^0 ⋅ 7^1 = 63. 



You have integers x and n. Calculate f(x, 1) ⋅ f(x, 2) ⋅ … ⋅ f(x, n) mod{(10^{9} + 7)}.

Input

The only line contains integers x and n (2 ≤ x ≤ 10^{9}, 1 ≤ n ≤ 10^{18}) — the numbers used in formula.

Output

Print the answer.

Examples

Input


10 2


Output


2


Input


20190929 1605


Output


363165664


Input


947 987654321987654321


Output


593574252

Note

In the first example, f(10, 1) = g(1, 2) ⋅ g(1, 5) = 1, f(10, 2) = g(2, 2) ⋅ g(2, 5) = 2.

In the second example, actual value of formula is approximately 1.597 ⋅ 10^{171}. Make sure you print the answer modulo (10^{9} + 7).

In the third example, be careful about overflow issue.
import javafx.beans.binding.When;

import java.io.*;
import java.util.*;

public class Main {

  public static void main(String[] args) throws Exception {
    Scanner sc = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);

    int x = sc.nextInt();
    int mod = 1000000007;
    long n = sc.nextLong();

    ArrayList<Integer> primes = new ArrayList<>();
    for (int i = 2; 1L * i * i <= x ; i++) {
      if (x % i == 0) {
        primes.add(i);
        while (x % i == 0) x /= i;
      }
    }

    if (x != 1) primes.add(x);

    long res = 1;
    for (int prime : primes) {
      long p_ = prime;
      while (true) {
        res *= modular_exponentiation(prime, n / p_, mod);
        res %= mod;
        if (p_ > n / prime) break;
        p_ *= prime;
      }
    }

    out.println(res);
    out.flush();
  }

  public static long modular_exponentiation (int a  , long  b , int c )
  {
    long ans = 1L;
    while(b!=0)
    {
      if((b & (1L)) == 1)
        ans = (ans*a) %c;

      a = (int)((1L * a * a)%c);
      b >>=1L ;
    }

    return ans;
  }

  private static boolean ok(int i) {
    String s = i + "";
    HashSet<Character> hashSet = new HashSet<>();
    for (int j = 0; j < s.length(); j++) {
      hashSet.add(s.charAt(j));
    }
    return s.length() == hashSet.size();
  }

  static class Scanner {
    StringTokenizer st;
    BufferedReader br;

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

    public Scanner(FileReader f) {
      br = new BufferedReader(f);
    }

    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();
    }

  }
}