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 java.io.BufferedReader;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class PrimesAndMultiplication implements Closeable {

  private InputReader in = new InputReader(System.in);
  private PrintWriter out = new PrintWriter(System.out);

  public void solve() {
    long x = in.nl(), n = in.nl();
    long result = 1L;
    List<Long> primes = factorize(x);
    for (long prime : primes) {
      long p = prime;
      BigInteger bi = BigInteger.valueOf(p);
      BigInteger N = BigInteger.valueOf(n);
      while (bi.compareTo(N) <= 0) {
        long times = n / p;
        result *= power(prime, times);
        result %= MOD;
        p *= prime;
        bi = bi.multiply(BigInteger.valueOf(prime));
      }
    }
    out.println(result);
  }

  private final long MOD = (long) 1e9 + 7;

  private long power(long a, long b) {
    if (b == 0) return 1L;
    long half = power(a, b >> 1) % MOD, result = half % MOD * half % MOD;
    if (b % 2 == 1) {
      result *= a;
      result %= MOD;
    }
    return result;
  }

  private List<Long> factorize(long n) {
    List<Long> result = new ArrayList<>();
    for (long i = 2L; i * i <= n; i++) {
      if (n % i == 0) {
        result.add(i);
        while (n % i == 0) {
          n /= i;
        }
      }
    }
    if (n > 1) {
      result.add(n);
    }
    return result;
  }

  @Override
  public void close() throws IOException {
    in.close();
    out.close();
  }

  static class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
      reader = new BufferedReader(new InputStreamReader(stream), 32768);
      tokenizer = null;
    }

    public String next() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.nextToken();
    }

    public int ni() {
      return Integer.parseInt(next());
    }

    public long nl() {
      return Long.parseLong(next());
    }

    public void close() throws IOException {
      reader.close();
    }
  }

  public static void main(String[] args) throws IOException {
    try (PrimesAndMultiplication instance = new PrimesAndMultiplication()) {
      instance.solve();
    }
  }
}
