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.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.StringTokenizer;
import java.util.*;

public class C {

    public BigInteger powermod(BigInteger x, BigInteger k, BigInteger mod) {
        return x.modPow(k, mod);
    }

    public Set<BigInteger> primes(BigInteger x) {
        Set<BigInteger> primes = new HashSet<>();
        BigInteger d = BigInteger.valueOf(2);
        while (d.multiply(d).compareTo(x) < 1) {
            while (x.mod(d).equals(BigInteger.ZERO)) {
                primes.add(d);
                x = x.divide(d);
            }
            d = d.add(BigInteger.ONE);
        }
        if (x.compareTo(BigInteger.ONE) > 0) {
            primes.add(x);
        }
        return primes;
    }

    void solve() throws Exception {
        BigInteger mod = BigInteger.valueOf(1000000007);
        BigInteger x = BigInteger.valueOf(nl());
        BigInteger n = BigInteger.valueOf(nl());
        BigInteger ans = BigInteger.ONE;
        Set<BigInteger> primes = primes(x);
        for (BigInteger p : primes) {
            BigInteger acc = p;
            BigInteger pow = BigInteger.ZERO;
            while (acc.compareTo(n) < 1) {
                pow = pow.add(n.divide(acc));
                acc = acc.multiply(p);
            }
            ans = ans.multiply(powermod(p, pow, mod)).mod(mod);
        }
        out.println(ans);
    }

    void run() throws Exception {
        initIO();
        solve();
        out.flush();
    }

    public static void main(String[] args) throws Exception {
        new C().run();
    }

    /**
     * IO.
     */

    PrintWriter out;
    BufferedReader br;
    StringTokenizer tokenizer;

    void initIO() {
        out = new PrintWriter(System.out);
        br = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = null;
    }

    int ni() throws Exception {
        return Integer.parseInt(ns());
    }

    long nl() throws Exception {
        return Long.parseLong(ns());
    }

    double nd() throws Exception {
        return Double.parseDouble(ns());
    }

    int[] nia(int n) throws Exception {
        int[] x = new int[n];
        for (int i = 0; i < x.length; i++) {
            x[i] = ni();
        }
        return x;
    }

    long[] nla(int n) throws Exception {
        long[] x = new long[n];
        for (int i = 0; i < x.length; i++) {
            x[i] = nl();
        }
        return x;
    }

    double[] nda(int n) throws Exception {
        double[] x = new double[n];
        for (int i = 0; i < x.length; i++) {
            x[i] = nd();
        }
        return x;
    }

    String ns() throws Exception {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(br.readLine());
        return tokenizer.nextToken();
    }

    String nline() throws Exception {
        tokenizer = null;
        return br.readLine();
    }
}
