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.*;
import java.math.BigInteger;
import java.util.*;

public class Task_C {

    static Set<Long> factorize(long x) {
        Set<Long> factors = new HashSet<>();

        for (long i = 2; i <= Math.sqrt(x); i++) {
            if (x % i == 0) {
                factors.add(i);
            }
            while (x % i == 0) {
                x /= i;
            }
        }

        if (x != 1) {
            factors.add(x);
        }

        return factors;
    }

    static long binpow(long a, long n) {
        if (n == 0)
            return 1;
        if (n % 2 == 1)
            return binpow(a, n - 1) * a % 1000000007;
        else {
            long b = binpow(a, n / 2);
            return b * b % 1000000007;
        }
    }

    static Map<Long, Long> factorize1(long x, Set<Long> divisors) {
        HashMap<Long, Long> result = new HashMap<>();

        for (Long divisor : divisors) {
            if (x < divisor) {
                continue;
            }

            long a = x / divisor;
            result.put(divisor, a);
            a = a / divisor;
            while (a != 0) {
                result.put(divisor, result.get(divisor) + a);
                a = a / divisor;
            }
        }

        return result;
    }

    public static void main(String[] args) throws FileNotFoundException {
        InputReader inputReader = new InputReader(System.in);
        long x = inputReader.nextLong();
        long n = inputReader.nextLong();

        Set<Long> factorsSet = factorize(x);
        Map<Long, Long> ff = factorize1(n, factorsSet);

        long result = 1;
        for (Long divisor : ff.keySet()) {
            result *= binpow(divisor, ff.get(divisor));
            result %= 1000000007;
        }
        System.out.println(result);
    }

    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 nextInt() {
            return Integer.parseInt(next());
        }

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

    }
}

