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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.StringTokenizer;

public class Main {

    public void solve(InputReader in, PrintWriter out) {
        int x = in.nextInt();
        long n = in.nextLong();

        int sqrt = (int) Math.sqrt(x);
        List<Integer> primes = new ArrayList<>();
        primes.add(2);
        for (int i = 3; i <= sqrt; i++) {
            boolean f = false;
            for (int j: primes) {
                if (i%j == 0) {
                    f = true;
                    break;
                }
            }
            if (!f) primes.add(i);
        }
        Set<Integer> set = new HashSet<>();
        for (int i: primes) {
            if (x == 1) break;
            int c = 0;
            while (x%i == 0) {
                x /= i;
                c++;
            }
            if (c > 0) set.add(i);
        }
        if (x > 1) set.add(x);
        long res = 1;
        Map<Integer, Long> pm = new HashMap<>();
        for (int val: set) {
            long count = 0;
            long r = n;
            while(r > 0) {
                count += r/val;
                r /= val;
            }
            if (count > 0) pm.put(val, count);
        }

        for (Map.Entry<Integer, Long> en: pm.entrySet()) {
            int k = en.getKey();
            long v = en.getValue();
             int v1 = pp(k,v);
            res *= v1;
            res = m(res);
        }
        out.println(res);
    }
    int mod = (int) 1e9 + 7;

    public int pp(int k, long v) {
        long r = 1;
        long base = k;
        while(v > 1) {
            if (v%2 == 1) {
                r *= base;
                r = m(r);
            }
            v /= 2;
            base *= base;
            base = m(base);
        }
        base *= r;
        base = m(base);
        return (int) base;
    }

    public long m(long val) {
        if (val >= mod) val %= mod;
        return val;
    }

    public int pow(int k, long v) {
        if (v == 1) return k;
        long l = v/2;
        long r = v-l;
        long a = pow(k, l);
        if (a >= mod) a %= mod;
        long b = pow(k, r);
        if (b >= mod) b %= mod;
        a *= b;
        if (a >= mod) a %= mod;
        return (int) a;
    }

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Main obj = new Main();
        obj.solve(in, out);
        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 nextInt() {
            return Integer.parseInt(next());
        }

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

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public float nextFloat() {
            return Float.parseFloat(next());
        }

    }
}
