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.math.BigInteger;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.TreeSet;

public class r589p3{

    private static InputReader sc;
    private static PrintWriter pw;
    private static TreeSet<Integer> primeSet;

    private static long gcd(long a, long b){ return (b == 0)?a:gcd(b, a%b); }

    private static long lcm(long a, long b){ return (a/gcd(a, b))*b; }

    private static void genPrime(int lim){
        boolean isPrime[] = new boolean[lim+1];
        Arrays.fill(isPrime, true);

        for(int i=2; i<=lim; i++){
            if(isPrime[i]){
                primeSet.add(i);
                for(long j=(long)i*i; j<=lim; j+=i)
                    isPrime[(int)j] = false;
            }
        }
    }

    static class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        InputReader(InputStream stream) {
            this.stream = stream;
        }

        int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        int nextInt() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        long nextLong() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        String readString() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        String nextLine() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public interface SpaceCharFilter {
            boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) {
        sc = new InputReader(System.in);
        pw = new PrintWriter(System.out);
        primeSet = new TreeSet<>();

        int t = 1;
        while(t-->0)
            solve();

        pw.flush();
        pw.close();
    }

    static long mod;

    private static long pow(long x, long y)
    {
        long res = 1;

        x = x % mod;

        while (y > 0)
        {
            if(y%2 != 0)
                res = (res * x) % mod;

            y = y >> 1;
            x = (x * x) % mod;
        }
        return res;
    }

    private static void solve(){

        long x = sc.nextLong(), n = sc.nextLong();
        //pw.println(+n);
        mod = (long)1e9+7;

        genPrime((int)1e5);

        TreeSet<Long> primeDiv = new TreeSet<>();

        for(Integer prime: primeSet){
            while(x%prime == 0){
                x /= prime;
                primeDiv.add((long)prime);
            }
            if(x == 1)
                break;
        }

        if(x > 1)
            primeDiv.add(x);

        long ans = 1;

        for(Long prime: primeDiv){
            long r = n/prime;
            //pw.println(+prime);

            while(r > 0){
                ans = (ans%mod * pow(prime, r)%mod)%mod;
                r /= prime;
            }
        }

        pw.println(ans);
    }
}