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.InputStreamReader;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

public class SolutionC {

    private static BigInteger mod = new BigInteger(String.valueOf(1000000007));

    private static BigInteger res = BigInteger.ONE;

    public static void main(String[] args) throws IOException {
        Reader reader = new Reader();
        StringTokenizer st = reader.getStringTokenizer();
        int x = reader.getNextInt(st);
        long n = reader.getNextLong(st);

        List<Integer> primes = new ArrayList<>();
        int xCopy = x;
        for (int i = 2; i <= Math.sqrt(xCopy); ) {
            if (xCopy % i == 0) {
                if (primes.size() == 0 || primes.get(primes.size() - 1) != i) {
                    primes.add(i);
                }
                xCopy /= i;
            } else {
                i++;
            }
        }

        if (xCopy != 1 && ((primes.size() > 0 && primes.get(primes.size() - 1) != xCopy) || primes.size() == 0)) {
            primes.add(xCopy);
        }

        count(primes, BigInteger.valueOf(n));
        System.out.print(res.mod(mod));
    }

    private static void count(List<Integer> primes, BigInteger n) {
        for (int i = 0; i < primes.size(); i++) {
            int prime = primes.get(i);
            BigInteger primePow = new BigInteger(String.valueOf(prime));
            long counts = 0;
            while (primePow.compareTo(n) <= 0) {
                long c = n.longValue() / primePow.longValue();
                counts += c;
                primePow = primePow.multiply(BigInteger.valueOf(prime));
            }
            BigInteger currValue = BigInteger.valueOf(binpow(prime, counts));
            res = res.multiply(currValue);
        }

    }

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


}


class Reader {

    BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));

    public StringTokenizer getStringTokenizer() throws IOException {
        String line = bufferedReader.readLine().replaceAll("\\s+$", "");
        return new StringTokenizer(line, " ");
    }

    public int getNextInt(StringTokenizer stringTokenizer) {
        while (stringTokenizer.hasMoreTokens()) {
            return Integer.parseInt(stringTokenizer.nextToken());
        }
        throw new RuntimeException("no more tokens in string");
    }

    public long getNextLong(StringTokenizer stringTokenizer) {
        while (stringTokenizer.hasMoreTokens()) {
            return Long.parseLong(stringTokenizer.nextToken());
        }
        throw new RuntimeException("no more tokens in string");
    }

    public String getNextString(StringTokenizer stringTokenizer) {
        while (stringTokenizer.hasMoreTokens()) {
            return stringTokenizer.nextToken();
        }
        throw new RuntimeException("no more tokens in string");
    }


    public String readStringValue() throws IOException {
        return bufferedReader.readLine().replaceAll("\\s+$", "");
    }

    public int readIntValue() throws IOException {
        String line = bufferedReader.readLine().replaceAll("\\s+$", "");
        int parsedToInt = Integer.parseInt(line);
        return parsedToInt;
    }

    public int[] readIntNumbers() throws IOException {
        String[] line = bufferedReader.readLine().replaceAll("\\s+$", "").split(" ");
        int[] parsedToInt = Arrays.stream(line).mapToInt(Integer::parseInt).toArray();
        return parsedToInt;
    }

    public long readLongValue() throws IOException {
        String line = bufferedReader.readLine().replaceAll("\\s+$", "");
        long parsedToLong = Long.parseLong(line);
        return parsedToLong;
    }

    public long[] readLongNumbers() throws IOException {
        String[] line = bufferedReader.readLine().replaceAll("\\s+$", "").split(" ");
        long[] parsedToLong = Arrays.stream(line).mapToLong(Long::parseLong).toArray();
        return parsedToLong;
    }


}