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.
// Working program using Reader Class 
import java.io.BufferedReader;
import java.io.DataInputStream; 
import java.io.FileInputStream; 
import java.io.IOException; 
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Scanner; 
import java.util.StringTokenizer;
import java.util.TreeSet; 

public class Main2{
    static long pow(long a, long b , long c){
        if(b==0){
            return 1;
        }
        long d=pow(a, b/2, c);
        d=(d*d)%c;
        if(b%2==1){
            d=(d*a)%c;
        }
        return d;
    }
    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] t = br.readLine().split(" ");
        int i;
        long x=Long.parseLong(t[0]), j, k=x;
        long n=Long.parseLong(t[1]);
        int[] z = new int[32000];
        for(i=2;i<32000;i++){
            if(z[i]==0){
                for(j=i*i;j<32000;j+=i){
                    z[(int)j]=1;
                }
            }
        }
        ArrayList<Long> pr = new ArrayList<>();
        for(i=2;i<32000;i++){
            if(k%i==0){
                pr.add((long)i);
                while(k%i==0){
                    k=k/i;
                }
            }
        }
        if(k!=1){
            pr.add(k);
        }
        long ans=1, mod=1000000007L;
        for(i=0;i<pr.size();i++){
            j=0;
            k=pr.get(i);
            while(n>=k){
                j+=n/k;
                if(pr.get(i)>n/k){
                    break;
                }
                k=k*pr.get(i);
            }
            ans=(ans*pow(pr.get(i), j, mod))%mod;
        }
        System.out.println(ans);
    }
}