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 math
from sys import *
from heapq import *
from collections import defaultdict
import os, sys
from io import IOBase, BytesIO
M=10**9+7

def powmod(a,b,m):
    res=1
    while b>0:
        if b&1:
            res=((res*a)%m)
        a*=a
        b>>=1
    return res

def primefactorisation(nn):
    lst=[]
    if nn%2==0:
        lst+=[2]
        while nn%2==0:
            nn/=2
    for i in range(3,int(nn**0.5)+1,2):
        if nn%i==0:
            lst+=[i]
            while nn%i==0:
                nn/=i
    if nn>2:
        lst+=[int(nn)]
    
    return lst
    



def main():
    x,n=list(map(int,input().split()))
    
    lst=primefactorisation(x)
    #print(lst)
    res=1
    for p in lst:
        
        
        val=p
        V=0
        while n>=val:
            V+=n//val
            val*=p
            
        res*=pow(p,V,M)
        res%=M
        
        
    print(res)
        








if __name__ == '__main__':
    main()
#threading.Thread(target=main).start()
