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 sympy as sp
#import time as t
import math
#import numpy as np
x,n = map(int, input().split())
    
def pfactors(x):
    prime_factors=[]    
    if(x&1==0):
        prime_factors.append(2)
        while(x&1==0):
            x=x>>1
            
    i=3
    limit= math.sqrt(x)
   
    while(i<=limit):
        if(x%i==0):
            prime_factors.append(i)
            x=x//i
            while(x%i==0):
                x=x//i            
        i+=2
    
    if(x>2):
        prime_factors.append(x)
    return prime_factors

pfacts= pfactors(x)  
res=1
l=len(pfacts)
M=10**9+7

for p in pfacts:
    k=math.log(n,p)
    k=math.ceil(k)
    
    h=0
    for i in range(1,k+1):
        h = h + n//pow(p,i)
        
    g = pow(p,h,M)
    res = (res*g)%M

print(res)

            
