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.
'''
Created on 2019. 9. 21.

@author: kkhh88
'''
'''
a, b = map(int,input().split(' '))

t = 0
for i in range(a, b+1):
    x = [0] * 10
    
    n = i
    while n:
        x[n%10] = x[n%10] + 1
        n = n // 10
    n = 0
    for n in range(10):
        if x[n] > 1:
            break
    
    if n == 9 and x[n] < 2:
        print (i)
        t = 1
        break
    
if t == 0:
    print (-1)
'''
x, n = map(int,input().split(' '))
pr = []
i = 2
while i*i <= x:
    if x % i == 0:
        pr.append(i)
        x = x // i
    else:
        i = i + 1
if n > 1:
    pr.append(x)

pr = list(set(pr))

res = 1    
for p in pr:
    tmp = n // p
    x = p * p
    while x <= n:
        tmp = tmp + (n // x)      
        x = x * p  
    x = p
    while tmp:
        if tmp % 2 == 1:
            res = res * x
        if res > 1000000007:
            res = res % 1000000007
        x = x * x % 1000000007
        tmp = tmp // 2

print (res)