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.
# alpha = "abcdefghijklmnopqrstuvwxyz"
prime = 1000000007#998244353 
# INF = 1000000000000000000000
 
# from sys import stdout
# from heapq import heappush, heappop
# from collections import defaultdict
# from collections import deque  
 
from math import sqrt    
# from math import gcd
# from math import log2
 
# t = 1# int(input())
 
# for test in range(t):
    # n = int(input())
x, n = list(map(int, input().split()))
count = 0
tmp = n
ans = 1
if x%2 == 0:
    count = 0
    tmp = n
    while tmp>1:
        tmp = tmp//2
        count += tmp
    ans = (ans*pow(2, int(count), prime))%prime
 
 
while x%2==0:
    x = x>>1
 
for i in range(3, int(sqrt(x))+1, 2):
    if x%i == 0:
        count = 0
        tmp = n
        while tmp>1:
            tmp = tmp//i
            count += tmp
        ans = (ans*pow(int(i), int(count), prime))%prime
 
    while x%i == 0:
        x = x/i
 
if x > 2:
    count = 0
    tmp = n
    while tmp>1:
        tmp = tmp//x
        count += tmp
    ans = (ans*pow(int(x), int(count), prime))%prime
 
print(ans)