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.
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sun Sep 29 20:05:37 2019

@author: kushagra
"""
import math 
p = []
MOD = 1000000007

def gen(n):
    if n%2 ==0:
      p.append(2)
      while n%2==0:
          n=n//2
    for i in range (3,int(math.sqrt(n))+1,2):
        if n%i==0:
            p.append(i)
            while n%i == 0:
                n= n//i
    if n>2:
        p.append(n)

ll = input().split(" ")
x = int(ll[0])
n = int(ll[1])

gen(x)


ans=1
for i in p:
    prime = i
    pp = prime
    v = []
    while 1:
        if pp>n:
            break
        v.append(n//pp)
        pp*=prime
    v.append(0)
    #print(v)
    for j in range(0,len(v)-1):
        val = int(v[j]-v[j+1])
        #val%=MOD-1
        x = pow(prime,j+1,MOD)
        ans*=pow(x,val,MOD)

print(ans%MOD)