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.
from itertools import accumulate,chain,combinations,groupby,permutations,product
from collections import deque,Counter
from bisect import bisect_left,bisect_right
from math import gcd,sqrt,sin,cos,tan,degrees,radians
from fractions import Fraction
from decimal import Decimal
import sys
input=sys.stdin.readline().rstrip
#from sys import setrecursionlimit
#setrecursionlimit(10**7)
MOD=10**9+7
INF=10**20
prime=[]
def prime_factorize(n):
    if n<=1:return
    l=int(sqrt(n))
    for i in range(2,l+1):
        if n%i==0:
            prime_factorize(i)
            prime_factorize(n//i)
            return
    prime.append(n)
    return
x,m=map(int,input().split())
prime_factorize(x)
prime=list(set(prime))
ans=1
for j in prime:
    ans_sub=0
    now=j
    while now<=m:
        ans_sub+=m//now
        now*=j
    ans*=pow(j,ans_sub,MOD)
    ans%=MOD
print(ans)
#print(prime)