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 math import sqrt

MOD = int(1e9 + 7)

def isPrime(n):
  if n==1:
    return False
  if n%2==0:
    return n==2
  r = int(sqrt(n+0.5))
  for i in range(3,r+1,2):
    if n%i==0:
      return False
  return True

def powmod(x,y):
  if y==0:
    return 1
  if y==1:
    return x
  t = powmod(x,y//2)
  t = t * t % MOD
  if y%2==1:
    t = t * x % MOD
  return t

x, n = input().split()
x = int(x)
n = int(n)

prime = []
r = int(sqrt(x+0.5))
for i in range(1,r+1):
  if x%i==0:
    if isPrime(i):
      prime.append(i)
    if i*i!=x and isPrime(x//i):
      prime.append(x//i)

#print(prime)

ans = 1
for p in prime:
  pk = p
  while pk <= n:
    m = n//pk - n//(pk*p)
    ans = ans * powmod(pk%MOD,m) % MOD
    pk = pk * p

print(ans)