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 ceil, floor, sqrt, log
	
def mod_expo(n, p, m):
	"""find (n^p)%m"""
	result = 1
	while p != 0:
		if p%2 == 1:
			result = (result * n)%m
		p //= 2
		n = (n * n)%m
	return result
	
def is_prime(n):
	for i in range(2, floor(sqrt(n)+1)):
		if n%i == 0:
			return False
	return True 
	
def find_k(n):
	for k in range(0, ceil(n/2)+1):
		if is_prime(k + n):
			return k
		

def get_graph(n):
	k = find_k(n)
	m = n+k
	print(m)
	for i in range(1, n):
		print(i, i+1)
	print(n, 1)
	for i in range(1, k+1):
		print(i, i+floor(n/2))
	
def alice_wins(n, k):
	if n < k:
		if n%3 != 0:
			return True
		return False
	if alice_wins(k-1, k):
		if (n - (k+1))%3 != 0:
			return True
	else:
		if (n - (k+2))%3 != 0:
			return True
	return False
	
def prime_factorization(x):
	answer = []
	i = 2
	while i*i <= x:
		if x%i == 0:
			answer.append(i)
			while x%i == 0: 
				x //= i
		i += 1
	if x > 1: 
		answer.append(x)
	return answer
	
def pf(X, N):
	answer = 1
	m = pow(10, 9) + 7
	x_primes = prime_factorization(X)
	for prime in x_primes:
		power = 0
		factor = prime
		while factor <= N:
			power += N // factor
			factor *= prime
		answer *= pow(prime, power, m)
		answer %= m
	return answer
	
t = 1 
#t = int(input())
while t:
	t = t - 1
	#n = int(input())
	# s = input()
	#x1, y1, x2, y2 = map(int, input().split())
	#
	x, n = map(int, input().split())
	#l = list(map(int, input().strip().split()))[:n]
	#str1 = input()
	#find_massive_x(n)
	#result = find_min(n, l)
	print(pf(x, n))
	#if alice_wins(n, k):
	#	print("Alice")
	#else:
	#	print("Bob")
	# find_arr(u, v)
