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.
import sys
def is_prime(n):
	if n == 1:
		return (False, 1);
	i = 2;
	while i * i <= n:
		if n % i == 0:
			return (False, i)
		i += 1
	return (True, n)

def fact(n):
	if n == 1:
		return []
	ans = []
	tmp = is_prime(n)
	while(not tmp[0]):
		while(n % tmp[1] == 0):
			n = n // tmp[1]
		ans.append(tmp[1])
		tmp = is_prime(n)
		if(tmp[1] == 1):
			break
	ans.append(n)
	return ans

def legendre(x, n):
	ans = 0;
	tmpx = x
	while n // tmpx > 0:
		ans += n // tmpx;
		tmpx *= x
	return ans

def fastpow(x, pow):
	if pow == 0:
		return 1;
	if pow % 2 == 0:
		tmp = fastpow(x, pow // 2)
		return (tmp ** 2) % 1000000007
	else:
		return (x * fastpow(x, pow - 1)) % 1000000007

x, n = input().split()
x = int(x)
n = int(n)
ans = 1
for i in fact(x):
	if i != 1:
		ans = (ans * fastpow(i, (legendre(i, n)))) % (10**9 + 7)
print(ans)