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 log
m = 10**9 + 7
factors = []
def primefactors(n):
	global factors
	while(n%2 == 0):
		factors += [2]
		n = n//2
	for i in range(3, int(n**0.5)+2):
		while(n%i == 0):
			factors += [i]
			n = n//i
	if(n > 2):
		factors += [n]
	factors = list(set(factors))

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

ans = 1
for i in factors:
	# if(i <= n):
		k = int(log(n)/log(i)) + 2
		num = []
		p = i
		for j in range(k):
			num += [p]
			p *= i
			if(p > n):
				break
		num = num[::-1]
		times = [n//num[0]]
		for j in range(1, k):
			try:	
				times += [n//num[j] - n//num[j-1]]
			except:
				break
		for h in range(len(num)):
			ans = (ans*pow(num[h], times[h], m))%m
print(ans)