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.
x, n = [int(x) for x in input().split()]

from math import sqrt, ceil, log

primes = [0]*(10**4*6)

for i in range(2, len(primes)):
	if primes[i] == 0:
		primes[i] = i
		for j in range(2*i, len(primes), i):
			primes[j] = -1

Primes = []
for prime in primes:
	if prime >= 2:
		Primes.append(prime)

primes = Primes

def containspower(base, num):
	l, r = 0, int(log(num, base)+1)
	while r-l > 1:
		c = (l + r) // 2
		if num % (base**c) == 0:
			l = c
		else:
			r = c
	return l

def factor(x):
	ans = []
	for i in primes:
		if x % i == 0:
			ans.append((i, containspower(i, x)) )
			x //= i**ans[-1][1]
	if x != 1:
		ans.append((x, 1))
	return ans


xx = factor(x)
# print(xx)

ans = 1
for p, power in xx:
	pa = 1
	for i in range(1, int(log(n, p))+5):
		a = pow(p, (n // p**i), 10**9+7)
		# print(f"{a = } {p = } {i = }")
		pa *= a if a != 0 else 1
	ans *= pa
	ans %= 10**9+7

print(ans % (10**9+7))
