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 math

def is_prime(x):
    i = 2
    while i * i <= x:
    	if x % i == 0:
    		return False
    	i += 1			
    return True

def phi(n):
	anw = n
	i = 2
	while (i * i <= n):
		if (n % i == 0):
			while (n % i == 0):
				n //= i;
			anw -= anw // i
		i += 1	
	if (n > 1):
		anw -= anw // n
	return anw

def fastpow(a, power, mod):
	if (power == 0):
		return 1
	elif (power % 2 == 0):
		tmp = fastpow(a, power // 2, mod)
		return tmp * tmp % mod
	else:
		tmp = fastpow(a, power // 2, mod)
		return tmp * tmp * a % mod

def add(p, mod, n):
    val = 1
    anw = 1
    while p * val <= n:
        val = val * p
    lst = 0
    while val > 0:
        cnt = n // val
        anw = anw * fastpow(val, cnt - lst, mod)
        anw = anw % mod
        lst = cnt
        val = val // p
    return anw

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

pr = []
i = 1
while i * i <= x:
	if (i * i == x):
		if (is_prime(i)):
			pr.append(i)
	else:
		if (i != 1 and x % i == 0 and is_prime(i)):
			pr.append(i)
		if (x % i == 0 and is_prime(x // i)):
			pr.append(x // i)
	i += 1

anw = 1
for z in pr:
	anw *= add(z, 1000000000 + 7, n)
	anw %= 1000000000 + 7

print(anw)