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

mod = 10 ** 9 + 7
x, n = map(int, input().split())

def mu(a, b):
    if (b == 0):
        return 1
    temp = mu(a, b // 2)
    temp = (temp * temp) % mod
    if (b % 2):
        temp = (temp * a) % mod
    
    return temp

def d(x, a, b):
    return x // a - x // (a * b)

def phantich(n):
    res = []
    w = int(math.sqrt(n)) + 1
    for i in range(2, w):
        if (n % i == 0):
            res.append(i)
        while n % i == 0:
            n //= i
    
    if (n > 1):
        res.append(n)

    return res

p = phantich(x)

answer = 1
for w in p:
    temp = w
    while (n >= temp):
        q = d(n, temp, w)
        answer = (answer * mu(temp, q)) % mod
        temp = temp * w

print(answer)