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.
mod = 1000000007

def sqrat(n):
    x = n
    y = (x+1) // 2
    while y < x:
        x = y
        y = (x + n // x) // 2
    return x

def paw(e, exp):
    if exp == 0: return 1
    if exp == 1: return e
    ret = paw(e, exp//2);
    l = ret * ret % mod
    if exp%2 == 1:
        l *= e
        l %= mod
    return l

def main():
    inp = input().split()
    x = int(inp[0])
    n = int(inp[1])
    prime = set()

    cur = x;
    for i in range(2,sqrat(x)+5):
        while cur % i == 0:
            cur //= i
            prime.add(i)
    if cur > 1:
        prime.add(cur)

    p = 1
    for e in prime:
        f = e
        exp = 0
        while f <= n:
            exp += n //f
            f *= e
        p *= paw(e, exp)
        p %= mod

    print(p)

main()
