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 ciur(n):
    lim = int(math.sqrt(n + 2))
    primes = []
    d = 2
    while d <= lim and n > 1:
        e = 0
        while n % d == 0:
            n //= d
            e += 1
        if e > 0:
            primes.append(d)
        d += 1
    return primes


def getFactors(primes, x):
    factors = []
    d = 0
    # print(len(primes))
    while x > 1 and d < len(primes) and primes[d] * primes[d] <= x:
        # print(primes[d])
        e = 0
        while x % primes[d] == 0:
            e += 1
            x //= primes[d]
        if e > 0:
            factors.append(primes[d])
        d += 1
    if x > 1:
        factors.append(x)
    return factors

def getExp(factor, n):
    s = 0
    while n > 0:
        s += n // factor
        n //= factor
    return s

def raisePut(x, y, mod):
    ret = 1
    while y > 0:
        if y % 2 == 1:
            ret = ret * x % mod
        x = x * x % mod
        y //= 2
    return ret

x, n = [int(i) for i in input().split()]
MOD = (10 ** 9) + 7

primes = ciur(x)
# print(primes)
factors = getFactors(primes, x)
# print(factors)
sol = 1
for factor in factors:
    e = getExp(factor, n)
    sol = (sol * raisePut(factor, e, MOD)) % MOD

print(sol)
