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 = int(1e9 + 7)
maxn = int(1e5 + 100)
primes = []
is_prime = [True] * maxn
def init():
    is_prime[0] = is_prime[1] = False
    for i in range(2, maxn):
        if is_prime[i]:
            primes.append(i)
        for p in primes:
            if p * i >= maxn:
                break
            is_prime[i * p] = False
            if i % p == 0:
                break

def qpow(base, t):
    ret = 1
    while t > 0:
        if t & 1:
            ret = ret * base % mod
        base = base * base % mod
        t >>= 1
    return ret

def solve():
    x, n = map(int, input().split())
    p = []
    for prime in primes:
        if x <= 1:
            break
        if x % prime == 0:
            p.append(prime)
            while x % prime == 0:
                x = x // prime
    if x > 1:
        p.append(x)
    
    ans = 1
    for prime in p:
        index = 0
        k = prime
        while k <= n:
            index += n // k
            k = k * prime
        ans = ans * qpow(prime, index) % mod
            
    print(ans)

if __name__ == "__main__":
    init()
    solve()

# 20190929 1605
# 363165664
   				    			  	  	 		