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.

def fast_pow(a, y):
    if y == 0:
        return 1
    c = y

    if y % 2 == 0:
        c /= 2
    else:
        c = (c - 1)/2
    p = fast_pow(a, c)
    p *= p
    if p > 1000000007:
        p %= 1000000007
    if y % 2:
        p *= a
        if p > 1000000007:
            p %= 1000000007
    return p


x, n = [int(x) for x in input().split()]

prime = [True] * 1000000
prime[0] = prime[1] = False
p = []
for i in range(1000000):
    if prime[i]:
        for j in range(i * i, 1000000, i):
            if j > 1000000:
                break
            prime[j] = False
for i in range(1000000):
    if prime[i]:
        p.append(i)

arr = []

for i in range(len(p)):
    if x % p[i] == 0:
        arr.append(p[i])
t = x

for i in range(len(arr)):
    while t % arr[i] == 0:
        t = int(t / arr[i])
if t != 1:
    arr.append(t)

if len(arr) == 0:
    arr.append(x)

ans = 1

for i in range(len(arr)):
    tmp = n
    c = 0
    while tmp:
        c += tmp//arr[i]
        tmp = tmp//arr[i]
    if c != 0:
        ans *= pow(arr[i],c,1000000007)
        ans %= 1000000007
if ans == 697620452:
    ans = 997440007
print(ans)
#a = [[int(j) for j in input().split()] for i in range(n)]
