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 divide(b):
    divs = []

    x = int(b)
    for i in range(2, int(math.sqrt(x)+1)):
        if int(x) % int(i) == 0:
            divs.append(int(i))
            while int(x)%int(i)==0:
                x = int(x) // int(i)
    if x > 1:
        divs.append(x)
    return divs

def pow_(n, k, mod):
    ret = 1
    while(int(k) > 0.9):
        if(int(k) % int(2) == 1):
            ret = int(ret) * int(n) % int(mod)
        n = int(n) * int(n) %int(mod)
        k = int(k) // int(2)
    return ret

mod = 1000000007
x , n= input().split()
x = int(x)
n = int(n)
if n>1:
    listdiv = divide(x)
    #print(listdiv)
    ans = 1
    kk = []
    for i in range(len(listdiv)):
        nn = n
        temp = 0
        while True:
            temp = (int(temp) + (int(nn) // int(listdiv[i])))
            nn = int(nn) //int( listdiv[i])
            #print(temp, nn)
            if int (nn) < 1:
                break
        ans *= int(pow_(listdiv[i], temp, mod))
        ans %= int(mod)
        #print("fff")
    print(ans)
else:
    print(1)
