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 findPowerPrime(fact, p): 
    res = 0
    while fact:  
        res += fact // p 
        fact //= p 
 
    return res 
 
 
def findPowerComposite(fact, n): 
    
    res = math.inf 
 
    for i in range(2, int(n**0.5) + 1): 
 
        count = 0
        if not n % i: 
            count += 1
            n = n // i 
 
        if count: 
 
            curr_pow = findPowerPrime(fact, i) // count 
            res = min(res, curr_pow) 
    if n >= 2: 
        curr_pow = findPowerPrime(fact, n) 
        res = min(res, curr_pow) 
 
    return res 
 
 
 
def primeFactors(n): 
     
    ans = set()
    while n % 2 == 0: 
        ans.add(2)
        n = n // 2
          
    for i in range(3,int(math.sqrt(n))+1,2): 
          
        # while i divides n , print i ad divide n 
        while n % i== 0: 
            # print i, 
            ans.add(i)
            n = n // i 
    if n > 2: 
        # print n 
        ans.add(n)
 
    return ans
 
 
x, n = map(int, input().split())
 
pf = primeFactors(x)
 
ans = 1
 
 
 

for i in pf:
    # print(i)
    tmp = findPowerComposite(n, i)
    ans *= pow(i, tmp, 1000000007)
    ans = ans%1000000007
 
print(ans)