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 power(x, y, p):
    res = 1
    x = x%p
    while (y>0):
        if ((y&1) == 1):
            res = (res * x) % p
        y = y >> 1  # y = y/2
        x = (x * x) % p
    return res

x,n = map(int,input().split())
r = int(x**0.5)
ans,p = 1,2

primes = set()

while(p<=r and p<=x):
    while(x%p==0):
        primes.add(p)
        x= int(x/p)
    p+=1

if(x>1):    primes.add(x)

for prime in primes:
    e = []
    p = prime
    while(p<=n):
        a = n//p
        #print("A ",a)
        if(len(e)==0):
            e.append(a)
        else:
            e[len(e)-1] -= a
            e.append(a)
        p *= prime
    total_expo = 0
    i = 1
    for expo in e:
        total_expo += (expo*i)
        i+=1
    #print(prime,total_expo)
    ans = ans*power(prime,total_expo,1000000007)
    ans %= 1000000007

print(ans)

