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.
input=__import__('sys').stdin.readline
import math 
mod = 1000000000+7
def prime(n): 
    while n % 2 == 0:
        if lis[-1][0]!=2:
            lis.append([2,1])
        else:
            lis[-1][1]+=1 
        n = n / 2
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0:
            if lis[-1][0]!=i:
                lis.append([i,1])
            else:
                lis[-1][1]+=1      
            n = n / i 
    if n > 2:
        if lis[-1][0]!=n:
            lis.append([n,1])
        else:
            lis[-1][1]+=1     
lis=[]
lis.append([0,0])
x,n = map(int,input().split())
prime(x)
#print(lis)
ans=1
for i in range(1,len(lis)):
    no = lis[i][0]
    tmp=0
    while no<=n:
        tmp+=(n//no)
        no*=lis[i][0]
#    print(lis[i][0],tmp,mod)    
    ans*=pow(int(lis[i][0]),int(tmp),mod)
print(ans%mod)        

       
          


