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.
x,n=map(int,input().split())
x1=x
l=[]
prime = [True for i in range(100001)] 
p = 2
while (p * p <= 100000): 
      
    # If prime[p] is not changed, then it is a prime 
    if (prime[p] == True): 
          
        # Update all multiples of p 
        for i in range(p * p, 100001, p): 
            prime[i] = False
    p += 1
  
# Print all prime numbers 
for p in range(2, 100000): 
    if prime[p]: 
        l.append(p)
l1=[]
for i in range(len(l)):
    if l[i]*l[i]>x1:
        break
    if x%l[i]==0:
        l1.append(l[i])
        while x%l[i]==0:
            x//=l[i]
if x!=1:
    l1.append(x)
ans=1
for i in l1:
    j=1
    while i**j<=n:
        x=n//(i**(j+1))
        y=n%(i**(j+1))
        z=y//(i**j)
        ans*=pow(i,j*x*(i-1),1000000007)
        ans*=pow(i,j*z,1000000007)
        ans%=1000000007
        j+=1
print(ans%1000000007)

        
