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 sys
import math 

def madd(a,b,m):
	return (a%m+b%m)%m

def legendre(n,p):
	
	ans=0
	k=1
	while(n//pow(p,k)!=0):
		ans+=n//pow(p,k)
		# ans=madd(ans,modDivide(n,pow(p,k),m),m)
		# ans=madd(ans,n//pow(p,k),m)
		k+=1
	return ans

def power(x, y, p) : 
    
	# Source: https://www.geeksforgeeks.org/write-a-c-program-to-calculate-powxn/ 

    res = 1     # Initialize result 
  
    # Update x if it is more 
    # than or equal to p 
    x = x % p  
  
    while (y > 0) : 
          
        # If y is odd, multiply 
        # x with result 
        if ((y & 1) == 1) : 
            res = (res * x) % p 
  
        # y must be even now 
        y = y >> 1      # y = y/2 
        x = (x * x) % p 
          
    return res   

def mmul(a,b,m):
	return ((a%m)*(b%m))%m
    
def isprime(x):

	e=2

	while(e*e<=x):
		if(x%e==0):
			return False
		e+=1

	return True


[x,n]=[int(i) for i in sys.stdin.readline().split()]

m=pow(10,9)+7

pfac=[]

w=2

while(w*w<=x):

	if(x%w==0):
		if(isprime(w)):
			pfac.append(w)
		
		if(w!=x//w and isprime(x//w)):
			pfac.append(x//w)

	w+=1

answ=1

if(len(pfac)==0):
	pfac.append(x)

for g in range(len(pfac)):
	answ=mmul(answ,power(pfac[g],legendre(n,pfac[g]),m),m)

print(answ)