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.
from math import sqrt
x,N=[int(x) for x in input().split(' ')]
factors=[]
temp=x

def factorize(n):
	count=0
	while ((n%2)>0)==False:
		n>>=1
		count+=1
	if count>0:
		factors.append(2);
	for i in range(3,int(sqrt(n))+1):
		count=0
		while n%i==0:
			count+=1
			n//=i
		if count>0:
			factors.append(i)
		i+=2
	if n>2:
		factors.append(n)

factorize(x)

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

div=[]

powers=[]
for fact in factors:
	temp=N
	t=0
	while temp:
		t+=(temp//fact)
		temp//=fact
	powers.append(t)
# print(powers)
mod=1000000007
ans=1
for i in range(len(factors)):
	temp=power(factors[i],powers[i],mod)
	ans=(ans*temp)%mod
print(ans)