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 math
def g(a,b):
    count=0
    while 1:
        if a%b==0:
            count+=1
            a=a//b
        else: return b**count
def p(n): 
    a=[]
    while n % 2 == 0: 
        a.append(2)
        n = n // 2
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            a.append(i) 
            n = n // i 
    if n > 2: a.append(n)
    return list(set(a))
def powmod(a,b,m):
    if b==1: return a%m
    elif b%2==0: return ((powmod(a,b//2,m))**2)%(m)
    else: return (a*powmod(a,b//2,m)**2)%m
k=list(map(int,input().split()))
x=k[0]
n=k[1]
a=p(x)
l=1
for itr in range(len(a)):
    k=a[itr]
    t=n
    count=0
    while 1:
        count=t//k
        if count==0: break
        ll=[]
        #print(a[itr],count)
        l*=powmod(a[itr],count,10**9+7)
        #l*=((a[itr])**count)%(10**9+7)
        l=l%(10**9+7)
        k*=a[itr]
        
print(l)