1228_C. Primes and Multiplication
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.
```python
"""

import math

MOD=1000000007

def powr(n,N):
    temp=1
    while(N>0):
        if(N%2!=0):
            temp=(temp*n)%MOD
        n=(n*n)%MOD
        N=N//2
    return (temp%MOD)

x,n=map(int,input().split())

n1=x
L=[]
while(n1%2==0): 
    L.append(2) 
    n1=n1//2

for i in range(3,int(math.sqrt(n1))+1,2): 

    while(n1%i==0): 
        L.append(i) 
        n1=n1//i 
 
if(n1>2): 
    L.append(n1)

L=list(set(L))
mul=1
for i in range(0,len(L)):
    d=L[i]
    nn=n
    tot=0
    while(nn>0):
        tot=(tot+(nn//d))%MOD
        nn=(nn//d)%MOD

    mul=(mul*powr(d,tot))%MOD

print(mul)
"""
"""

import math

MOD=1000000007

def powr(n,N):
    temp=1
    while(N>0):
        if(N%2!=0):
            temp=(temp*n)%MOD
        n=(n*n)%MOD
        N=N//2
    return (temp%MOD)

def MODI(a,b):
    ans=(powr(a,b)%MOD)
    return ans
 

x,n=map(int,input().split())

n1=x
L=[]
while(n1%2==0): 
    L.append(2) 
    n1=n1//2

for i in range(3,int(math.sqrt(n1))+1,2): 

    while(n1%i==0): 
        L.append(i) 
        n1=n1//i 
 
if(n1>2): 
    L.append(n1)

L=list(set(L))
mul=1
for i in range(0,len(L)):
    d=L[i]
    t=MODI(d,MOD-2)%MOD
    nn=n
    while(nn>0):
        rem=nn%d
        nn=(nn-rem)%MOD
        nn=(nn*t)%MOD
        mul=(mul*powr(d,nn))%MOD

    

print(mul)

"""

import math

MOD=1000000007

def powr(n,N):
    temp=1
    while(N>0):
        if(N%2!=0):
            temp=(temp*n)%MOD
        n=(n*n)%MOD
        N=N//2
    return (temp%MOD)

x,n=map(int,input().split())

n1=x
L=[]
while(n1%2==0): 
    L.append(2) 
    n1=n1//2

for i in range(3,int(math.sqrt(n1))+1,2): 

    while(n1%i==0): 
        L.append(i) 
        n1=n1//i 
 
if(n1>2): 
    L.append(n1)

L=list(set(L))
mul=1
for i in range(0,len(L)):
    d=L[i]
    nn=n
    while(nn>0):
        mul=(mul*powr(d,nn//d))%MOD
        nn=nn//d

print(mul)


```