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.
def powmod(base,exp,MOD):
    res=1
    while(exp>0):
        if(exp%2==1):
            res=(res*base)%MOD
        base=(base*base)%MOD
        exp/=2
    return (res%MOD)

s=raw_input()
s = s.split()
x = int(s[0])
n = int(s[1])
primes=[]
a = x
if(a%2==0):
    primes.append(2)
    while(a%2==0):
        a = a/2
i=3
while(i*i<=a):
    if(a%i==0):
        primes.append(i)
        while(a%i==0):
            a=a/i
    i+=2
if(a>1):
    primes.append(a)
#print primes
M = 1000000007
ans = 1
for y in primes:
    pwr=1
    ans = (ans*powmod(pwr,n,M))%M
    pwr=pwr*y
    while(pwr<=n):
        b = pwr/y
        a = n/pwr
        ans = (ans*powmod(pwr,a,M))%M
        ans = (ans*powmod(powmod(b,M-2,M),a,M))%M
        pwr = pwr*y
print(ans)
