Answer to Question #314892 in Functional Programming for Akash srivastava

Question

Is this prime?

Problem Statement

Let's assume some functional definitions for this problem.

We take prime(x) as the set of all prime divisors of x. For example, prime(140)={2,5,7}, prime(169)={13}.

Let f(x,p) be the maximum possible integer p**k where k is an integer such that x is divisible by p**k.

(Here a**b means a raised to the power b or pow(a, b))

For example:

f(99,3)=9 (99 is divisible by 3**2=9 but not divisible by 3**3=27),

f(63,7)=7 (63 is divisible by 7**1=7 but not divisible by 7**2=49).

Let g(x,y) be the product of f(y,p) for all p in prime(x).

For example:

g(30,70)=f(70,2)*f(70,3)*f(70,5)=2*1*5=10,

g(525,63)=f(63,3)*f(63,5)*f(63,7)=9*1*7=63.

You are given two integers x and n. Calculate g(x,1)*g(x,2)*…*g(x,n) mod (1000000007).

(Read modulo exponentiation before attempting this problem)

Input

The only line contains integers x and n — the numbers used in formula.

Constraints

2 ≤ x ≤ 1000000000

1 ≤ n ≤ 1000000000000000000

Output

Print the answer corresponding to the input.

Answer 1

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