A12912. 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:

- $f(30, 70) = g(70, 2) \cdot g(70, 3) \cdot g(70, 5) = 2^1 \cdot 3^0 \cdot 5^1 = 10$ ,
- $f(525, 63) = g(63, 3) \cdot g(63, 5) \cdot g(63, 7) = 3^2 \cdot 5^0 \cdot 7^1 = 63$ .

You have integers $x$ and $n$ . Calculate $f(x, 1) \cdot f(x, 2) \cdot \ldots \cdot f(x, n) \bmod{(10^{9} + 7)}$ .

The only line contains integers $x$ and $n$ ( $2 \le x \le 10^{9}$ , $1 \le n \le 10^{18}$ ) — the numbers used in formula.

Print the answer.

In the first example, $f(10, 1) = g(1, 2) \cdot g(1, 5) = 1$ , $f(10, 2) = g(2, 2) \cdot g(2, 5) = 2$ .

In the second example, actual value of formula is approximately $1.597 \cdot 10^{171}$ . Make sure you print the answer modulo $(10^{9} + 7)$ .

In the third example, be careful about overflow issue.