Problem:
Score : 400 points

Problem Statement

You are given positive integers N and M.

How many sequences a of length N consisting of positive integers satisfy a_1 \times a_2 \times ... \times a_N = M? Find the count modulo 10^9+7.

Here, two sequences a' and a'' are considered different when there exists some i such that a_i' \neq a_i''.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7.

Sample Input 1

2 6

Sample Output 1

4

Four sequences satisfy the condition: \{a_1, a_2\} = \{1, 6\}, \{2, 3\}, \{3, 2\} and \{6, 1\}.

Sample Input 2

3 12

Sample Output 2

18

Sample Input 3

100000 1000000000

Sample Output 3

957870001

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
)

const MOD = 1e9 + 7

func main() {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Scan()
	var N, M int
	fmt.Sscanf(scanner.Text(), "%d %d", &N, &M)

	facts := make(map[int]int)
	factoring(M, facts)

	ans := 1
	for _, p := range facts {
		ans = ans * comb(p+N-1, p) % MOD
	}
	fmt.Println(ans)
}

func comb(a, b int) int {
	if a < b {
		return comb(b, a)
	}
	prod := 1
	for i := 0; i < b; i++ {
		prod = prod * (a - i) % MOD
	}
	f := factorial(b)
	return prod * inverse(f) % MOD
}

func inverse(n int) int {
	return power(n, MOD-2)
}

func power(a, pow int) int {
	if pow == 1 {
		return a
	} else if pow%2 == 0 {
		rt := power(a, pow/2)
		return rt * rt % MOD
	} else {
		return a * power(a, pow-1) % MOD
	}
}

func factorial(n int) int {
	ret := 1
	for n >= 1 {
		ret = ret * n % MOD
		n--
	}
	return ret
}

func factoring(n int, facts map[int]int) {
	for i := 2; i*i <= n; i++ {
		for n%i == 0 {
			facts[i]++
			n = n / i
		}
	}
	if n != 1 {
		facts[n]++
	}
}