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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
import math
sys.setrecursionlimit(1000000) # 再帰上限を増やす

def calc_combi(n, m, mod=1000000007):
    """ nCmの組み合わせ数を数える """
    if n - m < m:
        return calc_combi(n, n - m)

    ans_mull, ans_div = 1, 1
    for i in range(m):
        ans_mull *= (n - i)
        ans_div *= (i + 1)
        ans_mull %= mod
        ans_div %= mod
    ans = ans_mull * pow(ans_div, mod - 2, mod) % mod
    return ans

def main():
    input = sys.stdin.readline  # 文字列に対してinputした場合は、rstripするのを忘れずに！
    N, M = map(int, input().rstrip().split())
    mod = 1000000007

    ans = 1
    for i in range(2, math.ceil(math.sqrt(M))):
        if M % i == 0:
            count = 0
            while M % i == 0:
                M /= i
                count += 1
            ans *= calc_combi(count + N - 1, N - 1, mod)
            ans %= mod
    if M != 1:
        ans *= calc_combi(N, 1, mod)
        ans %= mod
    print(ans)

if __name__ == '__main__':
    main()