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 Python (3.4.3) (judge verdict: Accepted)

import collections
from functools import reduce
from operator import mul


def trial_division(n):
    l = []
    f = 2
    while f * f <= n:
        if n % f == 0:
            l.append(f)
            n //= f
        else:
            f += 1
    if n > 1:
        l.append(n)
    return l


def combinations_count(n, r):
    r = min(n - r, r)
    if r == 0:
        return 1
    return reduce(mul, range(n, n - r, -1)) // reduce(mul, range(r, 0, -1))


N, M = map(int, input().split())

c = collections.Counter(trial_division(M))
a = 1
for i in c.values():
    a *= combinations_count(i + N - 1, i)

print(a % (10**9 + 7))