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: Time Limit Exceeded)

from collections import defaultdict
from functools import reduce
from operator import mul

MOD = 10 ** 9 + 7

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

def nHr(n, r):
    return nCr(n + r - 1, r)

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

factors = defaultdict(int)
i = 2
while M > 1:
    while M % i == 0:
        M //= i
        factors[i] += 1
    i += 1

ans = 1
for n in factors.values():
    ans *= nHr(N, n)
    ans %= MOD
print(ans)