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)

"""
---アルゴリズム概要---
Mを素因数分解する。
各素因数をa1 ~ an をどの場所にいくつ納めるかを考えれば、それが答えになる。
"""
import math
from collections import Counter
N,M = map(int,input().split())
a = []
def prime_factorize(n):
        while n % 2 == 0:
            a.append(2)
            n //= 2
        f = 3
        while f * f <= n:
            if n % f == 0:
                a.append(f)
                n //= f
            else:
                f += 2
        if n != 1:
            a.append(n)
        return a

prime_factorize(M)
#次に各要素の配置パターン数を求めて累積していく。
#combination関数を定義する
def combination(n,r):
    return math.factorial(n)//(math.factorial(n-r)*math.factorial(r))

factors = Counter(a)
ans = 1
for k,v in factors.items():
    ans *= combination(N+v-1,v)

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