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: Time Limit Exceeded)

import math

n, m=map(int, input().split())
t = {}
a = int(math.sqrt(m))

s=0

line = [2, 3] + [i%2*2 + i//2 * 6 + 5 for i in range(a//3)]
while s==0:
    for i in line:
        cnt = 0
        while m%i==0:
            m=m//i
            cnt += 1

        if cnt>0:
            t[i]=cnt

        if m==1:
            s=1
            break

def combi(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r)) 

out=1
for tk in t.keys():
    out *= combi(t[tk]+n-1, n-1)
print(out%(1000000007))