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)

from collections import defaultdict
import math
N,M=map(int,input().split())
dd=defaultdict(int)
m=M
mod=10**9+7
for i in range(2,10**5):
    s=0
    while m%i==0 and m>1:
        m=m//i
        s+=1
    if s>0:
        dd[i]=s
if m>1:
    dd[10**9]=1
def f(n,k):
    a=1
    for i in range(1,k+1):
        a=a*(n-i+1)
        a%=mod
        a*=pow(i,mod-2,mod)
        a%=mod
    return a
ans=1
for l,t in dd.items():
    ans*=f(N-1+t,t)
    ans%=mod
print(ans)