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: Wrong Answer)

import sys
import math
def input():
    return sys.stdin.readline()[:-1]

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

def trial_division(n):
    factor = []
    tmp = int(math.sqrt(n)) + 1
    for num in range(2,tmp):
        while n % num == 0:
            n //= num
            factor.append(num)
    if n!=1:
        factor.append(n)
    return factor

n,m=map(int,input().split())
mod=10**9+7
if m==1:
    print(1)
    quit()
li=trial_division(m)
tmp=li[0]
countli=[]
count=1
for i in range(1,len(li)):
    if tmp!=li[i]:
        countli.append(count)
        count=1
    else:
        count+=1
    tmp=li[i]
countli.append(count)
ans=1
for i in range(len(countli)):
    r=countli[i]
    s=n+r-1
    r=min(r,n-1)
    p=1
    for j in range(r):
        p*=n-j
        p//=j+1
    ans*=p
    ans%=mod
    
print(ans%mod)