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)

import sys
input = sys.stdin.buffer.readline

def main():
    N,M = map(int,input().split())
    MOD = 10**9+7
    
    def factorization(n):
        arr = []
        temp = n
        for i in range(2, int(-(-n**0.5//1))+1):
            if temp%i==0:
                cnt=0
                while temp%i==0:
                    cnt+=1
                    temp //= i
                arr.append([i, cnt])

        if temp!=1:
            arr.append([temp, 1])

        return arr
        
    cl = factorization(M)
    
    def combinations(x,y,N):
        fac = [0]*(N+1)
        fac[0],fac[1] = 1,1
        
        for i in range(2,N+1):
            fac[i] = (fac[i-1]*i)%MOD
            
        return (fac[x+y]*pow(fac[x],MOD-2,MOD)*pow(fac[y],MOD-2,MOD))%MOD
        
    ans = 1
    for pr,num in cl:
        ans *= combinations(N-1,num,N+num)
        ans %= MOD
    
    print(ans)
    
if __name__ == "__main__":
    main()