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: Runtime Error)

def factorize(n):
    b,e = 2,0
    fct = []
    while b*b <= n:
        while n%b==0:
            n//=b
            e+=1
        if e>0:
            fct.append((b,e))
        b+=1
        e=0
    if n!=1:
        fct.append((n,1))
    return fct
    
N,M = list(map(int,input().split()))
 
pl = factorize(M)
 
max_coef=max([p[1] for p in pl])
 
 
if max_coef==0:
    print(N)
else:
 
    comb_list = [1]
    c = 1
    mod = 10**9+7
    for i in range(max_coef):
        c *= N+i
        c *= pow(i+1,mod-2,mod)
        c %= mod
        comb_list.append(c)
 
    ans = 1
 
    for p in pl:
        ans*=comb_list[p[1]]
        ans %= mod
 
    print(ans)