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 Python (3.4.3) (judge verdict: Wrong Answer)

import math

nn,m=map(int,input().split())

mod=10**9+7

yak=[0 for i in range(10**5)]

p=1
for i in range(2,int(m**0.5)+2):

    while m%i==0 :
            m=m//i
            yak[i]+=1
            p=0

if p==1:
    yak[i]=1


ka=[1] # 階乗のリスト
for i in range(1,10**5*2):
    ka.append((ka[i-1]*i)%mod)

def inv(x): # mod上のxの逆数を求める関数（フェルマーの小定理）
    res=1
    k=mod-2
    y=x
    while k>0 :
        if k%2 == 1 :
            res = (res*y) % mod
        y = (y*y) % mod
        k //= 2
    return res

def modcomb(n,k): # mod上でのコンビネーションを求める関数(nCk)
    a=ka[n]
    b=ka[n-k]
    c=ka[k]

    bc=(b*c)%mod

    return a*inv(bc)%mod


    


ans=1

for i in range(10**5):
    if yak[i]>0 :
        n=nn+yak[i]-1
        k=yak[i]

        ans=(ans*modcomb(n,k))%mod

print(ans)