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)

N,M=map(int,input().split())
import math
a=[]
ans=1
def calc(n):#nの素因数分解
    for i in range(2,int(n**0.5)+10):
        count=0
        while n%i==0:
            n//=i
            count+=1
        if count>=1:
            a.append([i,count])
def conb(n,k):
    return math.factorial(n)//(math.factorial(n-k)*math.factorial(k))
calc(M)
for i in range(len(a)):
    ans*=conb(a[i][1]+N-1,a[i][1])
print(ans%(10**9+7))