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)

def nCr(n,r):
    a=1
    x=n
    while(x!=n-r):
      a*=x
      x-=1
    b=1
    x=r
    while(x!=0):
      b*=x
      x-=1
    return a//b

INF=10**9+7
N,m=map(int,input().split())


sum=1
yd = {}
i = 2
while m != 1:
  while m % i == 0:
    if i in yd:
      yd[i] += 1
    else:
      yd[i] = 1
    m //= i
  i += 1
for b in yd.values():
    if b<N-1:
        sum*=nCr(N-1+b,b)
    else:
        sum*=nCr(N-1+b,N-1)
    sum%=INF  
print(sum)