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())
mod=10**9+7
arr=[]
temp=M
for i in range(2,int(M**(1/2))+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])
if arr==[]:
  arr.append([M,1])
def comb(n,k):
  ans=n
  for i in range(1,k):
    ans=ans*((n-i)%mod)*pow(i+1,mod-2,mod)
    ans=ans%mod
  return ans
ans=1
for i in range(len(arr)):
  ans*=comb(arr[i][1]+N-1,arr[i][1])
  ans%=mod
print(ans)