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())
def prime_factorize(x):
    a=[]
    b=[]
    while x%2==0:
        if 2 not in b:
            a.append(2)
            b.append(2)
            x/=2
        else:
            a.append(2)
            x/=2
    f=3
    while f*f<=x:
        if x%f==0:
            if f not in b:
              a.append(f)
              b.append(f)
              x/=f
            else:
              a.append(f)
              x/=f
        else:
          f+=2        
    if x!=1:
      a.append(int(x))
      b.append(int(x))
    return a,b    

def comb(n, b):
    if b > n - b:
      b = n - b
    r = 1
    for k in range(n, n-b, -1):
      r = r * k
    d = 1
    for k in range(1, b+1):
      d = d * k
    return r // d 
  
ans=1
A,B=prime_factorize(m)

for i in range(len(B)):
  c=A.count(B[i])  
  ans*=comb(c+n-1,c)
  ans%=10**9+7

print(ans)