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: Runtime Error)

import math
n,m = list(map(int,input().split()))

#素数列挙
m_sqr = math.floor(math.sqrt(m))
tf = [True]*(m+1)
for i in range(2,math.floor(math.sqrt(m)+1)):
  if tf[i] == True:
    for j in range(i+1,m+1):
      if j % i == 0:
        tf[j] = False

prim = []
for i in range(2,m+1):
  if tf[i]:
    prim.append(i)

divm = m
ans = 1
for i in prim:
  cnt = 0
  if m%i == 0:
    while divm%i == 0:
      cnt += 1
      divm /= i
    
    ans *= math.factorial(cnt+n-1) / (math.factorial(n -1) * math.factorial(cnt))

print(int(ans) % 1000000007)