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: Accepted)

N, M = [int(i) for i in input().split()]

def prime_decomposition(n):
  table = []
  i = 2
  while i * i <= n:
    count = 0
    while n % i == 0:
      n //= i
      count += 1
    if count != 0:
        table.append((i, count))
    i += 1
  if n > 1:
    table.append((n, 1))
  return table

def cmb(n, r):
    N, R = n, r
    for i in range(1, r):
        N *= n - i
        R *= r - i
    return N // R

mod = 10 ** 9 + 7
A = prime_decomposition(M)
result = 1
for _, a in A:
    result = result * cmb(a + N - 1, a) % mod

print(result)