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 = list(map(int, input().split(' ')))
MOD = int(1e9 + 7)
primes = []
if M % 2 == 0:
  primes.append(2)

seeds = []
p = 2
while M > 1:
  if p*p > M:
    seeds.append(M)
    M = 1
  while M % p == 0:
    seeds.append(p)
    M = M // p
  p += 1

def comb(n, k):
  ans = 1
  for i in range(1, k + 1):
    ans = (ans * (n + 1 - i) // i)
  return ans

ans = 1
hogehoge = set(seeds)
for i in hogehoge:
  a_ct = seeds.count(i)
  ans = (ans * comb(a_ct + N-1, min(a_ct, N-1))) % MOD
print(ans)