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 PyPy3 (7.3.0) (judge verdict: Runtime Error)

import collections

def prime_factorize(n):
  a = []
  while n % 2 == 0:
    a.append(2)
    n //= 2
  f = 3
  while f * f <= n:
    if n % f == 0:
      a.append(f)
      n //= f
    else:
      f += 2
  if n != 1:
    a.append(n)
  return a

def nCr(n,r):
  return (FAC[n]*INV[n-r]*INV[r])%MOD

n,m = map(int,input().split())

MOD = 10**9 + 7
FAC = [1]
INV = [1]
N = 2*n
for i in range(1,N+1):
  FAC.append((FAC[i-1]*i) % MOD)
  INV.append(pow(FAC[-1],MOD-2,MOD))

c = collections.Counter(prime_factorize(m))
#print(c)
ans = 1
for k,v in c.items():
  ans *= nCr(v+n-1,v)
  ans %= MOD
print(ans)