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: Time Limit Exceeded)

# -*- coding: utf-8 -*-
# 
import math
import sys
import itertools
import numpy as np

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

def soin(a):
    fa = []
    i = 2
    d = a
    last = 1
    while d>1:
        if d % i == 0:
            if last == i:
                fa[-1][1]=fa[-1][1]+1
            else:
                fa.append([i,1])
            d=d//i
            last = i
        else:
            i += 1
    return(fa)

#print(soin(n))
q = soin(m)
answer = 1

for i in q:
#    print(i,i[1])
    r = i[1]
    answer = answer * (math.factorial(n+r-1)//math.factorial(n-1)//math.factorial(r))

answer = answer % (10**9+7)

print(answer)