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)

# coding: utf-8
import math

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

def C(n, r):
	return math.factorial(n) // (math.factorial(n-r) * math.factorial(r))


# m の素因数分解
prim_list = []
d = 2
while d*d <= m:
	while (m % d) == 0:
		prim_list.append(d)
		m //= d
	d += 1
if m > 1:
	prim_list.append(m)
print(prim_list)

sisuu_list = []
cnt = 1
target = prim_list[0]
for i in range(1, len(prim_list)):
	if target == prim_list[i]:
		cnt += 1
	else:
		target = prim_list[i]
		sisuu_list.append(cnt)
		cnt = 1
sisuu_list.append(cnt)
print(sisuu_list)

answer = 1
for sisuu in sisuu_list:
	answer *= C((n-1 + sisuu), sisuu)

print(answer)