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: Wrong Answer)

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

mod = 10 ** 9 + 7
def comb(x, y):
    if x // 2 < y:
        return comb(x, x - y)
    ans = 1
    for j in range(1, y + 1):
        ans *= pow(j, mod - 2, mod) * (x - y + j)
        ans %= mod
    return ans
def homoprod(x, y):
    return comb(x + y - 1, y)

ans = 1
for i in range(2, int(M ** 0.5) + 2):
    count = 0
    while M % i == 0:
        count += 1 
        M //= i
    if count > 0:
        ans *= homoprod(N, count)
        ans %= mod
print(ans)