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

def factorized(M):
    d = 2
    f = []
    while d <= M:
        count = 0
        while M % d == 0:
            M //= d
            count += 1
        if count > 0:
            f.append(count)
        d += 1
        if d < M and d * d > M:
            d = M
    return f

def tetra(n, m):
    x = 1
    for y in range(1, n):
        x = x * (m + y - 1) // y
    return x

x = 1
for f in factorized(M):
    x *= tetra(N, f + 1)
    x %= 10 ** 9 + 7

print(x)