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 = map(int, input().split())
mod = 10 ** 9 + 7


def factorization(n):  # => {p:count,...}
    fac = {}
    count = 0
    while n % 2 == 0:
        n //= 2
        count += 1
    if count > 0:
        fac[2] = count
    for i in range(3, int(n ** .5) + 2, 2):
        count = 0
        while n % i == 0:
            n //= i
            count += 1
        if count > 0:
            fac[i] = count
    if n > 1:
        fac[n] = 1
    return fac


def C(n, r, mod):
    r = min(n - r, r)
    if r == 0:
        return 1
    over = list(range(n, n - r, -1))
    for k in range(2, r + 1):
        for i, o in enumerate(over):
            if o % k == 0:
                over[i] //= k
                break
    ret = 1
    for o in over:
        ret *= o
        ret %= mod
    return ret


ans = 1
for c in factorization(m).values():
    ans *= C(c + n - 1, c, mod)
    ans %= mod
print(ans)