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)

import math


def is_prime(num):
    if (num < 2):
        return False
    elif(num == 2):
        return True
    elif (num % 2 == 0):
        return False
    sqrt_num = int(math.sqrt(num))
    for i in range(3, sqrt_num+1):
        if i % 2 == 0:
            continue
        if (num % i == 0):
            return False
    return True


def combination(n, r):
    if r > n-r:
        r = n-r
    a = 1
    for i in range(n, n-r, -1):
        a = a * i
    d = 1
    for i in range(1, r+1):
        d = d*i
    return a//d


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

m = {}
num = math.ceil(math.sqrt(M))
for i in range(2, num+1):
    if not(is_prime(i)):
        continue
    if M % i == 0:
        m[i] = 0
        _num = M
        while(True):
            if _num % i == 0:
                m[i] += 1
                _num /= i
            else:
                break

ans = 1
mod = 10**9+7
for v in m.values():
    ans *= combination(v+N-1, v)
    ans %= mod
print(ans)