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 PyPy3 (7.3.0) (judge verdict: Runtime Error)

from scipy.misc import comb

def solve(n,m):
    maxdiv = int(m**0.5)
    l = []
    tmp = 2
    num = 0
    while tmp <= maxdiv:
        if m % tmp == 0:
            m /= tmp
            num += 1
        else:
            tmp += 1
            if num != 0:
                l.append(num)
                num = 0
    if m != 1:
        l.append(1)
    res = 1
    for div in l:
        tmp = comb(n+div-1,div,exact=True)%(10**9+7)
        res = res * tmp % (10**9+7)
    return int(res)
        

if __name__ == '__main__':
    n,m = map(int,input().split())
    print(solve(n,m))