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)

from math import factorial, sqrt
N,M=map(int,input().split())
prms={}
tmp=M
for i in range(2, int(sqrt(M))+2):
    while not tmp%i:
        if not i in prms:
            prms[i]=1
        else:
            prms[i]+=1
        tmp //= i
if tmp != 1:
    prms[tmp] = 1

# print(prms)

res=1
def cmb(a,b):
    res=1
    if a - b < b:
        b = a-b
    for i in range(b):
        res *= (a-i)
        res //= (i+1)
    return res

for p, cnt in prms.items():
    res *= cmb(cnt+N-1, cnt)
    res %= 1000000007

print(res % 1000000007)