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: Runtime Error)

one=list(map(int,input().split()))
#print(one)
z=[0]
def multip(begin,goal,time):
    if time == 0 and begin == goal:
        z[0] += 1
        return
    if time==0:
        return 
    #if time==0:
    #    return
    #if begin > goal:
    #    return
    #else:
    for i in range(1,goal+1):
        if time==one[0]:
            multip(i,goal,time-1)
        else:
            if begin<=goal:
                multip(begin*i, goal, time - 1)
            else:
                return
    return
multip(0,one[1],one[0])
print(z[0])