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)

n,m=map(int,input().split())
def fctr2(n): #それぞれの素因数の指数だけ出力
    f=[]
    c=0
    r=int(n**0.5)
    for i in range(2,r+2):
        while n%i==0:
            c+=1
            n=n//i
        if c!=0:
            f.append(c)
            c=0
    if n!=1:
        f.append(1)
    return f

mod=10**9+7
fuc=[1]
def fucfun(n):
    for i in range(1,n):
        e=fuc[i-1]*i
        fuc.append(e%mod)
def com(n,k):
    com=(fuc[n]%mod)*pow(fuc[k],mod-2,mod)*pow(fuc[n-k],mod-2,mod)
    return com
f=fctr2(m)
a=max(f)+n
fucfun(a)
s=1
for i in range(len(f)):
    t=com(f[i]+n-1,f[i])
    s=(s*t)%mod
print(s)