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 (3.8.2) (judge verdict: Runtime Error)

n = int(input())
m = int(input())
a = list(map(int,input().split()))
M = 10000

dp = [[0]*(m+1) for i in range(n+1)]

for i in range(n+1):
    dp[i][0] = 1
    
for i in range(n):
    for j  in range(1,m+1):
        if j - 1 - a[i] >= 0:
            dp[i + 1][j] = (dp[i + 1][j - 1] + dp[i][j] - dp[i][j - 1 - a[i]] ) % M
        else:
            dp[i + 1][j] = (dp[i + 1][j - 1] + dp[i][j]) % M
            
print(dp)