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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

const int mod = 1000000007;

int dp[100005][40];
map < int, int > mp;
int main()
{
	int N, M;
	

	dp[0][0] = 1;

	cin >> N >> M;

	for ( int i = 1; i < 100005; i++ ) {
		for ( int j = 0; j < 40; j++ ) {
			dp[i][j] = dp[i - 1][j];
			if ( j > 0 ) (dp[i][j] += dp[i][j - 1]) %= mod;
		}
	}


	for ( int i = 2; i <= M; i++ ) {
		while ( M % i == 0 ) {
			mp[i]++;
			M /= i;
		}
	}

	int ans = 1;
	for ( auto &x : mp ) {
		ans = ((long long)ans * dp[N][x.second]) % mod;
	}

	cout << ans << endl;

	return ( 0 );
}