Problem:
Score : 100 points

Problem Statement

There is a directed graph G with N vertices and M edges.
The vertices are numbered 1, 2, \ldots, N, and for each i (1 \leq i \leq M), the i-th directed edge goes from Vertex x_i to y_i.
G does not contain directed cycles.

Find the length of the longest directed path in G.
Here, the length of a directed path is the number of edges in it.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq x_i, y_i \leq N

All pairs (x_i, y_i) are distinct.

G does not contain directed cycles.

Input

Input is given from Standard Input in the following format:

N M
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the length of the longest directed path in G.

Sample Input 1

4 5
1 2
1 3
3 2
2 4
3 4

Sample Output 1

3

The red directed path in the following figure is the longest:

Sample Input 2

6 3
2 3
4 5
5 6

Sample Output 2

2

The red directed path in the following figure is the longest:

Sample Input 3

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

Sample Output 3

3

The red directed path in the following figure is one of the longest:

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

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

#define node pair<long long, int>

long long journey(vector<int> &a, int k)
{
	int n = a.size();

	/* dp[i] is the maximum point that you can collect when you start at i */
	vector<long long> dp(n);
	multiset<node, greater<node>> mset;

	dp[n - 1] = a[n - 1];
	mset.insert({dp[n - 1], n - 1});

	for(int i = n - 2; i >= 0; i--)
	{
		int up = min(n - 1, i + k);

		/* Don't accidentally delete multiple copies */
		while(mset.begin()->second > up)
			mset.erase(mset.begin());

		assert(not mset.empty());

		dp[i] = a[i] + mset.begin()->first;
		mset.insert({dp[i], i});
	}

	return dp[0];
}

int main()
{
	int n;
	cin >> n;

	vector<int> path(n);
	for(auto &ele : path)
		cin >> ele;

	int k;
	cin >> k;

	auto res = journey(path, k);
	cout << res << endl;

	return 0;
}