Problem:
Score : 400 points

Problem Statement

There are N people standing on the x-axis.
Let the coordinate of Person i be x_i.
For every i, x_i is an integer between 0 and 10^9 (inclusive).
It is possible that more than one person is standing at the same coordinate.

You will given M pieces of information regarding the positions of these people.
The i-th piece of information has the form (L_i, R_i, D_i).
This means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.

It turns out that some of these M pieces of information may be incorrect.
Determine if there exists a set of values (x_1, x_2, ..., x_N) that is consistent with the given pieces of information.

Constraints

1 \leq N \leq 100 000

0 \leq M \leq 200 000

1 \leq L_i, R_i \leq N (1 \leq i \leq M)

0 \leq D_i \leq 10 000 (1 \leq i \leq M)

L_i \neq R_i (1 \leq i \leq M)

If i \neq j, then (L_i, R_i) \neq (L_j, R_j) and (L_i, R_i) \neq (R_j, L_j).

D_i are integers.

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1 D_1
L_2 R_2 D_2
:
L_M R_M D_M

Output

If there exists a set of values (x_1, x_2, ..., x_N) that is consistent with all given pieces of information, print Yes; if it does not exist, print No.

Sample Input 1

3 3
1 2 1
2 3 1
1 3 2

Sample Output 1

Yes

Some possible sets of values (x_1, x_2, x_3) are (0, 1, 2) and (101, 102, 103).

Sample Input 2

3 3
1 2 1
2 3 1
1 3 5

Sample Output 2

No

If the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.

Sample Input 3

4 3
2 1 1
2 3 5
3 4 2

Sample Output 3

Yes

Sample Input 4

10 3
8 7 100
7 9 100
9 8 100

Sample Output 4

No

Sample Input 5

100 0

Sample Output 5

Yes

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

class D
{
	static void Main()
	{
		Func<int[]> read = () => Console.ReadLine().Split().Select(int.Parse).ToArray();
		var h = read();
		var n = h[0];
		var rs = new int[h[1]].Select(_ => read()).ToArray();

		var map = new int[n + 1].Select(_ => new List<int[]>()).ToArray();
		foreach (var r in rs)
		{
			map[r[0]].Add(new[] { r[1], r[2] });
			map[r[1]].Add(new[] { r[0], -r[2] });
		}

		var u = Enumerable.Repeat(int.MinValue, n + 1).ToArray();
		var set = new HashSet<int>();
		var q = new Queue<int>();
		for (int i = 1; i <= n; i++)
		{
			if (u[i] > int.MinValue || !map[i].Any()) continue;

			set.Clear();
			set.Add(i);
			q.Enqueue(i);

			while (q.Any())
			{
				var p = q.Dequeue();
				foreach (var np in map[p])
				{
					if (u[np[0]] > int.MinValue)
						if (u[np[0]] == u[p] + np[1]) continue;
						else { Console.WriteLine("No"); return; }

					u[np[0]] = u[p] + np[1];
					set.Add(np[0]);
					q.Enqueue(np[0]);
				}
			}
			if (set.Max(x => u[x]) - set.Min(x => u[x]) > 1000000000) { Console.WriteLine("No"); return; }
		}
		Console.WriteLine("Yes");
	}
}