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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dx = { 0, 1, 0, -1 };
        static readonly int[] dy = { 1, 0, -1, 0 };

        static List<List<Edge>> G = new List<List<Edge>>();
        static bool[] seen;
        static long[] dis;
        
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            var p = cin.SplitRead();

            int N = p[0];
            int M = p[1];
            if (M == 0) { Console.WriteLine("Yes");
                return;
            }


            for (var i = 0; i < N; i++) G.Add(new List<Edge>());
            seen = new bool[N];
            dis = new long[N];

            for(var i = 0; i < M; i++)
            {
                var x = cin.SplitReadL();

                int L = (int)x[0] - 1;
                int R = (int)x[1] - 1;
                long D = x[2];

                G[L].Add(new Edge(R, D));
                G[R].Add(new Edge(L, -D));
            }


            
            for(var i = 0; i < N; i++)
            {
                if (!seen[i]) Dfs(i);
            }

            Console.WriteLine(dis.Max() != SINF ? "Yes" : "No");
            
            

            //Console.Out.Flush();
        }
        struct Edge
        {
            //int _from;
            public int _to;
            public long _dist;

            public Edge(int R,long d)
            {
                _to = R;
                _dist = d;
            }
        }
        static public void Dfs(int node)
        {
            seen[node] = true;
            if (G[node].Count() == 0) { return; }
            foreach(var e in G[node])
            {
                long d = dis[node] + e._dist;
                if (seen[e._to])
                {
                    if (d != dis[e._to]) { dis[e._to] = SINF; }
                }
                else
                {
                    dis[e._to] = d;
                    Dfs(e._to);
                }
            }
            
        }
            
    }
    

    public class Scanner
    {
        public int[] SplitRead()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReadL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }

    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
    }
}