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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
using Pair = System.Tuple<int, int>;
using Edge = System.Tuple<int, int, long>;
//using Debug;
//using static System.Globalization.CultureInfo;

class Program
{
    static void Main(string[] args)
    {
        //Solve();
        WriteLine(Solve());
    }
    static int[] nm;
    static P[] ps;
    static bool[] th;
    static string Solve()
    {
        nm = Input.ar;
        var lrd = Input.ar2D(nm[1]);
        th = new bool[nm[0]];
        ps = Enumerable.Range(0, nm[0]).Select(v => new P(v)).ToArray();
        for(var i = 0; i < nm[1]; i++)
        {
            for(var j = 0; j < 2; j++)
            {
                ps[lrd[i][j] - 1].adj.Add(lrd[i][1 - j] - 1);
                ps[lrd[i][j] - 1].dist[lrd[i][1 - j] - 1] = (1 - j * 2) * lrd[i][2];
            }
        }
        for (var i = 0; i < nm[0]; i++)
            if (!th[i] && !dfs(i)) return "No";
        return "Yes";
    }
    static bool dfs(int index)
    {
        th[index] = true;
        foreach (var ad in ps[index].adj)
        {
            if (!th[ad])
            {
                ps[ad].Weight = ps[index].Weight + ps[index].dist[ad];
                if (!dfs(ad)) return false;
            }
            if (ps[ad].Weight - ps[index].Weight != ps[index].dist[ad])
                return false;
        }
        return true;
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static char[][] gred(int h) 
        => Enumerable.Repeat(0, h).Select(v => read.ToCharArray()).ToArray();
    public static int[][] ar2D(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] arL2D(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}

public class P : IComparable<P>
{
    public int index;
    public List<int> adj;
    public List<int> rev;
    public Dictionary<int, int> dist;
    public int parent;
    public long Weight { get; set; }
    public P(int index,long Weight=Input.Inf)
    {
        this.index = index;
        adj = new List<int>();
        rev = new List<int>();
        dist = new Dictionary<int, int>();
        this.Weight = Weight;
    }
    public static P[] Make(int num, int edge = 0, bool isNotDirected = true, bool isWeighted = true)
    {
        var ps = Enumerable.Range(0, num).Select(v => new P(v)).ToArray();
        for (var i = 0; i < edge; i++)
        {
            var inp = Input.ar;
            inp[0]--;
            inp[1]--;
            for (var j = 0; j <= ToInt32(isNotDirected); j++)
            {
                ps[inp[j]].adj.Add(inp[1 - j]);
                if (!isNotDirected)
                    ps[inp[1 - j]].rev.Add(inp[j]);
                if (isWeighted)
                    ps[inp[j]].dist[inp[1 - j]] = inp[2];
            }
        }
        return ps;
    }
    public override string ToString()
        => $"{index + 1} {Weight}";
    public override int GetHashCode()
        => index.GetHashCode();
    public int CompareTo(P p)
        => Weight.CompareTo(p.Weight);
}