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 System.IO;
using System.Text;
using System.Text.RegularExpressions;
using System.Globalization;
using System.Diagnostics;
using static System.Console;
//using System.Numerics;
//using static System.Math;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;

    List<int>[] G;
    int N, M;
    int[] L, R, D;
    bool[] used_n;
    bool[] used_m;
    Queue<int> Q;
    int[] A;

    bool ans = true;
    void solve()
    {
        N = cin.nextint;
        M = cin.nextint;
        Q = new Queue<int>();
        used_n = new bool[N];
        used_m = new bool[M];
        G = Enumerable.Range(0, N).Select(i => new List<int>()).ToArray();
        L = new int[M];
        R = new int[M];
        D = new int[M];
        for (int i = 0; i < M; i++)
        {
            L[i] = cin.nextint - 1;
            R[i] = cin.nextint - 1;
            D[i] = cin.nextint;

            G[L[i]].Add(i);
            G[R[i]].Add(i);
        }
        A = Enumerable.Repeat(int.MaxValue, N).ToArray(); //iが位置kにいる
        for (int i = 0; i < N; i++)
        {
            if (used_n[i]) continue;
       
            A[i] = 0;
            Q.Enqueue(i);

            while (Q.Any())
            {
                int d = Q.Dequeue();
                if (used_n[d]) continue;
                calc(d);
                used_n[d] = true;
            }

        }
        WriteLine(ans ? "Yes" : "No");
    }
    void calc(int u)
    {
        foreach (var v in G[u])
        {
            if (used_m[v]) continue;
            used_m[v] = true;
            if (L[v] == u)
            {
                if (A[R[v]] != int.MaxValue)
                {
                    if (A[R[v]] != A[u] + D[v])
                    {
                        ans = false;
                    }
                }
                else
                {
                    A[R[v]] = A[u] + D[v];
                    Q.Enqueue(R[v]);
                }
            }
            else
            {
                if (A[L[v]] != int.MaxValue)
                {
                    if (A[L[v]] != A[u] - D[v])
                    {
                        ans = false;
                    }
                }
                else
                {
                    A[L[v]] = A[u] - D[v];
                    Q.Enqueue(L[v]);
                }
            }
        }
    }
}



class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
}