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;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

public static class TemplateExtension
{
    public static X[] MakeArray<X>(this int count, Func<int, X> func)
    {
        var xs = new X[count];
        for (var i = 0; i < count; i++)
        {
            xs[i] = func(i);
        }
        return xs;
    }

    public static int[] Range(this int count, int start = 0)
    {
        return count.MakeArray(i => i + start);
    }

    public static string Intercalate<X>(this IEnumerable<X> @this, string separator)
    {
        return string.Join(separator, @this);
    }

    public sealed class ValueIndexPair<T>
        : Tuple<T, int>
    {
        public T Value { get { return Item1; } }
        public int Index { get { return Item2; } }

        public ValueIndexPair(T value, int index)
            : base(value, index)
        {
        }
    }

    public static IEnumerable<ValueIndexPair<X>> Indexed<X>(this IEnumerable<X> @this)
    {
        var i = 0;
        foreach (var x in @this)
        {
            yield return new ValueIndexPair<X>(x, i);
            i++;
        }
    }
}

public sealed class Scanner
{
    private readonly TextReader _reader;
    private readonly StringBuilder _sb = new StringBuilder();

    /// <summary>
    /// Reads next word separated by spaces.
    /// </summary>
    public string Word()
    {
        _sb.Clear();

        while (true)
        {
            var r = _reader.Read();

            if (r == ' ' || r == '\r' || r == '\n')
            {
                if (r == '\r' && _reader.Peek() == '\n')
                {
                    _reader.Read();
                }

                // Ignore leading spaces.
                if (_sb.Length == 0) continue;

                break;
            }
            else if (r == -1)
            {
                break;
            }
            else
            {
                _sb.Append((char)r);
            }
        }

        return _sb.ToString();
    }

    /// <summary>
    /// Reads next word as <see cref="int"/>.
    /// </summary>
    public int N()
    {
        return int.Parse(Word().Trim());
    }

    /// <summary>
    /// Reads next word as <see cref="long"/>.
    /// </summary>
    public long L()
    {
        return long.Parse(Word());
    }

    /// <summary>
    /// Reads next word as <see cref="double"/>.
    /// </summary>
    public double F()
    {
        return double.Parse(Word());
    }

    /// <summary>
    /// Reads next line and splits it by spaces.
    /// </summary>
    public X[] Words<X>(Func<string, X> func)
    {
        return _reader.ReadLine().Split(' ').Select(func).ToArray();
    }

    public Scanner(TextReader reader)
    {
        _reader = reader;
    }
}

public partial class Program
{
    private readonly TextReader _input;
    private readonly TextWriter _output;
    private readonly Scanner _scanner;

    private void WriteLine(int value)
    {
        _output.WriteLine(value);
    }

    private void WriteLine(long value)
    {
        _output.WriteLine(value);
    }

    private void WriteLine(double value)
    {
        _output.WriteLine(value);
    }

    private void WriteLine(char value)
    {
        _output.WriteLine(value);
    }

    private void WriteLine(string value)
    {
        _output.WriteLine(value);
    }

    public Program(TextReader input, TextWriter output)
    {
        _input = input;
        _output = output;
        _scanner = new Scanner(input);
    }

    public static void Main(string[] args)
    {
        new Program(Console.In, Console.Out).EntryPoint();
    }
}

// i -> e: i が分かったら x_V = x_i + D;
public struct Edge
{
    public int V;
    public long D;
}

public sealed partial class Program
{
    int N, M;

    List<Edge>[] Q;
    long?[] X;
    HashSet<int> unsolveds;

    bool SolveRec(int i)
    {
        foreach (var e in Q[i])
        {
            Debug.Assert(X[i].HasValue);

            if (X[e.V].HasValue)
            {
                if (X[e.V] != X[i] + e.D)
                {
                    return false;
                }
            }
            else
            {
                X[e.V] = X[i] + e.D;
                unsolveds.Remove(e.V);

                if (!SolveRec(e.V)) return false;
            }
        }

        return true;
    }

    bool SolveNext()
    {
        var u = unsolveds.First();
        Debug.Assert(!X[u].HasValue);

        X[u] = 0;
        unsolveds.Remove(u);

        return SolveRec(u);
    }

    bool SolveAll()
    {
        unsolveds = new HashSet<int>();

        X[0] = 0;
        if (!SolveRec(0)) return false;

        for (var i = 0; i < N; i++)
        {
            if (!X[i].HasValue)
            {
                unsolveds.Add(i);
            }
        }

        while (unsolveds.Count > 0)
        {
            if (!SolveNext()) return false;
        }

        return true;
    }

    public void EntryPoint()
    {
        var I = _scanner;
        var ok = true;

        N = I.N();
        M = I.N();

        Q = N.MakeArray(i => new List<Edge>());
        X = new long?[N];

        for (var q = 0; q < M; q++)
        {
            var l = I.N() - 1;
            var r = I.N() - 1;
            var d = I.L();

            Q[l].Add(new Edge() { V = r, D = d });
            Q[r].Add(new Edge() { V = l, D = -d });
        }

        ok = SolveAll();

        WriteLine(ok ? "Yes" : "No");
    }
}