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;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Text;
using System.Text.RegularExpressions;
using System.Linq;
using System.IO;
using System.Diagnostics;

class Scanner
{
    private readonly char Separator = ' ';
    private int Index = 0;
    private string[] Line = new string[0];
    public string Next()
    {
        if (Index >= Line.Length)
        {
            Line = Console.ReadLine().Split(Separator);
            Index = 0;
        }
        var ret = Line[Index];
        Index++;
        return ret;
    }

    public int NextInt()
    {
        return int.Parse(Next());
    }

    private long NextLong()
    {
        return long.Parse(Next());
    }
}

struct S
{
    public int R, D;
    public S(int r, int d)
    {
        R = r;
        D = d;
    }
}

class Program
{
    private int N;
    private int M;
    private int[] L, R, D;
    private void Scan()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        M = sc.NextInt();
        L = new int[M];
        R = new int[M];
        D = new int[M];
        for (int i = 0; i < M; i++)
        {
            L[i] = sc.NextInt() - 1;
            R[i] = sc.NextInt() - 1;
            D[i] = sc.NextInt();
        }
    }

    public void Solve()
    {
        Scan();
        var list = new List<S>[N];
        for (int i = 0; i < N; i++)
        {
            list[i] = new List<S>();
        }
        for (int i = 0; i < M; i++)
        {
            list[L[i]].Add(new S(R[i], D[i]));
            list[R[i]].Add(new S(L[i], -D[i]));
        }
        var pos = (new long[N]).Select(i => long.MinValue).ToArray();
        pos[0] = 0;
        for (int i = 0; i < N; i++)
        {
            foreach (var s in list[i])
            {
                if (pos[s.R] == long.MinValue)
                {
                    pos[s.R] = pos[i] + s.D;
                }
                else
                {
                    if (pos[s.R] != pos[i] + s.D)
                    {
                        Console.WriteLine("No");
                        return;
                    }
                }
            }
        }
        Console.WriteLine("Yes");
    }

    static public void Main()
    {
        new Program().Solve();
    }
}