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.Linq;
using System.Collections.Generic;
using System.IO;
 
class Program
{
    static void Solve()
    {
        var n = sc.Int();
        var m = sc.Int();

        var G = new List<Edge>[n];
        var used = new bool[n];
        var cost = new int[n];

        for (int i = 0; i < n; i++)
        {
            G[i] = new List<Edge>();
        }

        for (int i = 0; i < m; i++)
        {
            var l = sc.Int() - 1;
            var r = sc.Int() - 1;
            var d = sc.Int();

            G[l].Add(new Edge{ to = r, cost = d });
            G[r].Add(new Edge{ to = l, cost = -d });
        }

        bool ok = true;
        for (int i = 0; i < n; i++)
        {
            if (!dfs(G, i, cost[i], used, cost))
            {
                ok = false;
                break;
            }
        }
        
        if (ok)
            pr.WriteLine("Yes");
        else
            pr.WriteLine("No");
    }

    static bool dfs(List<Edge>[] G, int curr, int currCost, bool[] used, int[] cost)
    {
        if (used[curr])
            return currCost == cost[curr] ? true : false;
        
        used[curr] = true;
        cost[curr] = currCost;

        foreach (var nxt in G[curr])
            if (!dfs(G, nxt.to, currCost + nxt.cost, used, cost))
                return false;

        return true;
    }

    class Edge
    {
        public int to;
        public int cost;
    }

    static void Main(string[] args)
    {
        // pr.AutoFlush = true;
        Solve();
        pr.Flush();
    }
 
    static Scanner sc = new Scanner();
    static Printer pr = new Printer();
}
 
#region IO
class Scanner
{
    private int _i = 0; 
    private string[] line = new string[0];
 
    private T[] Enumerate<T>(int n, Func<T> f)
    {
        T[] ret = new T[n];
        for (int i = 0; i < n; i++)
            ret[i] = f();
        return ret;
    }
 
    public string Str()
    {
        if (line.Length <= _i)
        {
            line = Console.ReadLine().Split(' ');
            _i = 0;
        }
 
        return line[_i++];
    }
 
    public int Int() => int.Parse(Str());
    public long Long() => long.Parse(Str());
    public double Double() => double.Parse(Str());
    public int[] Int(int n) => Enumerate(n, Int);
    public long[] Long(int n) => Enumerate(n, Long);
    public double[] Double(int n) => Enumerate(n, Double);
    public string[] Str(int n) => Enumerate(n, Str);
}
 
class Printer : StreamWriter
{
    public Printer() : base(Console.OpenStandardOutput())
    {
        AutoFlush = false;
    }
}
#endregion