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.IO;
using System.Linq;

namespace D
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var NM = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var N = NM[0];
            var M = NM[1];
            var LRD = new Info[M];
            var min = 0;
            for (var i = 0; i < M; i++)
            {
                var lrd = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
                var l = lrd[0] - 1;
                var r = lrd[1] - 1;
                var d = lrd[2];
                if (l > r)
                {
                    var tmp = l;
                    l = r;
                    r = tmp;
                    d = -d;
                }
                LRD[i] = new Info { L = l, R = r, D = d };
            }
            if (M == 0)
            {
                Console.WriteLine("Yes");
                return;
            }
            LRD = LRD.OrderBy(x => x.L).ThenBy(x => x.R).ToArray();
            var points = Enumerable.Repeat(0, N).ToArray();
            points[LRD[0].L] = min;
            var checker = new bool[N];
            checker[LRD[0].L] = true;
            var answer = true;
            foreach (var info in LRD)
            {
                if (!checker[info.R])
                {
                    points[info.R] = points[info.L] + info.D;
                    min = Math.Min(min, points[info.R]);
                    checker[info.R] = true;
                }
                else
                {
                    if (points[info.R] != points[info.L] + info.D)
                    {
                        answer = false;
                        break;
                    }
                }
            }
            foreach (var point in points)
            {
                var p = point - min;
                if (p > (int)1e9)
                {
                    answer = false;
                    break;
                }
            }

            Console.WriteLine(answer ? "Yes" : "No");
        }

        public class Info
        {
            public int L { get; set; }
            public int R { get; set; }
            public int D { get; set; }
        }
    }
}