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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO.IsolatedStorage;
using System.Linq;

namespace AtCoder.D
{
    public class Program
    {
        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var (N, M) = Read2Longs();

            // なんでもあり
            if (M == 0) return "Yes";

            var infos = new List<Info>();
            for (int i = 0; i < M; i++)
            {
                var (l, r, d) = Read3Longs();
                infos.Add(new Info
                {
                    L = l - 1,//インデックス変換
                    R = r - 1,//インデックス変換
                    D = d,
                });
            }

            // TODO UnionFindTreeの前処理を行う

            var people = new PersonInfo[N];
            // すべての基準となる絶対原点のインデックス
            var firstOrigine = -1;
            // 原点となっている人間の絶対座標
            var originePersonAbsolutePoints = Enumerable.Repeat(-1, (int)N).ToArray();
            foreach (var info in infos)
            {
                var l = people[info.L];
                var r = people[info.R];
                if (l == null && r == null)
                {
                    // 新たに情報追加 ※Lを原点とする
                    people[info.L] = new PersonInfo { OriginIndex = (int)info.L, RelativePosition = 0, };
                    people[info.R] = new PersonInfo { OriginIndex = (int)info.L, RelativePosition = (int)info.D, };

                    if (firstOrigine == -1)
                    {
                        firstOrigine = (int)info.L;
                        originePersonAbsolutePoints[firstOrigine] = 0;
                    }
                }
                else if (l != null && r == null)
                {
                    people[info.R] = new PersonInfo
                    {
                        OriginIndex = l.OriginIndex,
                        RelativePosition = l.RelativePosition + (int)info.D,
                    };
                }
                else if (l == null && r != null)
                {
                    people[info.L] = new PersonInfo
                    {
                        OriginIndex = r.OriginIndex,
                        RelativePosition = r.RelativePosition - (int)info.D,
                    };
                }
                else
                {
                    // 独立情報の場合、原点情報を更新する
                    if (l.OriginIndex != r.OriginIndex)
                    {
                        if (originePersonAbsolutePoints[r.OriginIndex] == -1)
                        {
                            originePersonAbsolutePoints[r.OriginIndex] = originePersonAbsolutePoints[l.OriginIndex] + (int)info.D - r.RelativePosition;
                        }
                        else if (originePersonAbsolutePoints[l.OriginIndex] == -1)
                        {
                            originePersonAbsolutePoints[l.OriginIndex] = originePersonAbsolutePoints[r.OriginIndex] - (int)info.D + l.RelativePosition;
                        }
                    }

                    // 原点を考慮して判定処理
                    var absoL = l.RelativePosition + originePersonAbsolutePoints[l.OriginIndex];
                    var absoR = r.RelativePosition + originePersonAbsolutePoints[r.OriginIndex];
                    if (info.D != absoR - absoL)
                    {
                        return "No";
                    }
                }
            }

            return "Yes";
        }

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

        class PersonInfo
        {
            public int OriginIndex { get; set; }
            public int RelativePosition { get; set; }
        }
        class OriginePerson
        {
            public int AbsolutePosition { get; set; }
        }

        #region Console.Read

        public static string ReadText() { return Console.ReadLine(); }
        public static List<string> ReadTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long ReadLong() { return long.Parse(Console.ReadLine()); }
        public static (long, long) Read2Longs() { var ls = ReadLongs(); return (ls[0], ls[1]); }
        public static (long, long, long) Read3Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2]); }
        public static (long, long, long, long) Read4Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3]); }
        public static (long, long, long, long, long) Read5Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3], ls[4]); }
        public static List<long> ReadLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }

        #endregion
    }
}