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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace D {
    class questionD {
        static void Main(string[] args) {
            int[] NMInput = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();//2つ以上のスペース区切り入力の取得
            int N = NMInput[0];
            int M = NMInput[1];
            int[] groupNums = new int[N];
            List<List<int>> groupMembers = new List<List<int>>();
            groupMembers.Add(new List<int>());
            int[] points = new int[N];
            int nowGroup = 0;
            bool answer = true;
            for (int i = 0; i < M; i++) {
                int[] input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();//2つ以上のスペース区切り入力の取得
                int L = input[0] - 1;
                int R = input[1] - 1;
                int D = input[2];
                if (groupNums[L] == 0 && groupNums[R] == 0) {
                    nowGroup++;
                    groupNums[L] = nowGroup;
                    groupNums[R] = nowGroup;
                    List<int> newGroup = new List<int>();
                    newGroup.Add(L);
                    newGroup.Add(R);
                    groupMembers.Add(newGroup);
                    points[R] = D;
                } else if (groupNums[L] == 0 && groupNums[R] != 0) {
                    groupNums[L] = groupNums[R];
                    groupMembers[groupNums[R]].Add(L);
                    points[L] = points[R] - D;
                } else if (groupNums[L] != 0 && groupNums[R] == 0) {
                    groupNums[R] = groupNums[L];
                    groupMembers[groupNums[L]].Add(R);
                    points[R] = points[L] + D;
                } else {
                    if (groupNums[L] != groupNums[R]) {
                        int group = groupNums[R];
                        int diff = groupNums[R] - (groupNums[L] + D);
                        for (int j = 0; j < groupMembers[group].Count; j++) {
                            int RMenber = groupMembers[group][0];
                            groupNums[RMenber] = groupNums[L];
                            groupMembers[group].RemoveAt(0);
                            groupMembers[groupNums[L]].Add(RMenber);
                            points[RMenber] -= diff;
                        }
                    } else {
                        if (points[R] != points[L] + D) {
                            answer = false;
                        }
                    }
                }
            }
            // Console.Write("改行なし a = {0} b = {1} c = {2}", a, b, c)//改行なし出力
            // Console.WriteLine("改行あり a = {0} b = {1} c = {2}", a, b, c);//改行付き出力
            if (answer) {
                Console.WriteLine("Yes");
            } else {
                Console.WriteLine("No");
            }
        }
    }
}