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.Collections.Generic;
using static Assistant.Input;
using static Assistant.Debug;
using System.Linq;
using Assistant;

namespace ABC087D_2
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ReadInt;
            var M = ReadInt;

            List<Edge>[] edges = new List<Edge>[N].Select(x => new List<Edge>()).ToArray();
            for (int i = 0; i < M; i++)
            {
                var L = ReadInt - 1;
                var R = ReadInt - 1;
                var D = ReadInt;
                edges[L].Add(new Edge() { from = L, to = R, cost = D });
                edges[R].Add(new Edge() { from = R, to = L, cost = -D });
            }

            int[] position = new int[N];
            bool[] accessed = new bool[N];
            for (int i = 0; i < N; i++) // スタート頂点
            {
                if (accessed[i]) continue;
                accessed[i] = true;

                Queue<int> que = new Queue<int>();
                que.Enqueue(i);
                while (que.Count > 0)
                {
                    int now = que.Dequeue();

                    foreach (var e in edges[now])
                    {
                        if (accessed[e.to] && position[e.to] != position[now] + e.cost)
                        {
                            Console.WriteLine("No");
                            return;
                        }
                        if (accessed[e.to]) continue;

                        position[e.to] = position[now] + e.cost;
                        que.Enqueue(e.to);
                        accessed[e.to] = true;
                    }
                }
            }

            Console.WriteLine("Yes");
        }

        struct Edge
        {
            public int from;
            public int to;
            public int cost;
        }
    }


}

namespace Assistant
{
    static class Input
    {
        static List<string> line = new List<string>();
        static int index = 0;
        static String ReadNext()
        {
            if (line.Count <= index) line.AddRange(Console.ReadLine().Split());
            return line[index++];
        }
        public static int ReadInt => int.Parse(ReadNext());
        public static long ReadLong => long.Parse(ReadNext());
        public static int[] ReadInts => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] ReadLongs => Console.ReadLine().Split().Select(long.Parse).ToArray();
    }

    static class Debug
    {
        static public void Draw2D(int[,] map, int mode = 1)
        {
#if DEBUG
            int W = map.GetLength(0);
            int H = map.GetLength(1);

            int[,] map2 = new int[W + 1, H + 1];
            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (i == 0 && j == 0) map2[i, j] = 0;
                    else if (i == 0) map2[i, j] = j - 1;
                    else if (j == 0) map2[i, j] = i - 1;
                    else map2[i, j] = map[i - 1, j - 1];
                }
            }

            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (mode == 0) Console.Write(map2[i, j] % 10);
                    if (mode == 1) Console.Write(map2[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
#endif
        }

        public static void Draw1D(int[] array, int mode = 0)
        {
#if DEBUG
            Console.WriteLine(string.Join(" ", array));
#endif
        }
    }
}