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: Runtime Error)

using System;
using System.Linq;
using System.Collections.Generic;

namespace ABC
{
    class ProgramD
    {
        struct Info
        {
            public int next;
            public int dist;
        }

        static List<Info>[] _graph;

        static void Main(string[] args)
        {
            var inputs = Console.ReadLine().Split(" ");
            var n = int.Parse(inputs[0]);
            var m = int.Parse(inputs[1]);

            _graph = new List<Info>[n];
            for (var i = 0; i < n; i++)
            {
                _graph[i] = new List<Info>();
            }

            for (var i = 0; i < m; i++)
            {
                var inputsM = Console.ReadLine().Split(" ");
                var l = int.Parse(inputsM[0]) - 1;
                var r = int.Parse(inputsM[1]) - 1;
                var d = int.Parse(inputsM[2]);

                // 辺追加
                _graph[l].Add(new Info()
                {
                    next = r,
                    dist = d,
                });
                _graph[r].Add(new Info()
                {
                    next = l,
                    dist = -d,
                });

                // 探索
                if (dfs(l, r, d, 0))
                {
                    Console.WriteLine("No");
                    return;
                }
            }

            Console.WriteLine("Yes");
        }

        // dfs
        // trueが返ったら矛盾
        static bool dfs(int b, int e, int d, int sum)
        {
            foreach (var i in _graph[b])
            {
                var next = i.next;

                var nSum = sum + i.dist;
                // 矛盾チェック
                if (next == e && d != nSum) return true;

                if (dfs(next, e, d, nSum))
                {
                    return true;
                }
            }
            return false;
        }
    }
}