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 System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using Debug;
//using static System.Globalization.CultureInfo;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
        Solve();
        //WriteLine(Solve());
    }
    public class WeightedUnionFind
    {
        private int _num;
        private int[] _parent, _size, _rank;
        private long[] _dif;
        public WeightedUnionFind(int num)
        {
            _num = num;
            _parent = new int[num]; _size = new int[num]; _rank = new int[num];_dif=new long[num];
            for (var i = 0; i < num; i++) { _parent[i] = i; _size[i] = 1; }
        }
        private int Find(int i)
        {
            if (_parent[i] == i) return i;
            var r = Find(_parent[i]);
            _dif[i] += _dif[_parent[i]];
            return _parent[i] = r;
        }
        private long Weight(int i) { Find(i);return _dif[i]; }
        public long Dif(int v1, int v2)
            => Weight(v2) - Weight(v1);
        public int Parent(int i)
            => Find(i);
        public int Size(int i)
            => _size[Find(i)];
        public bool Union(int v1, int v2,long weight)
        {
            weight += Weight(v1);weight -= Weight(v2);
            v1 = Find(v1); v2 = Find(v2);
            if (v1 == v2) return false;
            _num--;
            if (_rank[v1] > _rank[v2])
            {
                _parent[v2] = v1;
                _size[v1] += _size[v2];
                _dif[v2] = weight;
            }
            else
            {
                _parent[v1] = v2;
                _size[v2] += _size[v1];
                _dif[v1] = -weight;
                if (_rank[v1] == _rank[v2])
                    _rank[v2]++;
            }
            return true;
        }
        public bool IsSame(int v1, int v2)
            => Find(v1) == Find(v2);
    }
    static void Solve()
    {
        var nm = Input.ar;
        var uf = new WeightedUnionFind(nm[0]);
        for (var i = 0; i < nm[1]; i++)
        {
            var lrd = Input.ar;
            lrd[0]--;lrd[1]--;
            if (uf.IsSame(lrd[0], lrd[1]))
            {
                if (uf.Dif(lrd[0], lrd[1]) != lrd[2])
                {
                    WriteLine("No"); return;
                }
            }
            else uf.Union(lrd[0], lrd[1], lrd[2]);
        }WriteLine("Yes");
    }
}

public class Input
{
    public static string read => ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public  static int num => ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public  static long numL => ToInt64(read);
    public static char[][] gred(int h) 
        => Enumerable.Repeat(0, h).Select(_ => read.ToCharArray()).ToArray();
    public static int[][] ar2D(int num)
        => Enumerable.Repeat(0, num).Select(_ => ar).ToArray();
    public static long[][] arL2D(int num)
        => Enumerable.Repeat(0, num).Select(_ => arL).ToArray();
    public static T getValue<T>(string g)
    {
        var t = typeof(T);
        if (t == typeof(int))
            return (T)(object)int.Parse(g);
        if (t == typeof(long))
            return (T)(object)long.Parse(g);
        if (t == typeof(string))
            return (T)(object)g;
        if (t == typeof(char))
            return (T)(object)char.Parse(g);
        if (t == typeof(double))
            return (T)(object)double.Parse(g);
        if (t == typeof(bool))
            return (T)(object)bool.Parse(g);
        return default(T);
    }
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public  const string alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}