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: Time Limit Exceeded)

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

namespace Competitive
{
    internal class Solution
    {
        public int N, M;
        public int[] L, R;
        public long[] D;
        public Graph G;

        public void Run()
        {
            // インプット
            {
                var line = Input.ReadIntArray();
                N = line[0];
                M = line[1];
            }

            // グラフの構築
            G = new Graph(N);

            for(int i = 0; i < M; i++)
            {
                var line = Input.ReadIntArray();
                int l = line[0];
                int r = line[1];
                int d = line[2];
                l--;
                r--;
                var e1 = new Edge(l, r, d);
                var e2 = new Edge(r, l, -d);
                e1.ReverseEdge = e2;
                e2.ReverseEdge = e1;
                G.Nodes[l].Edges.Add(e1);
                G.Nodes[r].Edges.Add(e2);
            }

            bool ret = true;
            for (int i = 0; i < N; i++)
            {
                G[i].Dist = 0;
                bool success = DFS(new Edge(i, i, 0));
                if (!success)
                {
                    ret = false;
                    break;
                }
            }

            Console.WriteLine(ret ? "Yes" : "No");
        }

        public bool DFS(Edge e)
        {
            Node n = G[e.To];
            long fromDist = G[e.From].Dist;

            e.Used = true;
            if(e.ReverseEdge != null) e.ReverseEdge.Used = true;

            // 距離のセット
            if (n.Dist == long.MaxValue)
            {
                n.Dist = fromDist + e.D;
            }
            else
            {
                if (n.Dist != fromDist + e.D)
                {
                    return false;
                }
            }

            // 次のステップ
            foreach (var ee in n.Edges)
            {
                if (!ee.Used)
                {
                    bool success = DFS(ee);
                    if (!success) return false;
                }
            }

            return true;
        }
    }

    // libs ----------
    // 通常はIComparableのみが必要
    class EdgeData : IComparable<EdgeData>, IComparable
    {
        public int Dist;
        public Edge Edge;
        public EdgeData(int dist, Edge edge)
        {
            Dist = dist;
            Edge = edge;
        }

        public int CompareTo(EdgeData other)
        {
            return Dist.CompareTo(other.Dist);
        }

        public int CompareTo(object obj)
        {
            if (obj == null) return 1;
            if (GetType() != obj.GetType()) throw new ArgumentException();
            return CompareTo((EdgeData)obj);
        }
    }

    internal class Graph
    {
        public List<Node> Nodes;

        public Node this[int i]
        {
            set { Nodes[i] = value; }
            get { return Nodes[i]; }
        }

        public Graph(int N)
        {
            Nodes = new List<Node>();
            for (int i = 0; i < N; i++)
            {
                Nodes.Add(new Node(i));
            }
        }

    }

    internal class Node
    {
        public List<Edge> Edges;
        public long Dist;
        public int No;

        public Node(int no)
        {
            this.No = no;
            Dist = long.MaxValue;
            Edges = new List<Edge>();
        }
    }

    internal class Edge
    {
        public int From;
        public int To;
        public int D;
        public bool Used;
        public Edge ReverseEdge;

        public Edge(int fr, int to, int d = 0)
        {
            From = fr;
            To = to;
            D = d;
            Used = false;
        }

    }

    // common ----------

    internal static class Input
    {
        public static string ReadString()
        {
            string line = Console.ReadLine();
            return line;
        }

        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();
        }

        public static long ReadLong()
        {
            string line = Console.ReadLine();
            return long.Parse(line);
        }

        public static long[] ReadLongArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }

    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}