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 BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using System.Text;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var N = consoleReader.Int;
            var M = consoleReader.Int;
            var gb = new GraphBuilder(N);
            foreach (var cr in consoleReader.Repeat(M))
                gb.Add(cr.Int - 1, cr.Int - 1, cr.Int);
            graph = gb.ToArray();
            rootLen = new long[N];

            for (int i = 0; i < N; i++)
            {
                if (rootLen[i] != 0) continue;
                if (!CalcImpl(i, 0)) return "No";
            }

            return "Yes";
        }
        bool CalcImpl(int index, long len)
        {
            if (rootLen[index] != 0)
                return rootLen[index] == len;
            rootLen[index] = len;
            foreach (var child in graph[index].children)
            {
                if(!CalcImpl(child.to, child.length + len))
                    return false;
            }
            return true;
        }

        Node[] graph;
        long[] rootLen;

        class GraphBuilder
        {
            private List<Next>[] roots;
            private List<Next>[] children;
            public GraphBuilder(int count)
            {
                this.roots = new List<Next>[count];
                this.children = new List<Next>[count];
                for (int i = 0; i < count; i++)
                {
                    this.roots[i] = new List<Next>();
                    this.children[i] = new List<Next>();
                }
            }
            public GraphBuilder(int count, IEnumerable<int[]> arrays) : this(count)
            {
                foreach (var item in arrays)
                    this.Add(item[0], item[1], item[2]);
            }
            public void Add(int from, int to, int length)
            {
                children[from].Add(new Next { to = to, length = length });
                roots[to].Add(new Next { to = from, length = length });
            }
            public Node[] ToArray() =>
                Enumerable
                .Zip(roots, children, (r, c) => Tuple.Create(r, c))
                .Select((t, i) => new Node(i, t.Item1.ToArray(), t.Item2.ToArray()))
                .ToArray();
        }
        public struct Next
        {
            public int to;
            public int length;
        }
        public class Node : IEquatable<Node>
        {
            public Node(int i, Next[] roots, Next[] children)
            {
                this.index = i;
                this.roots = roots;
                this.children = children;
            }
            public int index;
            public Next[] roots;
            public Next[] children;

            public override bool Equals(object obj)
            {
                if (obj is Node)
                    return this.Equals((Node)obj);
                else
                    return false;
            }
            public bool Equals(Node other) => this.index == other.index;
            public override int GetHashCode() => this.index;
        }

        #region いつもの
#pragma warning disable
        private ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    }
    public class ConsoleReader
    {
        private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries);
        private string[] line = Array.Empty<string>();
        private int linePosition;
        private TextReader textReader;
        public ConsoleReader(TextReader tr) { textReader = tr; }
        public int Int => int.Parse(String);
        public long Long => long.Parse(String);
        public double Double => double.Parse(String);
        public string String
        {
            get
            {
                if (linePosition >= line.Length)
                {
                    linePosition = 0;
                    line = ReadLineSplit();
                }
                return line[linePosition++];
            }
        }
        public class SplitLine
        {
            private string[] splited;
            public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); }
            public int[] Int => String.Select(x => int.Parse(x)).ToArray();
            public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray();
            public long[] Long => String.Select(x => long.Parse(x)).ToArray();
            public double[] Double => String.Select(x => double.Parse(x)).ToArray();
            public string[] String => splited;
        }
        public SplitLine Split => new SplitLine(this);
        public class RepeatReader : IEnumerable<ConsoleReader>
        {
            ConsoleReader cr; int count;
            public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; }
            public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator();
            System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator();

            public IEnumerable<string> String => this.Select(cr => cr.String);
            public IEnumerable<int> Int => this.Select(cr => cr.Int);
            public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1);
            public IEnumerable<long> Long => this.Select(cr => cr.Long);
            public IEnumerable<double> Double => this.Select(cr => cr.Double);
        }
        public RepeatReader Repeat(int count) => new RepeatReader(this, count);
    }
    #endregion
}