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;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int n = cin.Int();
			int m = cin.Int();

			var to = new List<Edge>[n];
			for (int i = 0; i < n; i++) {
				to[i] = new List<Edge>();
			}

			for (int i = 0; i < m; i++) {
				int l = cin.Int() - 1;
				int r = cin.Int() - 1;
				long dis = cin.Long();
				to[l].Add(new Edge { To = r, D = dis });
			}

			long[] d = new long[n];
			for (int i = 0; i < n; i++) {
				d[i] = -1;
			}

			d[0] = 0;
			int index = 1;
			var q = new Queue<int>();
			q.Enqueue(0);
			while (q.Count > 0) {
				int cur = q.Dequeue();
				foreach (var next in to[cur]) {
					if (d[next.To] == -1) {
						d[next.To] = d[cur] + next.D;
						q.Enqueue(next.To);
					} else {
						if (d[cur] + next.D != d[next.To]){
							Console.WriteLine("No");
							return;
						}
					}
				}

				for (int i = index; i < n; i++) {
					index++;
					if (d[i] == -1) {
						q.Enqueue(i);
						break;
					}
				}
			}

			Console.WriteLine("Yes");
		}
	}

	public struct Edge
	{
		public int To { get; set; }
		public long D { get; set; }
	}

	public class PriorityQueue<T>
	{
		private readonly List<T> heap_;
		private readonly Comparison<T> comparison_;
		private readonly bool reverses_;

		public T Top => heap_[0];
		public int Count => heap_.Count;

		public PriorityQueue(bool reverses = false)
			: this(Comparer<T>.Default, reverses) { }

		public PriorityQueue(int capacity, bool reverses = false)
			: this(capacity, Comparer<T>.Default.Compare, reverses) { }

		public PriorityQueue(IComparer<T> comparer, bool reverses = false)
			: this(16, comparer.Compare, reverses) { }

		public PriorityQueue(Comparison<T> comparison, bool reverses = false)
			: this(16, comparison, reverses) { }

		public PriorityQueue(
			int capacity,
			Comparison<T> comparison,
			bool reverses = false)
		{
			heap_ = new List<T>(capacity);
			comparison_ = comparison;
			reverses_ = reverses;
		}

		public void Enqueue(T item)
		{
			int c = heap_.Count;
			heap_.Add(item);
			while (c > 0) {
				int p = (c - 1) >> 1;
				if (Compare(p, c) < 0) {
					Swap(p, c);
				} else {
					break;
				}

				c = p;
			}
		}

		public T Dequeue()
		{
			T ret = heap_[0];
			int n = heap_.Count - 1;

			heap_[0] = heap_[n];
			heap_.RemoveAt(n);
			for (int p = 0, c; (c = (p << 1) + 1) < n; p = c) {
				if (c != n - 1 && Compare(c + 1, c) > 0) {
					++c;
				}

				if (Compare(p, c) < 0) {
					Swap(p, c);
				} else {
					break;
				}
			}

			return ret;
		}

		public void Clear() => heap_.Clear();

		private int Compare(int x, int y)
			=> comparison_(heap_[x], heap_[y]) * (reverses_ ? -1 : 1);

		private void Swap(int x, int y)
		{
			var t = heap_[x];
			heap_[x] = heap_[y];
			heap_[y] = t;
		}
	}

	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private readonly Func<string> reader_;
		private string[] buf_;
		private int index_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}