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;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class D
{
	public static void Main()
	{
		int N = GetInt();
		int M = GetInt();
		int[] L = new int[M];
		int[] R = new int[M];
		long[] D = new long[M];
		for(int i = 0; i < M; i++)
		{
			L[i] = GetInt();
			R[i] = GetInt();
			D[i] = GetLong();
		}

		UnionFind uf = new UnionFind(N+1);
		for(int i = 0; i < M; i++)
		{
			if(uf.IsSame(L[i], R[i]))
			{
				long d = uf.Diff(L[i], R[i]);
				if(d != D[i])
				{
					Console.WriteLine("No");
					return;
				}
			}
			else
				uf.Merge(L[i], R[i], D[i]);
		}
		Console.WriteLine("Yes");
	}
}


// https://qiita.com/drken/items/cce6fc5c579051e64fab (2019/05/26)
public class UnionFind
{
	private int[] par = null;
	private int[] rank = null;
	private long[] diffWeight = null;
	
	public UnionFind(int n)
	{
		par = new int[n];
		rank = new int[n];
		diffWeight = new long[n];
		for(int i = 0; i < n; i++)
		{
			par[i] = i;
			rank[i] = 0;
			diffWeight[i] = 0;
		}
	}

	public bool IsSame(int x, int y)
	{
		return (root(x) == root(y));
	}

	private int root(int x)
	{
		if(par[x] == x)
			return x;

		int r = root(par[x]);
		diffWeight[x] += diffWeight[par[x]];
		par[x] = r;
		return r;
	}
	
	public bool Merge(int x, int y, long w)
	{
		long wp = w + weight(x) - weight(y);
		int rx = root(x);
		int ry = root(y);
		if(rx == ry)
			return false;
		
		if(rank[rx] < rank[ry])
		{
			int tmp = rx;
			rx = ry;
			ry = tmp;
			wp = -wp;
		}
		else if(rank[rx] == rank[ry])
			rank[rx]++;

		par[ry] = rx;
		diffWeight[ry] = wp;
		return true;
	}

	public long Diff(int x, int y)
	{
		return weight(y) - weight(x);
	}

	private long weight(int x)
	{
		root(x);
		return diffWeight[x];
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}