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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;

public class Main{
	public static void main(String[] args)
	{
		
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		
		Map<Integer,ArrayList> infoMap = new HashMap<Integer,ArrayList>();
		Tuple ts = null;
		Tuple td = null;
		for(int i=0;i<m;i++)
		{
			int a,b,c;
			a = sc.nextInt();
			b = sc.nextInt();
			c = sc.nextInt();
			if(!infoMap.containsKey(a))
				infoMap.put(a,new ArrayList<Tuple>());
			if(!infoMap.containsKey(b))
				infoMap.put(b,new ArrayList<Tuple>());
			ts = new Tuple(a,b,c);
			td = new Tuple(b,a,-c);
			infoMap.get(a).add(ts);
			infoMap.get(b).add(td);
		}
		
		
		Set<Integer> visited = new HashSet<Integer>();
		Deque<Integer> frontier = new LinkedList<Integer>();
		long[] distance=null;
		
		
		for(int j=1;j<=n;j++)
		{	
			if(visited.contains(j))
				continue;
			else{
				if(infoMap.get(j)!=null){
					distance = new long[n];
					frontier.addFirst(j);
				}
					
			}
			while(!frontier.isEmpty())
			{
				int toVisit = frontier.removeFirst();
				//System.out.print(toVisit+",");
				
					for(int i=0; i<infoMap.get(toVisit).size();i++)
					{	
						Tuple tmp = (Tuple)(infoMap.get(toVisit).get(i));
						if(!visited.contains(toVisit))
						{
							frontier.addFirst(tmp.dest);
							if(distance[tmp.dest-1]==0)
							{
								distance[tmp.dest-1]=tmp.cost+distance[tmp.source-1];
							}
							else if(distance[tmp.dest-1]!=tmp.cost+distance[tmp.source-1])
							{
								System.out.println("No");
								System.exit(1);
							}
							
						}
							
					}
					visited.add(toVisit);
			}
			
			
			
		}
		
		System.out.println("Yes");
	}
	
}
class Tuple
{
	public int source;
	public int dest;
	public int cost;
	public Tuple(int s,int d,int c)
	{
		source = s;
		dest = d;
		cost = c;
	}
	public String tString()
	{
		return "("+source+","+dest+","+cost+")";
	}
}