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: Wrong Answer)

import java.util.*;
import java.io.*;
class Main
{

	static Scanner  s=new Scanner(System.in);
	static int n , queries , left ,right ,dist , flag , sum ,chk  ;
	static HashMap<String,Integer> hmap = new HashMap<>();
	static int[] visit ;
	static Stack<Integer> stk ,l,r,d;
	static Queue<Integer> queue ;
	public static void init()
	{
		sum =0 ;
		visit = new int[n+1];
		// stk = new Stack<>();
		queue = new LinkedList<>();
	}

	public static void start()
	{
		l = new Stack<>();
		r = new Stack<>();
		d = new Stack<>();
	}

	public static void dfs()
	{
		
		abc:while(!l.isEmpty())
		{
			int i = l.pop();
			if(visit[i]==0)
			{
				visit[i]=1;
				for(int j=1;j<=n;j++)
				{
					if(hmap.containsKey(i+" "+j) && visit[j]==0)
					{
					queue.add(j);				
					// visit[j] = 1;
					}
				}
			}
			// System.out.println("queue = "+queue);
			while(!queue.isEmpty())
			{
				int q = queue.remove();
				// System.out.println("q = "+q);
				visit[q] =1;
				sum = hmap.get(i+" "+q);
				// System.out.println("sum = "+sum);
				for(int j=1;j<=n;j++)
				{
					if(hmap.containsKey(q+" "+j) && visit[j]==0)
					{
						sum+=hmap.get(q+" "+j);
						if(hmap.containsKey(i+" "+j))
						{
							if( Math.abs(hmap.get(i+" "+j)) != Math.abs(sum))
							{
								chk = 1 ;
								break abc;
							}
						}	
						else
						{
							String line = i+" "+j;
							hmap.put(line,sum);
						}
					}
				}
			}



		}
		
	}



	public static void main(String[] args)
	{
		n = s.nextInt();
		queries = s.nextInt();
		start();


		
		for(int i =0; i<queries	;i++)
		{
			int lval = s.nextInt();
			int rval = s.nextInt();
			int dval = s.nextInt();
				
			l.push(lval);
			r.push(rval);
			d.push(dval);


			String line1 = lval+" "+rval;
			String line2 = rval+" "+lval;
			if(hmap.containsKey(line1))
			{
				Integer p = hmap.get(line1);
				int chk = Math.abs((int)p);
				if(chk!=dval)
					flag = 1;
			}
			
			if(hmap.containsKey(line2))
			{
				Integer p = hmap.get(line2);
				int chk = Math.abs((int)p);
				if(chk!=dval)
					flag = 1;
			}
			
			if(!hmap.containsKey(line1))
			{
				hmap.put(line1,dval);
			}
			
			if(!hmap.containsKey(line2))
			{
				hmap.put(line2,-dval);
			}
			
		}

		if(flag == 0)
		{
			init();
			dfs();
			if(chk == 0)
				System.out.println("Yes");
			else
				System.out.println("No");
		}
		else
			System.out.println("No");

	}

	
}