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: Time Limit Exceeded)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map.Entry;

public class Main
{

  static Integer[] x = new Integer[114514];
  static int v = 1;
  static boolean z = false;
  static int next = 1;

  public static void main(String[] args) throws IOException
  {
    BufferedReader r = new BufferedReader(new InputStreamReader(System.in), 1);
    String s = r.readLine();
    String[] sl = s.split("[\\s]+");

    int n = Integer.parseInt(sl[0]);
    int m = Integer.parseInt(sl[1]);

    HashMap<Integer, HashMap<Integer, Integer>> map = new HashMap<Integer, HashMap<Integer, Integer>>();

    for(int i = 0; i <= n; i++)
    {
      map.put(i, new HashMap<Integer, Integer>());
    }

    for(int i = 0; i < m; i++)
    {
      s = r.readLine();
      sl = s.split("[\\s]+");
      int left = Integer.parseInt(sl[0]);
      int right = Integer.parseInt(sl[1]);
      int dist = Integer.parseInt(sl[2]);

      HashMap<Integer, Integer> h = map.get(left);
      h.put(right, dist);
      h = map.get(right);
      h.put(left, - dist);
    }

    for(int i = 1; i <= n; i++)
    {
      x[i] = null;
    }
    x[1] = 0;

    while(v < n)
    {
      z = false;

      sub(map, next);

      if(!z)
      {
        for(int i = 1; i <= n; i++)
        {
          if(x[i] == null)
          {
            x[i] = 0;
            v++;
            next = i;
            break;
          }
        }
      }
    }


    for(int i = 1; i <= n; i++)
    {
      HashMap<Integer, Integer> h = map.get(i);
      for(Entry<Integer, Integer> e : h.entrySet())
      {
        if(x[e.getKey()] != x[i] + e.getValue())
        {
          System.out.println("No");
          System.exit(0);
        }
      }
    }

    System.out.println("Yes");

  }

  public static void sub(HashMap<Integer, HashMap<Integer, Integer>> map, int i)
  {
    HashMap<Integer, Integer> h = map.get(i);
    HashSet<Integer> a = new HashSet<Integer>();
    for(Entry<Integer, Integer> e : h.entrySet())
    {
      if(x[e.getKey()] == null)
      {
        x[e.getKey()] = x[i] + e.getValue();
        next = i;
        a.add(e.getKey());
        v++;
        z = true;
      }
      else
      {
        if(x[e.getKey()] != x[i] + e.getValue())
        {
          System.out.println("No");
          System.exit(0);
        }
      }
    }

    for(Integer n : a)
    {
      sub(map, n);
    }
  }
}