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.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;

public class Main {

    public static ArrayList[] al;
    public static int[] pos;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int m = sc.nextInt();

        al = new ArrayList[n];
        pos = new int[n];

        for(int i=0; i<n; i++){
            al[i] = new ArrayList<Integer[]>();
            pos[i] = Integer.MAX_VALUE;
        }

        for(int i=0; i<m; i++){
            int l = sc.nextInt() - 1;
            int r = sc.nextInt() - 1;
            int d = sc.nextInt();
            al[l].add(new int[]{r, d});
            al[r].add(new int[]{l, -d});
        }
        sc.close();

        boolean ret = true;

        for(int i=0; i<n; i++){
            if(al[i].size() != 0){
                pos[i] = 0;
                ret = bfs(i, 0);
            }
            if(!ret) break;
        }

        if(ret){
            System.out.println("Yes");
        }else{
            System.out.println("No");
        }
    }

    public static boolean bfs(int i, int p){
        if(al[i].size() == 0) return true;
        for(int j=0; j<al[i].size(); j++){
            int[] tmp = (int[])(al[i].remove(0));
            if(pos[tmp[0]] == Integer.MAX_VALUE){
                pos[tmp[0]] = p + tmp[1];
            }else if(pos[tmp[0]] != p + tmp[1]){
                return false;
            }
            if(!bfs(tmp[0], p + tmp[1])) return false;
        }
        return true;
    }
}