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.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;

public class Main implements Runnable {

    private static Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        new Thread(null, new Main(), "", 128 * 1024 * 1024).start();
    }

    public void run() {
        int N = sc.nextInt(), M = sc.nextInt();
        int[] L = new int[M], R = new int[M], D = new int[M];
        Set<Integer> H = new HashSet<>();
        for (int i = 0; i < M; i++) {
            L[i] = sc.nextInt();
            R[i] = sc.nextInt();
            D[i] = sc.nextInt();
            H.add(L[i]);
            H.add(R[i]);
        }

        Map<Integer, Integer> P = new HashMap<>(); //key-> H, val-> pos

        for (Integer human : H) { // base human
            for (int i = 0; i < M; i++) {
                if (P.isEmpty()) {
                    P.put(L[i], 0);
                }
                if (P.get(human) != null) {
                    if (human.equals(L[i])) {
                        if (P.get(R[i]) != null && P.get(R[i]) != P.get(human) + D[i]) {
                            System.out.println("No");
                            return;
                        } else {
                            P.put(R[i], P.get(human) + D[i]);
                        }
                    } else if (human.equals(R[i])) {
                        if (P.get(L[i]) != null && P.get(L[i]) != P.get(human) - D[i]) {
                            System.out.println("No");
                            return;
                        } else {
                            P.put(L[i], P.get(human) - D[i]);
                        }
                    }
                }
            }
        }
        System.out.println("Yes");
    }
}