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: Accepted)

import java.util.*;

public class Main {
    private class Node {
        Integer x = null;
        List<Edge> edge = new ArrayList<>();
    }

    private class Edge {
        int src, dst, cost;

        public Edge(int src, int dst, int cost) {
            this.src = src;
            this.dst = dst;
            this.cost = cost;
        }
    }

    public void main(Scanner sc) {
        int n = sc.nextInt();
        int m = sc.nextInt();

        Node nodes[] = new Node[n];
        for (int i = 0; i < n; i++) {
            nodes[i] = new Node();
        }

        for (int i = 0; i < m; i++) {
            int l = sc.nextInt();
            int r = sc.nextInt();
            int d = sc.nextInt();

            nodes[l - 1].edge.add(new Edge(l, r, d));
            nodes[r - 1].edge.add(new Edge(r, l, -d));
        }

        Queue<Node> queue = new ArrayDeque<>();
        for (int i = 0; i < n; i++) {
            if (nodes[i].x != null) {
                continue;
            }

            queue.add(nodes[i]);
            while (!queue.isEmpty()) {
                Node node = queue.poll();
                if (node.x == null) {
                    node.x = 0;
                }
                for (Edge e : node.edge) {
                    Node next = nodes[e.dst - 1];
                    if (next.x == null) {
                        next.x = node.x + e.cost;
                        queue.add(next);
                    } else if (next.x != node.x + e.cost) {
                        System.out.println("No");
                        return;
                    }
                }
            }
        }

        System.out.println("Yes");
    }

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