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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        PeopleLine solver = new PeopleLine();
        solver.solve(1, in, out);
        out.close();
    }

    static class PeopleLine {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            WeightedUnionFind uf = new WeightedUnionFind(n + 1);
            for (int i = 0; i < m; i++) {
                int l = in.nextInt();
                int r = in.nextInt();
                int w = in.nextInt();
                if (uf.same(l, r)) {
                    int d = uf.diff(l, r);
                    if (d != w) {
                        out.println("No");
                        return;
                    }
                } else {
                    uf.unite(l, r, w);
                }
            }
            out.println("Yes");
        }

        public class WeightedUnionFind {
            private int[] rank;
            private int[] parents;
            private int[] weight;

            public WeightedUnionFind() {
            }

            public WeightedUnionFind(int size) {
                this.rank = new int[size];
                this.parents = new int[size];
                this.weight = new int[size];

                for (int i = 0; i < size; i++) {
                    makeSet(i);
                }
            }

            public void makeSet(int x) {
                parents[x] = x;
                rank[x] = 0;
            }

            public int findSet(int x) {
                if (x != parents[x]) {
                    int r = findSet(parents[x]);
                    weight[x] += weight[parents[x]];
                    parents[x] = r;
                }
                return parents[x];
            }

            public int weight(int x) {
                findSet(x);
                return weight[x];
            }

            public int diff(int x, int y) {
                return weight(y) - weight(x);
            }

            public boolean unite(int x, int y, int w) {
                if (same(x, y)) {
                    return false;
                }
                int px = findSet(x);
                int py = findSet(y);

                if (rank[px] > rank[py]) {
                    // xにくっつける
                    parents[py] = px;
                    weight[py] = w + weight[y] - weight[x];
                } else {
                    // yにくっつける
                    parents[px] = py;
                    weight[px] = -w - weight[y] + weight[x];
                    if (rank[px] == rank[py]) {
                        rank[py]++;
                    }
                }
                return true;
            }

            public boolean same(int x, int y) {
                return findSet(x) == findSet(y);
            }

        }

    }
}