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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner() {
        s = new string[0];
        i = 0;
    }

    public string next() {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int Int() {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0) {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++) {
            Array[i] = Int() + add;
        }
        return Array;
    }

    public long Long() {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0) {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++) {
            Array[i] = Long() + add;
        }
        return Array;
    }
}
class WeightedUnionFind {
    int[] parent;
    long[] weightDiff;
    int count;

    public WeightedUnionFind(int size) {
        var b = new int[size];
        for (int i = 0; i < b.Length; i++) {
            b[i] = -1;
        }
        parent = b;
        weightDiff = new long[size];
        count = size;
    }

    int Find(int x) {
        if (parent[x] < 0) {
            return x;
        }
        else {
            var r = Find(parent[x]);
            weightDiff[x] += weightDiff[parent[x]];
            return parent[x] = r;
        }
    }

    long Weight(int x) {
        Find(x);
        return weightDiff[x];
    }

    public long Diff(int x, int y) => Weight(y) - Weight(x);

    public bool Same(int x, int y) => Find(x) == Find(y);

    public void Unite(int x, int y, long w) {
        w += weightDiff[x] - weightDiff[y];
        x = Find(x);
        y = Find(y);
        if (x == y) return;
        count--;
        if (parent[x] > parent[y]) {
            parent[y] += parent[x];
            parent[x] = y;
            weightDiff[x] = -w;
        }
        else {
            parent[x] += parent[y];
            parent[y] = x;
            weightDiff[y] = w;
        }
    }

    public int Size(int x) => -parent[Find(x)];

    public int Count() => count;
}
class Program {
    static Scanner cin = new Scanner();
    static void Main() {
        int N = cin.Int();
        int M = cin.Int();

        var uf = new WeightedUnionFind(N);
        for (int i = 0; i < M; i++) {
            int L = cin.Int() - 1;
            int R = cin.Int() - 1;
            long D = cin.Long();
            if (uf.Same(L, R)) {
                if (uf.Diff(L, R) != D) {
                    Console.WriteLine("No");
                    return;
                }
            }
            else uf.Unite(L, R, D);
        }
        Console.WriteLine("Yes");
        Console.ReadLine();
    }
}