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;
class Node
{
    public bool Visited { get; set; }
    public ArrayList Children = new ArrayList();
    public ArrayList EdgeLength = new ArrayList();
    public int x = int.MaxValue;
}
static class DFS
{
    public static void DepthFirstSearch(Node root)
    {
        if (root.Visited)
            return;
        {
            if (root.x == int.MaxValue)
                root.x = 0;
            for (int i = 0; i < root.Children.Count; i++)
            {
                if (((Node)root.Children[i]).x == int.MaxValue || ((Node)root.Children[i]).x == root.x + (int)root.EdgeLength[i])
                    ((Node)root.Children[i]).x = root.x + (int)root.EdgeLength[i];
                else
                {
                    Console.WriteLine("No");
                    Environment.Exit(0);
                }
            }
        }
        root.Visited = true;
        if (root.Children.Count != 0)
        {
            for (int i = 0; i < root.Children.Count; i++)
            {
                DepthFirstSearch((Node)root.Children[i]);
            }
        }
    }
}
class Program
{
    static int Main()
    {
        string[] str = Console.ReadLine().Split(' ');
        int n, m;
        n = int.Parse(str[0]);
        m = int.Parse(str[1]);
        Node[] nodes = new Node[n];
        for (int i = 0; i < n; i++)
            nodes[i] = new Node();
        for (int i = 0; i < m; i++)
        {
            str = Console.ReadLine().Split(' ');
            int l, r, d;
            l = int.Parse(str[0]) - 1;
            r = int.Parse(str[1]) - 1;
            d = int.Parse(str[2]);
            nodes[l].Children.Add(nodes[r]);
            nodes[l].EdgeLength.Add(d);
            nodes[r].Children.Add(nodes[l]);
            nodes[r].EdgeLength.Add(-d);
        }
        for (int i = 0; i < n; i++)
            DFS.DepthFirstSearch(nodes[i]);
        Console.WriteLine("Yes");
        return 0;
    }
}