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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
using namespace std;
// #define mdfs
int N,M;
vector<pair<int,int>> adj[100001];
bool visited[100001];
int dist[100001];
int res = 0;
bool flag = true;

void dfs(int s) {
    // if (visited[s] == true) return;
    visited[s] = true;
    // dist[s] += dist[s] + u.second; 
    for (auto u: adj[s]){
        // cout << dist[s] << ":" << s << ":" << u.first << ":" << u.second << endl;
        if (visited[u.first] == true) 
        {   
            // cout << dist[s] << ":" << s << ":" << u.first << ":" << u.second << endl;
            flag = (dist[u.first] == (dist[s] + u.second));
            continue;}
        dist[u.first] = dist[s] + u.second; 
        // res = max(u.second + res,res);
        
        dfs(u.first);
    }
    return;
    
}

int main(void){
    // Your code here!
    cin >> N >> M;
    for (int i = 0; i < M; i++){
        int l,r,d;
        cin >> l >> r >> d;
        adj[l].push_back({r,d});
        adj[r].push_back({l,-d});
    }
    
    for (int i = 1; i <= N; i++){
        // for (int j = i; j <= N; j++) visited[j] = 0;
        // fill(&visited[0],&visited[N],0);
        // if (visited[i] == 0) dfs(i);
        dfs(i);
        if (flag == false) {
            cout << "No" << endl;
            break;
        }
    }
    if (flag == true) cout << "Yes" << endl;
    // dfs(7);

    // if (flag == true) cout << "Yes" << endl;
    // else cout << "No" << endl;
}