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 <bits/stdc++.h>
using namespace std;

vector<int> parent;
vector<long long> position;

int root(int i) {
    if (i == parent[i]) return i;
    else {
        auto r = root(parent[i]);
        position[i] += position[r];
        return parent[i] = r;
    }
}
long long weight(int i) {
    root(i);
    return position[i];
}
void unit(int i, int j, long long d) {
    parent[root(j)] = root(i);
    position[i] = weight(i);
    position[j] = position[i] + d;
}

int N, M;

int main() {
    cin >> N >> M;

    parent.resize(N);
    iota(parent.begin(), parent.end(), 0);

    position.resize(N, 0);

    bool ans = true;

    for (int i = 0; i < M; ++i) {
        int l, r, d;
        cin >> l >> r >> d;
        --l, --r;
        if (root(l) == root(r)) {
            if (weight(r) - weight(l) != d) {
                ans = false;
                break;
            }
        } else {
            unit(l, r, d);
        }
    }

    cout << (ans ? "Yes" : "No") << endl;
}