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: Accepted)

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cassert>
#include <functional>
#include <algorithm>
#include <string>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <stack>
using namespace std;
using llong = long long;

//===
//#include <vector>
//#include <functional>
template<typename Abel>
struct WeightedUnionFind {
    using OP = function<Abel(Abel, Abel)>;

    vector<int> parent;
    vector<Abel> diff_weight; // distance from root
    const OP add;
    const OP sub;
    const Abel e;
    
    WeightedUnionFind(int nmemb,
                      const Abel &e = 0,
                      const OP &add = [](Abel x, Abel y){return x+y;},
                      const OP &sub = [](Abel x, Abel y){return x-y;}):
        e(e), add(add), sub(sub)
    {
        parent.assign(nmemb, -1);
        diff_weight.assign(nmemb, e);
    };

    int root(int x) {
        if (parent[x] < 0) {
            return x;
        }
        
        int p = root(parent[x]);
        diff_weight[x] = add(diff_weight[x], diff_weight[parent[x]]);
        parent[x] = p;

        return p;
    };

    bool unite(int x, int y, Abel w) {
        Abel wx = weight(x);
        Abel wy = weight(y);
        x = root(x);
        y = root(y);

        if (x == y) return false;
        w = sub(add(w, wx), wy);
        if (size(x) < size(y)) swap(x, y), w = -w;

        parent[x] += parent[y];
        parent[y] = x;
        diff_weight[y] = w;
        
        return true;
    };
    
    bool same(int x, int y) {
        return root(x) == root(y);
    };
    
    Abel weight(int x) {
        root(x);
        return diff_weight[x];
    };

    Abel diff(int x, int y) {
        return sub(weight(y), weight(x));
    };

    int size(int x) {
        return -parent[root(x)];
    };
};
//===

WeightedUnionFind<llong> uf(100005);
llong n, m;
llong l, r, d;

int main() {
    cin >> n >> m;
    for (int i = 0; i < m; i++) {
        cin >> l >> r >> d;

        if (uf.same(l, r)) {
            if (uf.diff(l, r) != d) {
                cout << "No" << endl;
                return 0;
            }
        }
        else {
            uf.unite(l, r, d);
        }
    }

    cout << "Yes" << endl;

    return 0;
}