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)

#define LOCAL

#include <map>
#include <unordered_map>
#include <unordered_set>
#include <set>
#include <vector>
#include <numeric>
#include <algorithm>
#include <iostream>
#include <string>
#include <cstring>
#include <sstream>
#include <functional>
#include <queue>
#include <deque>
#include <stack>
#include <cmath>
#include <iomanip>

using namespace std;

// From Errichto's Youtube stream
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
  enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
  ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
  *this << "[";
  for (auto it = d.b; it != d.e; ++it)
    *this << ", " + 2 * (it == d.b) << *it;
  ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "

using int64 = long long;

/////////////////////
// Code starts here//
/////////////////////
const int INF = (1<<30);

int N, M;
vector<vector<pair<int, int>>> g;
priority_queue<pair<int, int>> heap;
vector<int> dist;

bool dfs(int el, int delta) {
    //debug() << el << " -> " << delta;
    if (dist[el] != -INF) {
        //debug() << dist[el] << " " << delta;
        return dist[el] == delta;
    }

    dist[el] = delta;

    for (auto entry : g[el]) {
        if (!dfs(entry.first, delta + entry.second)) {
            return false;
        }
    }

    return true;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    cin >> N >> M;
    g.resize(N);

    for (int i = 0; i < M; i++) {
        int l, r, d;
        cin >> l >> r >> d;
        l--, r--;
        g[l].emplace_back(r, d);
        g[r].emplace_back(l, -d);
    }

    dist.assign(N, -INF);

    for (int i = 0; i < N; i++) {
        if (dist[i] == -INF) {
            if (!dfs(i, 0)) {
                cout << "No\n";
                return 0;
            }
        }
    }
    
    cout << "Yes\n";

    return 0;
}