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)

/// Containers Start
#include <algorithm>
#include <bitset>
#include <cstdlib>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
/// C Header Files
#include <cassert>
#include <cctype>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <ctime>
#include <math.h>
#include <stdio.h>
/// Containers End

using namespace std;

/// Math Start
#define PI acos(-1.0)
#define Pi 3.141592653589793
#define EPS (1e-7)
#define INF (0x3f3f3f3f)
// #define INF 9e+18

/// Math End

/// Extra Start
#define nn '\n'
#define pb push_back
#define ull unsigned long long
#define ll long long
#define MOD 1000000007
#define sz(a) int((a).size())
#define space " "
#define All(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
/// Extra End

#define rep(i, n) for (int i = 0; i < n; i++)
#define Cini(a)                                                                \
    int a;                                                                     \
    cin >> a;
#define Cinii(a, b)                                                            \
    int a, b;                                                                  \
    cin >> a >> b;
#define Ciniii(a, b, c)                                                        \
    int a, b, c;                                                               \
    cin >> a >> b >> c;
#define Cins(s)                                                                \
    string s;                                                                  \
    cin >> s;
#define Cinss(s1, s2)                                                          \
    string s1, s2;                                                             \
    cin >> s1 >> s2;
#define Cinc(c)                                                                \
    char c;                                                                    \
    cin >> c;
/// Functions End

/// Debug Start
#define deb(x) cout << #x << ": " << x << endl
#define deb2(x, y) cout << #x << ": " << x << '\t' << #y << ": " << y << endl;
#define deb3(x, y, z)                                                          \
    cout << #x << ": " << x << '\t' << #y << ": " << y << '\t' << #z << ": "   \
         << z << endl;
/// Debug End

int dx[] = {1, 0, -1, 0};
int dy[] = {0, 1, 0, -1};
// int dx[] = {-1, 0, 1};
// int dy[] = {-1, 0, 1};

/**>>>>>>>>>>>>>>>>>>> END <<<<<<<<<<<<<<<<<<**/

/// template

#define int long long

signed main(void) {
    cin.sync_with_stdio(false);
    cin.tie(0);
    Cinii(N, M);
    if (M == 0) {
        cout << "Yes" << nn;
        return 0;
    }
    vector<vector<pair<int, int> > > out(N);
    rep(i, M) {
        int l, r, d;
        cin >> l >> r >> d;
        l--;
        r--;
        out[l].push_back(make_pair(r, d));
        out[r].push_back(make_pair(l, -d));
    }
    bool used[N];
    int d[N];
    fill(used, used + N, false);
    fill(d, d + N, 0);
    rep(i, N) {
        used[i] = true;
        if (out[i].size() == 0) continue;
        for (auto &e :out[i]) {
            if (used[e.first]) {
                if (d[e.first] != d[i] + e.second) {
                    cout << "No" << nn;
                    return 0;
                }
            } else {
                used[e.first] = true;
                d[e.first] = d[i] + e.second;
            }
        }
    }
    cout << "Yes" << nn;
    return 0;
}