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;
typedef long long ll;
#define rep(i, n) for (ll i = 0; i < (ll)(n); ++i)
const long long MODNUM = 7;

int main() {

    ll n,m; cin >> n >> m;
    vector<ll> l(m);
    vector<ll> r(m);
    vector<ll> d(m);
    rep(i, m) {
        cin >> l[i] >> r[i] >> d[i];
        l[i]--;
        r[i]--;
    }

    vector<ll> x(n, -LLONG_MAX);
    // xの仮位置を作成
    // 構築できなかったらNG
    rep(i, m) {
        if(x[r[i]] == -LLONG_MAX) {
            x[r[i]] = 0;
            if(x[l[i]] == -LLONG_MAX) {
                x[l[i]] = -d[i];
            } else {
                x[r[i]] = x[l[i]] + d[i];
            }
        } else {
            if(x[l[i]] == -LLONG_MAX) {
                x[l[i]] = x[r[i]]-d[i];
            } else {
                if(x[l[i]] != x[r[i]]-d[i]) {
                    cout << "No" << endl;
                    return 0;
                }
            }
        }

    }

    cout << "Yes" << endl;

    return 0;

}