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;

const long long big = 2e18;

struct in {
    int l, r, d;
};

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

    int n, m;
    cin >> n >> m;
    long long p[n];
    in inf[m];

    for (int i = 0; i < n; i++)
        p[i] = big;

    for (int i = 0; i < m; i++)
        cin >> inf[i].l >> inf[i].r >> inf[i].d;

    for (int i = 0; i < 15; i++) {
        bool ok = true;

        for (auto x : inf) {
            int l, r, d;
            l = x.l;
            r = x.r;
            d = x.d;
            l--;
            r--;

            if (p[l] == big && p[r] == big)
                p[l] = 0, p[r] = d;
            else if (p[l] == big)
                p[l] = p[r] - d;
            else if (p[r] == big)
                p[r] = p[l] + d;
            else if (p[r] != p[l] + d)
                ok = false, p[r] = p[l] + d;
        }

        if (ok)
            return cout << "Yes\n", 0;
    }

    cout << "No\n";

    return 0;
}