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: Runtime Error)

#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <stdio.h>
#include <cstring>
#include <queue>
#include <functional>
#include <random>
using namespace std;
#define Would
#define you

const int MOD = 1e9 + 7;
const int INF = 999999999;

int a, b, exi[100005], loc[100005];
int main() {
	cin >> a >> b;
	vector<pair<int, pair<int, int>>>v(b);
	for (int i = 0; i < b; ++i) {
		cin >> v[i].first >> v[i].second.first >> v[i].second.second;
		if (v[i].first > v[i].second.first) {
			swap(v[i].first, v[i].second.first);
			v[i].second.second *= -1;
		}
	}
	sort(v.begin(), v.end());
	exi[v[0].first] = true, exi[v[0].second.first] = true;
	loc[v[0].first] = 0, loc[v[0].second.first] = v[0].second.second;
	for (int i = 1; i < b; ++i) {
		if (exi[v[i].first] && exi[v[i].second.first] && loc[v[i].first] - loc[v[i].second.first] != v[i].second.second) {
			cout << "No" << endl;
			return 0;
		}
		exi[v[i].second.first] = true;
		loc[v[i].second.first] = v[i].second.second - loc[v[i].first];
	}
	cout << "Yes" << endl;
}