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;
int x,y,z,mi[200001],ma[200001];
int n,m,fa[200001],dis[200001];
void add(int x,int y,int z)
{
	fa[x]=y;dis[x]=z;
}
int getfa(int x)
{
	if(fa[x]==x) return x;
	else
	{
		int tem=getfa(fa[x]);
		dis[x]+=dis[fa[x]];
		return fa[x]=tem;
	}
}
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++)
		fa[i]=i;
	for(int i=1;i<=m;i++)
	{
		scanf("%d%d%d",&x,&y,&z);
		if(getfa(x)!=getfa(y))
		{
			add(getfa(x),getfa(y),dis[x]-dis[y]+z);
		}
		else
		{
			if(dis[x]-dis[y]!=z)
			{
				puts("No");
				exit(0);
			}
		}
	}
	for(int i=1;i<=n;i++)
		mi[getfa(i)]=min(mi[getfa(i)],dis[i]),
		ma[getfa(i)]=max(ma[getfa(i)],dis[i]);
	for(int i=1;i<=n;i++)
		if(ma[i]-mi[i]>1000000000)
		{
			puts("No");
			exit(0);
		}
	puts("Yes");
	return 0;
}