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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

struct node{
  int parent;
  long int distance;
};

int root(int i, struct node *x){
  int k = i;
  while(x[k].parent != k){
    k = x[k].parent;
  }
  return k;
}

long int get_distance(int i, struct node *x){
  int k = i; long int d = 0;
  while(x[k].parent != k){
    d += x[k].distance;
    k = x[k].parent;
  }
  return d;
}

int
main(int argc, char *argv[])
{
  int n, m, l, r, flag = 0; long int d;
  struct node x[100000];
  scanf("%d %d", &n, &m);
  for(int i = 0; i < n; i++){
    x[i].parent = i;
    x[i].distance = 0;
  }
  for(int i = 0; i < m; i++){
    scanf("%d %d %ld", &l, &r, &d);
    l--; r--;
    if(x[r].parent == r){
      if(root(l, x) == r) flag++;
      x[r].parent = root(l, x);
      x[r].distance = d + get_distance(l, x);
    }
    else{
      if(root(r, x) != root(l, x)){
	long c = get_distance(l, x), e = get_distance(r, x);
	int u = root(l, x), v = root(r, x);
	x[r].parent = u;
	x[r].distance = c + d;
	long int D = c + d - e;
	if(D >= 0){
	  x[v].parent = u;
	  x[v].distance = D;
	}
	else{
	  x[u].parent = v;
	  x[u].distance = -D;
	}
      }
      else{
	if(get_distance(l, x) - get_distance(r, x) !=  -d){
	  flag++;
	}
      }
    }
  }

  if(flag > 0) printf("No\n");
  else printf("Yes\n");

  return 0;
}