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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
public class Main {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);


//入力変数
int N=sc.nextInt();
int M=sc.nextInt();
int[] L=new int[M];
int[] R=new int[M];
int[] D=new int[M];
for(int i=0;i<M;i++){
    L[i]=sc.nextInt();
    R[i]=sc.nextInt();
    D[i]=sc.nextInt();
}

//入力値変換
int[] x=new int[N];
for(int i=0;i<N;i++){
    x[i]=0;
}
boolean[] changed=new boolean[N];
for(int i=0;i<N;i++){
    changed[i]=false;
}

//出力変数
String ans="Yes";

//計算

for(int i=0;i<M;i++){
  if(!changed[L[i]-1]&&!changed[R[i]-1]){
    x[R[i]-1]=D[i];
    changed[L[i]-1]=true;
    changed[R[i]-1]=true;
  }
  if(!changed[L[i]-1]&&changed[R[i]-1]){
    x[L[i]-1]=x[R[i]-1]-D[i];
    changed[L[i]-1]=true;
  }
  if(changed[L[i]-1]&&!changed[R[i]-1]){
    x[R[i]-1]=x[L[i]-1]+D[i];
    changed[R[i]-1]=true;
  }
  if(changed[L[i]-1]&&changed[R[i]-1]){
    if(x[R[i]-1]-x[L[i]-1]!=D[i]){
        ans="No";
    }
  }
}


//出力
System.out.println(ans);

}}