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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

function Main(input) {
	input = input.split("\n");
	var M = input[0].split(" ").map(a => parseInt(a));
	var N = M[0];
	M = M[1];
	var L = [], R = [], D = [];
	for(var i = 0; i < M; i++){
		L[i] = input[i+1].split(" ").map(a => parseInt(a));
		R[i] = L[i][1];
		D[i] = L[i][2];
		L[i] = L[i][0];
	}
	var x = new Array(N+1);
	var ans = "Yes";
	var i = L.length - 1, j, k;
	var ary = [];
	
	top:
	while(i >= 0){
		x[L[i]] = 0;
		x[R[i]] = D[i];
		ary = [L[i], R[i]];
		L.pop();
		R.pop();
		D.pop();
		j = 2;
		
		while(j){
			k = ary[j - 1];
			ary.pop();
			i = L.findIndex(a => a === k);
			while(i >= 0){
				if(x[R[i]] !== undefined){
					if(x[R[i]] !== x[L[i]] + D[i]){
						ans = "No";
						break top;
					}
				}else{
					x[R[i]] = x[L[i]] + D[i];
					ary.push(R[i]);
				}
				L.splice(i, 1);
				R.splice(i, 1);
				D.splice(i, 1);
				i = L.findIndex(a => a === k);
			}
			i = R.findIndex(a => a === k);
			while(i >= 0){
				if(x[L[i]] !== undefined){
					if(x[L[i]] !== x[R[i]] - D[i]){
						ans = "No";
						break top;
					}
				}else{
					x[L[i]] = x[R[i]] - D[i];
					ary.push(L[i]);
				}
				L.splice(i, 1);
				R.splice(i, 1);
				D.splice(i, 1);
				i = R.findIndex(a => a === k);
			}
			j = ary.length;
		}
		i = L.length - 1;
	}
	
	console.log(ans);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));