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.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main
{

	public static void main(String[] args)
	{
		Scanner sc = new Scanner(System.in);
		String in = sc.nextLine();
		String[] ins = in.split(" ");

		//人の数
		int people = Integer.parseInt(ins[0]);
		//与えられる情報の数
		int infoNum = Integer.parseInt(ins[1]);

		//人の数分の配列を作成
		int[] arrays = new int[people];
		//初期値に0を設定
		for (int i = 0; i < people; i++)
		{
			arrays[i] = 0;
		}
		Map<Integer, Map<Integer, Integer>> map = new HashMap<>();
		boolean result = true;
		for (int i = 0; i < infoNum; i++)
		{
			String line = sc.nextLine();
			String[] lines = line.split(" ");

			//基準
			int base = Integer.parseInt(lines[0]);
			//対象
			int target = Integer.parseInt(lines[1]);
			//右にずれる位置
			int rightPoint = Integer.parseInt(lines[2]);

			//基準の位置を取得
			int basePoint = arrays[base - 1];
			//移動先の位置
			int targetPoint = basePoint + rightPoint;
			//対象の現在の位置
			int currentPoint = arrays[target - 1];

			//マップのキーに設定されていない、かつ
			//対象の現在位置が0の場合は未設定とみなす
			if (!map.containsKey(target) && currentPoint == 0)
			{
				arrays[target - 1] = targetPoint;
				currentPoint = targetPoint;
			}
			//対象の現在の位置と移動先の位置が異なる場合
			if (targetPoint != currentPoint)
			{
				result = false;
				break;
			}

			Map<Integer, Integer> map2 = map.get(basePoint);
			if (map2 == null)
			{
				map2 = new HashMap();
			}
			map2.put(target, rightPoint);
			map.put(base, map2);

			//依存している座標の再計算
			Map<Integer, Integer> map3 = map.get(target);
			if (map3 == null)
			{
				continue;
			}
			for (int j : map3.keySet())
			{
				int k = arrays[j - 1];
				k += rightPoint;
				arrays[j - 1] = k;
			}

		}
		String resultStr = result ? "Yes" : "No";
		System.out.println(resultStr);
	}

}