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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

fun bd090(args: Array<String>) {
    val (N, M) = args[0].split(" ").map { it.toInt() }
    val edgeList = args.drop(1).map { line -> line.split(" ").map { it.toInt() } }
    val sourceToDestCost = Array(N) { mutableListOf<Pair<Int, Int>>() }
    edgeList.forEach {
        val (source, dest, cost) = it
        sourceToDestCost[source - 1].add(Pair(dest - 1, cost))
        sourceToDestCost[dest - 1].add(Pair(source - 1, -cost))
    }
    val visited = Array(N) { false }
    var numList: Array<Long>
    val queue = mutableListOf<Int>()
    var ans = true
    while (!visited.all { it }) {
        numList = Array(N) { -1L }
        val firstIndex = visited.indexOfFirst { !it }
        queue.add(firstIndex)
        numList[firstIndex] = 1
        while (!queue.isEmpty()) {
            val source = queue.removeAt(0)
            visited[source] = true
            for (destCost in sourceToDestCost[source]) {
                val (dest, cost) = destCost
                if (numList[dest] != -1L && numList[dest] != numList[source] + cost) {
                    ans = false
                    break
                }
                numList[dest] = numList[source] + cost
                if (!visited[dest]) {
                    queue.add(dest)
                }
            }
        }
    }
    println(if (ans) "Yes" else "No")
}

fun main(args: Array<String>) {
    bd090(readLineList())
}

fun readLineList(): Array<String> {
    val lineList = mutableListOf<String>()
    while (true) {
        val line = readLine()
        if (line.isNullOrBlank()) {
            break
        } else {
            lineList.add(line!!)
        }
    }
    return lineList.toTypedArray()
}