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: Accepted)

private fun readIntArray(): List<Int> {
    return readLine()!!.split(" ").map{ it.toInt() }
}

private fun readInt(): Int {
    return readLine()!!.toInt()
}

private fun bfs(x: Int, graph: MutableList<MutableList<Pair<Int, Int>>>, people: MutableList<Int>) {
    if(people[x] != Int.MAX_VALUE) {
        return
    }

    val unvisited = mutableListOf(x)
    people[x] = 0
    while (unvisited.size > 0) {
        val now = unvisited[0]
        unvisited.removeAt(0)
        for(next in graph[now]) {
            if (people[next.first] == Int.MAX_VALUE) {
                people[next.first] = people[now] + next.second
                unvisited.add(next.first)
            }
        }
    }
}

fun main(args: Array<String>) {
    val (N, M) = readIntArray()

    val graph: MutableList<MutableList<Pair<Int, Int>>> = mutableListOf()
    val people: MutableList<Int> = mutableListOf()
    for(i in 0 until N + 1) {
        people.add(Int.MAX_VALUE)
    }
    for(i in 0 until N + 1) {
        graph.add(mutableListOf())
    }

    for (i in 0 until M) {
        val (L, R, D) = readIntArray()
        graph[L].add(Pair(R, D))
        graph[R].add(Pair(L, -D))
    }

    for (i in 1 until N + 1) {
        bfs(i, graph, people)
    }

    for (i in 1 until N + 1) {
        for (p in graph[i]) {
            if (people[p.first] - people[i] != p.second) {
                println("No")
                return
            }
        }
    }

    println("Yes")
}