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)

import java.util.*

fun main(args: Array<String>) {
    val (n, m) = readLine()!!.split(' ').map { it.toInt() }
    val g = mutableMapOf<Int, MutableList<Pair<Int, Int>>>()
    repeat(m) {
        val (l, r, d) = readLine()!!.split(' ').map { it.toInt() }
        g.getOrPut(l) { mutableListOf() }.add(r to d)
        g.getOrPut(r) { mutableListOf() }.add(l to -d)
    }

    val visited = mutableMapOf<Int, Int>()
    var ans = true

    for (root in g.keys) {
        if (visited.containsKey(root)) continue

        val stack = ArrayDeque<Pair<Int, Int>>()
        stack.addLast(root to 0)
        visited[root] = 0
        
        while (stack.isNotEmpty()) {
            val (u, x) = stack.removeLast()
            for ((v, d) in g[u]!!) {
                if (visited.containsKey(v)) {
                    if (visited[v] != x + d) {
                        ans = false
                        break
                    }
                } else {
                    stack.addLast(v to x + d)
                    visited[v] = x + d
                }
            }
        }

        if (!ans) break
    }

    println(if (ans) "Yes" else "No")
}