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)

import java.util.*
import java.io.PrintWriter

val pw = PrintWriter(System.out)
val MOD = 1000000007L
val INF = 2147483647
val LINF = 9223372036854775807L

fun main(args: Array<String>){
    solve()
    pw.flush()    
}

fun solve(){
    val (n, m) = nextIntList()
    val nodes: Array<Node> = Array(n) { i -> Node(i)}
    repeat(m) { 
        val (l, r, d) = nextIntList()
        nodes[l - 1].edges.add(Edge(l - 1, r - 1, d.toLong()))
        nodes[r - 1].edges.add(Edge(r - 1, l - 1, -1L * d))
    }

    for (node in nodes) {
        if(node.past != -1) continue
        node.past = 0
        if(bfs(nodes, node.id)){
            println("No")
            return
        }
    }
    println("Yes")
}

fun bfs(nodes: Array<Node>, start: Int) : Boolean {
    val queue = ArrayDeque<Int>()
    queue.add(start)
    val dist: Array<Long> = Array(nodes.size) { -LINF }
    dist[start] = 0
    while(queue.isNotEmpty()){
        val now = queue.poll()
        for (edge in nodes[now].edges) {
            if(dist[edge.to] != -LINF && dist[edge.to] - dist[now] != edge.cost){
                return true
            }
            if(dist[edge.to] != -LINF) continue
            dist[edge.to] = dist[now] + edge.cost
            nodes[edge.to].past = 0
            queue.add(edge.to)
        }
    }
    return false
}

// Print
fun println(v: String){
    pw.println(v)
}
fun print(v: String){
    pw.print(v)
}

// Read
fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextList() = next().split(" ")
fun nextIntList() = next().split(" ").map{ it.toInt() }
fun nextLongList() = next().split(" ").map{ it.toLong() }
fun nextDoubleList() = next().split(" ").map{ it.toDouble() }
fun nextAryln(n: Int) = Array(n){ next() }
fun nextIntAryln(n: Int) = IntArray(n){ nextInt() }
fun nextLongAryln(n: Int) = LongArray(n){ nextLong() }
fun nextDoubleAryln(n: Int) = DoubleArray(n) { nextDouble() }

// Math
fun abs(n: Long) : Long = Math.abs(n)
fun max(a: Long = -LINF, b: Long = -LINF, c: Long = -LINF, d: Long = -LINF, e: Long = -LINF): Long = listOf(a, b, c, d, e).max()!!.toLong()
fun min(a: Long = LINF, b: Long = LINF, c: Long = LINF, d: Long = LINF, e: Long = LINF): Long = listOf(a, b, c, d, e).min()!!.toLong()
fun prime(from: Long, to: Long = from) : List<Long>{
    return (from..to).filter{ i ->
        val max = Math.sqrt(i.toDouble()).toLong()
        (2..max).all{ j -> i % j != 0L}
    }
}
fun gcd(a: Long, b: Long) : Long = if(a % b == 0L) b else gcd(b, (a % b))
fun lcm(a: Long, b: Long) : Long = a / gcd(a, b) * b
fun modpow(a: Long, n: Long, p:Long = MOD) : Long {
    var res = 1L
    var ar = a
    var nr = n
    while(nr > 0){
        if((nr and 1) == 1L) res = res * ar % p
        ar = ar * ar % p
        nr = nr shr 1
    }
    return res
}
fun modinv(a: Long, p: Long = MOD) : Long = modpow(a, p - 2, p)
fun ncr(n: Long, r: Long) : Long {
    var a = 1L
    var b = 1L
    for (i in 1..r) {
        a = a * (n + 1 - i) % MOD
        b = b * i % MOD
    }
    return modinv(b, MOD) * a % MOD
}

data class Node(val id: Int, var past: Int = -1, var edges: MutableList<Edge> = mutableListOf())
data class Edge(val from: Int, val to: Int, val cost: Long = 1L)