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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import scala.collection.mutable.ListBuffer
import scala.util.Try
object Main extends App {
  val sr = new StdinReader
  val n, m = sr.nextInt

  val lst = new ListBuffer[(Int, Int, Int)]
  (1 to m).foreach{i => 
    val l, r, d = sr.nextInt
    lst += ((l, r, d))
    lst += ((r, l, -d))
  }

  val conditions: Map[Int, List[(Int, Int, Int)]] = lst.toList.groupBy(_._1)

  val checked = Array.fill(n + 1)(Int.MaxValue)

  case class Check(index: Int, position: Int)

  @scala.annotation.tailrec
  def check(cs: List[Check]): Unit = {
    val checks = new ListBuffer[Check]
    if (cs.nonEmpty) {
      cs.foreach{c =>
        if (checked(c.index) == Int.MaxValue) {
          checked(c.index) = c.position
          checks ++= conditions.getOrElse(c.index, Nil).map{case (_, to, d) => Check(to, c.position + d)}
        } else if (checked(c.index) != c.position) {
          throw new Exception
        }
      }
      check(checks.toList)
    }
  }

  val result = try{
    (1 to n).foreach{i => if (checked(i) == Int.MaxValue) check(List(Check(i, 0)))}
    true
  } catch {
    case e: Throwable => false
  }
  println(if (result) "Yes" else "No")
}

class StdinReader {
  val buffer = new Array[Byte](1024 * 1024)
  var size = 0
  var pos = 0

  private def readByte: Byte = {
    if (pos >= size) {
      pos = 0;
      size = System.in.read(buffer);
    }
    if (size < 0) -1
    else {
      val ret = buffer(pos)
      pos += 1
      ret
    }
  }

  def next: String = {
    @scala.annotation.tailrec
    def r(sb: StringBuilder, reading: Boolean): String = {
      readByte match {
        case b if ('!' <= b && b <= '~') => r(sb.append(b.asInstanceOf[Char]), true)
        case _ => if (reading) sb.toString else r(sb, false)
      }
    }
    r(new StringBuilder, false)
  }

  def nextInt: Int = {
    @scala.annotation.tailrec
    def r(i: Int, reading: Boolean): Int = {
      readByte match {
        case '-' => r(i * -1, true)
        case b if '0' <= b && b <= '9' => r(i * 10 + (b - '0'), true)
        case _ => if (reading) i else r(i, false)
      }
    }
    r(0, false)
  }
}