Problem:
Problem I: A Piece of Cake

In the city, there are two pastry shops. One shop was very popular because its cakes are pretty tasty.
However, there was a man who is displeased at the shop. He was an owner of another shop. Although cause of his shop's unpopularity is incredibly awful taste of its cakes, he never improved it. He was just growing hate, ill, envy, and jealousy.

Finally, he decided to vandalize the rival.

His vandalize is to mess up sales record of cakes. The rival shop sells K kinds of cakes and sales quantity is recorded for each kind. He calculates sum of sales quantities for all pairs of cakes. Getting K(K-1)/2 numbers, then he rearranges them randomly, and replace an original sales record with them.

An owner of the rival shop is bothered. Could you write, at least, a program that finds total sales quantity of all cakes for the pitiful owner?

Input

Input file contains several data sets.
A single data set has following format:

K
c1 c2 ... cK×(K-1)/2

K is an integer that denotes how many kinds of cakes are sold. ci is an integer that denotes a number written on the card.

The end of input is denoted by a case where K = 0. You should output nothing for this case.

Output

For each data set, output the total sales quantity in one line.

Constraints

Judge data contains at most 100 data sets.

2 ≤ K ≤ 100

0 ≤ ci ≤ 100

Sample Input

2
2
3
5 4 3
0

Output for the Sample Input

2
6

Solution in Scala (judge verdict: Accepted)

import java.util.Scanner

import scala.collection.Searching._
import scala.annotation.tailrec
import scala.collection.immutable.{NumericRange, Queue}
import scala.collection.mutable
import scala.io.StdIn.readLine

class IUnionFind(val size: Int) {

  private case class Node(var parent: Option[Int], var treeSize: Int)

  private val nodes = Array.fill[Node](size)(new Node(None, 1))

  def union(t1: Int, t2: Int): IUnionFind = {
    if (t1 == t2) return this

    val root1 = root(t1)
    val root2 = root(t2)
    if (root1 == root2) return this

    val node1 = nodes(root1)
    val node2 = nodes(root2)

    if (node1.treeSize < node2.treeSize) {
      node1.parent = Some(t2)
      node2.treeSize += node1.treeSize
    } else {
      node2.parent = Some(t1)
      node1.treeSize += node2.treeSize
    }
    this
  }

  def connected(t1: Int, t2: Int): Boolean = t1 == t2 || root(t1) == root(t2)

  def root(t: Int): Int = nodes(t).parent match {
    case None => t
    case Some(p) => root(p)
  }
}


object Main {
  def solve(sc: => Scanner): Unit = {
    val N = sc.nextInt
    if (N != 0) {
      println(Array.fill(N * (N - 1) / 2)(sc.nextInt).sum / (N - 1))
      solve(sc)
    }
  }

  def gcd(i: Long, j: Long): Long = {
    if (i < j) (gcd(j, i)) else (if (j == 0) (i) else (gcd(j, i % j)))
  }

  def main(args: Array[String]): Unit = {
    val sc: Scanner = new Scanner(System.in)
    solve(sc)
  }
}