main.sc

package main.scala

import java.io.{FileInputStream, FileOutputStream}

import scala.io.StdIn

/**
 * Created by bongster on 14. 12. 26..
 */
object Main extends App {

  Console.setIn(new FileInputStream("B-large-practice.in.txt"))

  Console.setOut(new FileOutputStream("B-large-practice.out.txt"))

  def solve(lists: List[BigInt]): BigInt = {
    val a1 = lists.flatMap(n => {
      lists.map(b => n - b)
    }).filter(n => n > 0).toSet

    val result = a1.foldLeft(a1.head)((a2, b2) => {
      a2.gcd(b2)
    })

    if (lists.head % result == 0) 0 else result - lists.head % result
  }


  val cases = StdIn.readLine().toInt

  (1 to cases) foreach { n =>
    val list = StdIn.readLine().split(" ").map(BigInt(_)).toList.tail
    println(s"Case #$n: ${solve(list)}")
  }
}