Problem:
Score : 200 points

Problem Statement

There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.
During the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.
That is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.
The kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.
Find the earliest possible time to reach coordinate X.

Constraints

X is an integer.

1≤X≤10^9

Input

The input is given from Standard Input in the following format:

X

Output

Print the earliest possible time for the kangaroo to reach coordinate X.

Sample Input 1

6

Sample Output 1

3

The kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.

Sample Input 2

2

Sample Output 2

2

He can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.

Sample Input 3

11

Sample Output 3

5

Solution in Scala (2.11.7) (judge verdict: Accepted)

import scala.io.StdIn._
object Main extends App {
  val x = readLong
  println(binSearch(500000000, 1, 1000000000))

  @scala.annotation.tailrec
  def binSearch(n: Long, l: Long, r: Long): Long = {
    val (min, max) = range(n)
    if (min < x && x <= max) n
    else if (x <= min) binSearch((l + n) / 2, l, n)
    else binSearch((r + n) / 2, n, r)
  }

  def range(n: Long): (Long, Long) = {
    val sum = n * (n + 1) / 2
    (sum - n, sum)
  }
}