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  1. All Contests
  2. ProjectEuler+
  3. Project Euler #222: Sphere Packing

Project Euler #222: Sphere Packing

What is the length of the shortest pipe, of internal radius , that can fully contain balls of radii where ?

Give your answer in micrometres ( ) rounded to the nearest integer.

Input Format

The first line of each test file contains two-separated integers and .
The next line contains space-separated integers .

Constraints

  • .
  • .
  • .
  • are pairwise distinct.

Output Format

Print your answer in one line.

Sample Input 0

2 1
2

Sample Output 0

4000

Sample Input 1

5 2
3 4

Sample Output 1

13325

Sample Input 2

100 5
61 62 63 64 65

Sample Output 2

530707