Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.

Snuke can perform the following two actions:

* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.

* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.




Find the minimum time that Snuke needs to have slimes in all N colors.

Constraints

* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9

Input

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


N x
a_1 a_2 ... a_N


Output

Find the minimum time that Snuke needs to have slimes in all N colors.

Examples

Input

2 10
1 100


Output

12


Input

3 10
100 1 100


Output

23


Input

4 10
1 2 3 4


Output

10
using System;
using System.Linq;
using System.Collections.Generic;

namespace ABC
{
	class MainClass
	{
		public static void Main (string[] args)
		{
			var a = Console.ReadLine ().Split().Select(x=>int.Parse(x)).ToArray();
			int N = a [0];
			int X = a [1];
			var b = Console.ReadLine ().Split().Select(x=>int.Parse(x)).ToArray();
			Array.Sort (b);
			int time = b [0];
			int i = 1;
			int count = 1;
			while (count < N) {
				if (b [i] <= X) {
					time += b [i];
					i++;
					count++;
				} else {
					time +=X;
					i = 0;
				}
			}
			Console.WriteLine (time);
		}
	}
}
