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();
			int time = 0;
			var dp = new int[N,N];
			int min = 400000000;
			dp [0,0] = 0;
			for (int k = 0; k < N; k++) {
				time = k * X;
				for (int i = 0; i < N; i++) {
					dp [i,k] = k==0?b[i]: Math.Min (dp [i,k - 1], b [(i - k + N) % N]);
					time += dp [i,k];
				}
				if (time <= min) {
					min = time;
				}
			}
			Console.WriteLine (min);
		}
	}
}
