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.Diagnostics;
using System.Collections.Generic;
using static System.Math;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
 
class P
{
    static void Main()
    {
        var nx = Console.ReadLine().Split().Select(int.Parse).ToList();
        int n = nx[0];
        long x = nx[1];
        //どっか決め打ちして二分探索!(素振り)
        //増殖回数決め撃ちしそう(こなみかん
        var a = Console.ReadLine().Split().Select(long.Parse).ToList();
        long[][] costMin = Enumerable.Repeat(0, n).Select(_ => new long[n]).ToArray();
        costMin[0] = a.ToArray();
        long min = a.Sum();
        for (int i = 1; i < n; i++)
        { 
            for (int j = 0; j < n; j++) costMin[i][(j + i) % n] = Min(costMin[i - 1][(j + i) % n], costMin[i - 1][j]);
            min = Min(min, costMin[i].Sum() + i * x);
        }
        Console.WriteLine(min);
    }
}
