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;

namespace AGC004B{
    public class Program{
        public static void Main(string[] args){
            var sr = new StreamReader();
            //---------------------------------
            var N = sr.Next<int>();
            var X = sr.Next<long>();
            var A = sr.Next<long>(N);

            var dp = new long[N];
            for(var i = 0; i < N; i++){
                dp[i] = A[i];
            }

            var res = long.MaxValue;
            for(var k = 0; k < N; k++){
                for(var i = 0; i < N; i++){
                    dp[i] = Math.Min(dp[i], dp[(i - k + N) % N]);
                }
                res = Math.Min(res, dp.Sum() + k * X);
            }

            Console.WriteLine(res);
            //---------------------------------
        }
    }

    public class StreamReader{
        private readonly char[] _c = {' '};
        private int _index = -1;
        private string[] _input = new string[0];
        private readonly System.IO.StreamReader _sr = new System.IO.StreamReader(Console.OpenStandardInput());

        public T Next<T>(){
            if(_index == _input.Length - 1){
                _index = -1;
                while(true){
                    string rl = _sr.ReadLine();
                    if(rl == null){
                        if(typeof(T).IsClass) return default(T);
                        return (T)typeof(T).GetField("MinValue").GetValue(null);
                    }
                    if(rl != ""){
                        _input = rl.Split(_c, StringSplitOptions.RemoveEmptyEntries);
                        break;
                    }
                }
            }
            return (T)Convert.ChangeType(_input[++_index], typeof(T), System.Globalization.CultureInfo.InvariantCulture);
        }

        public T[] Next<T>(int x){
            var ret = new T[x];
            for(var i = 0; i < x; ++i) ret[i] = Next<T>();
            return ret;
        }

        public T[][] Next<T>(int y, int x){
            var ret = new T[y][];
            for(var i = 0; i < y; ++i) ret[i] = Next<T>(x);
            return ret;
        }
    }
}