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;


class A {
    int N;
    long x;
    long[] a,aa;
    long[] ini;
    long[] cost;
    public A() {
        a = new long[2002];
        aa = new long[2002];
        ini = new long[2002];
        cost = new long[2002];
        
    }
    public void run(){
        string[] str = Console.ReadLine().Split(' ');
        N = int.Parse(str[0]);
        x = long.Parse(str[1]);
        str =  Console.ReadLine().Split(' ');
        for(int i=0;i<N;i++){
            aa[i] = a[i] = long.Parse(str[i]);
            ini[i] = a[i];
            cost[i] = 0;
        }
        
        //long maxC = 0;
        //int maxI = -1;
        for(int cnt = 0; cnt < 2*N+2 ; cnt++){
            int now = cnt % N;
            int prev = (cnt+N-1)%N;
            if(a[prev]+x<=a[now]){
                a[now] = a[prev]+x;
                ini[now] = ini[prev];
                cost[now] = cost[prev]+1; 
                /*
                if(cost[now]>maxC){
                    //maxC = cost[now];
                    //maxI = now;
                }*/
            }
        }
        long an = -1;
        for(int maxC = 0; maxC<N+1;maxC++){
            long ans=0;
            for(int i=0;i<N;i++){
                long min = 10000000000;
                for(int j=0;j<=maxC;j++){
                    int now = (i+j)%N;
                    min = Math.Min(min, aa[now]);
                }
                ans += min;
            }
            ans += x* maxC;
            if(an==-1) an = ans;
            an = Math.Min(an, ans);
        }
        /*
        
        long ans=0;
        for(int i=0;i<N;i++){
            if(cost[i]==0) ans += a[i];
        }
        for(int t=1;t<N+1;t++){
            bool changed = false;
            for(int i=0;i<N;i++){
                if(cost[i]>=t){
                    changed = true;
                    if(cost[i]==t){
                        ans += ini[i];
                    }
                }
            }
            if(changed){
                ans += x;
            } else {
                break;
            }
        }*/
        Console.WriteLine(an);
    }
}

class Program {
    static void Main(string[] args){
        A a = new A();
        a.run();
    }
}