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
import java.util.Scanner;
import java.util.Arrays;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long x = sc.nextLong();
        long min = Integer.MAX_VALUE;
        int minpos = 0;
        long[] a = new long[n];
        for(int i=0; i<n; i++){
            a[i] = sc.nextLong();
            if(a[i] < min){
                 min = a[i];
                 minpos = i;
            }
        }
        sc.close();
        
        long ans = 0;
        long len = 0;
        long maxlen = 0;
        long ca = Integer.MAX_VALUE;

        for(int i=0; i<n; i++){
            int mpos = i + minpos;
            if(mpos >= n) mpos -= n;
            if(a[mpos] <= ca + (len+1) * x){
                len = 0;
                ca = a[mpos];
            }else{
                len++;
                if(len > maxlen) maxlen = len;
            }
        }

        ans += min;

        for(int i=1; i<n; i++){
            int mpos = i + minpos;
            if(mpos >= n) mpos -= n;
            long nmin = a[mpos];
            for(int j=0; j<maxlen+1; j++){
                int npos = mpos - j;
                if(npos < 0) npos += n;
                if(a[npos] < nmin) nmin = a[npos];
            }
            ans += nmin;
        }
        
        ans += maxlen * x;

        System.out.println(ans);
	}
}
