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.*;
import java.util.stream.*;
import java.io.*;

public class Main {
    
    public static void main(String[] args) throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] in1 = br.readLine().split(" ");
        int N = Integer.parseInt(in1[0]);
        long x = Long.parseLong(in1[1]);
        
        in1 = br.readLine().split(" ");
        long[] a = Stream.of(in1).mapToLong(Long::parseLong).toArray();
        br.close();

        long[] b = a.clone();
        long ans = 0L;
        for(int i = 0; i < N; i++){
            ans += b[i];
        }

        for(int i = 1; i < N; i++){
            for(int j = 0; j < N; j++){
                b[j] = Math.min(b[j], a[(j - i + N)%N]);
            }
            long tmp_ans = i * x;
            for(int j = 0; j < N; j++){
                tmp_ans += b[j];
            }
            ans = Math.min(ans, tmp_ans);
        }

        System.out.println(ans);
    }
}