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.awt.geom.Line2D;
import java.awt.geom.Point2D;
import java.awt.geom.Point2D.Double;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.TreeSet;
import java.lang.Object;
 
public class Main {
    Scanner sc = new Scanner(System.in);
   
    public static void main(String[] args) {
        new Main(); 
    }
   
    public Main() {
        new B().doIt();
    }
    class B{
    	void doIt(){
    		int N = sc.nextInt();
    		long x = sc.nextLong();
    		long a[][] = new long[N][N];
    		for(int i = 0;i < N;i++){
    			a[i][0] = sc.nextLong();
    		}
    		long sum = 0;
    		for(int j = 0;j < N;j++){
    			for(int i = 0;i < N;i++){
    				a[(j+i) % N][i] = a[j][0];
    			}
    		}
    		int cnt = 0;
    		for(int j = 0;j < N;j++){
    			int pos = 0;
    			for(int i = 0;i < N;i++){
    				if(a[j][pos] >= a[j][i] + (x * i)){
    					pos = i;
    					cnt = Math.max(cnt, i);
    				}
//    				System.out.print(a[j][i]+" ");
    			}
    			sum = sum + a[j][pos];
//    			System.out.println();
    		}
    		sum = sum + (x * (long)cnt);
    		System.out.println(sum);
    	}
    }
}