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 scan = new Scanner(System.in);
		
		int n = scan.nextInt();
		int x = scan.nextInt();
		int[] a = new int[n];
		int min = 1000000000;
		int minf = 0;
		
		for(int i = 0 ; i < n ; i++){
			
			a[i] = scan.nextInt();
			if(min > a[i]){
				min = a[i];
				minf = i;
			}
			
		}
		
		long sum = 0;
		int max = 0;
		int cnt = 1;
		
		for(int i = 1 ; i < n ; i++){
			//最少の値からスタート
			//System.out.println((minf + i) % n);
			if((a[(minf + i) % n] >= x)){
				cnt++;
			} else {
				sum += a[minf] * cnt;
				minf = (minf + i) % n;
				if(max < cnt){
					max = cnt - 1;
				}
				cnt = 1;
			}
			if((i == (n - 1))){
				sum +=a[minf] * cnt;
				if(max < cnt){
					max = cnt - 1;
				}
			}
		}
		
		sum += max * x;
		System.out.println(sum);
	}
}
