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;

public class Main {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int N = s.nextInt();
		int x = s.nextInt();
		int[] a = new int[N];
		int[] a2 =new int[N];
		for(int i=0;i<N;i++){
			a[i]=s.nextInt();
		}
		int min=a[0];
		int minno=0;
		for(int i=1;i<N;i++){
			min=Math.min(min, a[i]);
			if(min==a[i]){
				minno=i;
			}
		}
		
		long t= a[minno];
		int count = 0;
		int countm = 0;
		int t2=a[minno];
		a2[minno]=a[minno];

		for(int i=minno+1;i<N;i++){
			if(a[i]<=t+x){
				count=0;
				t=a[i];
				a2[i]=a[i];
				t2=a[i];
			}else{
				count++;
				t=t+x;
				a2[i]=t2;
			}
			if(count>countm){
				countm=count;
			}
		}
		for(int i=0;i<minno;i++){
			if(a[i]<=t+x){
				count=0;
				t=a[i];
				a2[i]=a[i];
				t2=a[i];
			}else{
				count++;
				t=t+x;
				a2[i]=t2;
			}
			if(count>countm){
				countm=count;
			}
		}
		
		long result=(long)countm*x;
		for(int i=0;i<N;i++){
			result+=(long)a2[i];
		}
		System.out.println(result);
	}
}