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) {
		new Main().solve();
	}
	
	void solve(){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int x=sc.nextInt();
		int[]a=new int[n];
		for(int i=0;i<n;i++)a[i]=sc.nextInt();
		
		int[] magic=new int[n];
		
		for(int k=0;k<n;k++){
		for(int i=0;i<n;i++){
			if(i==0){
				if(a[i]>a[n-1]+x){
					a[i]=a[n-1]+x;
					magic[i]++;
				}
			}else{
				if(a[i]>a[i-1]+x){
					a[i]=a[i-1]+x;
					magic[i]++;
				}
			}
		}
		}
		int magic_max=0;
		for(int i=0;i<n;i++){
			magic_max=Math.max(magic_max, magic[i]);
			a[i]-=magic[i]*10;
		}
		long sum_time=0;
		for(int i=0;i<n;i++){
			sum_time+=a[i];
		}
		sum_time+=magic_max*10;
		System.out.println(sum_time);
	}

}