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 sc = new Scanner(System.in);
		long n = sc.nextLong();
		long x= sc.nextLong();
		long[] a = new long[2*(int)n];
		for (int i = 0; i<n; i++) {
			a[i]=sc.nextLong();
			a[i+(int)n]=a[i];
		}
		long[][] costs = new long[(int)n][(int)n];
		for (int i = (int)n; i<2*n; i++) {
			long best=a[i];
			for (int j=0; j<n; j++) {
				best=Math.min(best, a[i-j]);
				costs[i-(int)n][j]=best;
			}
		}
		long best = n*1000000000;
		for (int j = 0; j<n;j++) {
			long curr = j*x;
			for (int i = 0; i<n; i++) {
				curr+=costs[i][j];
			}
			best=Math.min(best, curr);
		}
		System.out.println(best);
	}
}