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);
		Integer n = sc.nextInt();
		Integer x = sc.nextInt();
		Long[] cost = new Long[n];
		Long[] tmpA = new Long[n];
		Long[] a = new Long[n];
		Integer minIdx = 0;
		for (int i = 0; i < n; i++) {
			cost[i] = 0L;
			tmpA[i] = sc.nextLong();
		}
		for (int i = 0; i < n; i++) {
			if (tmpA[minIdx] > tmpA[i])
				minIdx = i;
		}
		for (int i = minIdx; i < n; i++) {
			a[i - minIdx] = tmpA[i];
		}
		for (int i = 0; i < minIdx; i++) {
			a[i + (n - minIdx)] = tmpA[i];
		}

		for (int i = 0; i < n; i++) {
			if (i == 0) {
				cost[i] = a[i];
			} else {
				Long direct = a[i];
				Long indirect = a[0] + x;
				if (direct > indirect) {
					cost[i] = cost[i - 1] + indirect;
				} else {
					cost[i] = cost[i - 1] + direct;
				}
			}
		}
		System.out.println(cost[n - 1]);
	}
}
