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 {

	static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) {
		int N = sc.nextInt();
		long X = sc.nextInt();
		int[] A = new int[N];
		int[][] min = new int[N][N];
		for (int i = 0; i < N; ++i) {
			A[i] = sc.nextInt();
		}
		for (int i = 0; i < N; ++i) {
			min[i][i] = A[i];
		}
		for (int i = 0; i < N; ++i) {
			for (int j = i + 1; j < N; ++j) {
				min[i][j] = Math.min(min[i][j - 1], A[j]);
			}
		}
		long ans = Long.MAX_VALUE;
		for (int i = 0; i < N; ++i) {
			long cur = X * i;
			for (int j = 0; j < N; ++j) {
				if (j >= i) {
					cur += min[j - i][j];
				} else {
					cur += Math.min(min[0][j], min[N - (i - j)][N - 1]);
				}
			}
			ans = Math.min(ans, cur);
		}
		System.out.println(ans);
	}

}
