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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int N = scan.nextInt();
		long x = scan.nextLong();

		List<Long> srimeList = new ArrayList<>(N);
		for (long i = 0; i < N; i++) {
			srimeList.add(scan.nextLong());
		}

		List<Long[]> costList = new ArrayList<>();
		for (int i = 0; i < N; i++) {
			costList.add(new Long[N]);
		}
		for (int i = 0; i < N; i++) {
			costList.get(i)[0] = srimeList.get(i);
			for (int castNum = 1; castNum < N; castNum++) {
				costList.get(i)[castNum] = Math.min(costList.get(i)[castNum - 1],
						srimeList.get((i - castNum + N) % N));
			}
		}
		List<Long> result = new ArrayList<>();
		for (int i = 0; i < N; i++) {
			final int j = i;
			result.add(i * x + costList.stream().mapToLong(costArray -> costArray[j]).sum());
		}
		System.out.println(result.stream().mapToLong(i -> i).min().getAsLong());
	}

}
