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 {
    static int n;
    static int x;
    static int[][] dp;
    static int[] a;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        x = sc.nextInt();
        a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        dp = new int[n][n];
        for (int i = 0; i < n; i++) {
            dp[0][i] = a[i];
        }
        for (int i = 1; i < n; i++) {
            for (int j = 0; j < n; j++) {
                dp[i][j] = Math.min(dp[i-1][(n+j-1)%n], dp[i-1][j]);
            }
        }

        int ret = (int) 1e9;
        for (int i = 0; i < n; i++) {
            int sum = 0;
            for (int j = 0; j < n; j++) {
                sum += dp[i][j];
            }
            ret = Math.min(ret, sum+x*i);
        }

        System.out.println(ret);
    }
}
