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.*;

import static java.lang.System.*;

public class Main {
    static Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        int N = ni();
        long x = nl();
        long[] a = nlarr(N);

        int[] magicCnt = new int[N];
        long[] baseCost = new long[N];
        long pre = a[0];
        // repeat twice to check if N - 1 to 0 works.
        for (int i = 1; i < 2 * N - 1; i++) {
            int ii = i < N ? i : i - N;
            int ipre = i - 1 < N ? i - 1 : i - 1 - N;

            if (a[ii] > pre + x * (magicCnt[ipre] + 1)) {
                magicCnt[ii] = magicCnt[ipre] + 1;
            } else {
                pre = a[ii];
            }
            baseCost[ii] = pre;
        }

        int maxMagicCnt = 0;
        long time = 0;
        for (int i = 0; i < N; i++) {
            if (magicCnt[i] != 0) {
                maxMagicCnt = Math.max(maxMagicCnt, magicCnt[i]);
            }
            time += baseCost[i];
        }

        out.println(time + maxMagicCnt * x);
    }

    static int ni() {
        return sc.nextInt();
    }

    static long nl() {
        return sc.nextLong();
    }

    static String ns() {
        return sc.next();
    }

    static int[] niarr(int N) {
        int[] a = new int[N];
        for (int i = 0; i < N; i++) {
            a[i] = sc.nextInt();
        }
        return a;
    }

    static long[] nlarr(int N) {
        long[] a = new long[N];
        for (int i = 0; i < N; i++) {
            a[i] = sc.nextLong();
        }
        return a;
    }
}