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.io.*;
import java.util.*;
public class Main {
  public static void main(String[] args) throws Exception {
    String line = null;
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    line = br.readLine();
    String[] in1 = line.split(" ");
    int nn = Integer.parseInt(in1[0]);
    int xx = Integer.parseInt(in1[1]);
    line = br.readLine();
    String[] cc = line.split(" ");
    int[] data = new int[cc.length];
    for (int i = 0; i < cc.length; i++) {
      data[i] = Integer.parseInt(cc[i]);
    }
// 最小値と合計を求める
    int min = data[0];
    long sum1 = 0L;
    for (int i = 0; i < nn; i++) {
      if (data[i] < min) {
        min = data[i];
      }
      sum1 = sum1 + data[i];
    }
// 毎回魔法を唱える
    long sum2 = 0L;
    sum2 = (min * nn) + (xx * (nn - 1));
// 比較する
    long answer = 0L;
    if (sum1 < sum2) {
      answer = sum1;
    } else {
      answer = sum2;
    }
    System.out.println(answer);
  }
}