Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

2 10
1 100

Sample Output 1

12

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Cast the spell. The color of the slime changes: 1 → 2. This takes 10 seconds.

Catch a slime in color 1. This takes 1 second.

Sample Input 2

3 10
100 1 100

Sample Output 2

23

Snuke can act as follows:

Catch a slime in color 2. This takes 1 second.

Cast the spell. The color of the slime changes: 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Cast the soell. The color of each slime changes: 3 → 1, 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Sample Input 3

4 10
1 2 3 4

Sample Output 3

10

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Catch a slime in color 2. This takes 2 seconds.

Catch a slime in color 3. This takes 3 seconds.

Catch a slime in color 4. This takes 4 seconds.

Solution in Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.*;

class Main{
  public static void main(String[] args) {
    Scanner scan = new Scanner(System.in);

    int n = scan.nextInt();
    long x = scan.nextLong();
    long[][] dp = new long[n][n];
    for(int j = 0; j < n; j++) {
      dp[0][j] = scan.nextLong();
    }
    for(int i = 1; i < n; i++) {
      for(int j = 0; j < n; j++) {
        dp[i][j] = Math.min(dp[i-1][j], dp[0][(j-i+n)%n]);
      }
    }
    long result = 1L<<60;
    for(int i = 0; i < n; i++) {
      long dummyResult = i*x;
      for(int j = 0; j < n; j++) {
        dummyResult += (long)dp[i][j];
      }
      result = Math.min(result,dummyResult);
    }
    System.out.println(result);
  }
}