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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#define INF 1e18

long long min(long long a,long long b){
  if(a < b){
    return a;
  }
  return b;
}

int main(void){
  int N;
  long long x;
  scanf("%d%lld", &N, &x);

  long long a[N];
  for (int i = 0; i < N; i++) {
    scanf("%lld", &a[i]);
  }

  long long ans = INF;
  long long b[N][N+1];
  for (int i = 0; i < N; i++) {
    b[i][0] = a[i];
  }

  for (int k = 0; k < N; k++) {
    long long sum = 0;
    for (int i = 0; i < N; i++) {
      b[i][k+1] = min(b[i][k], a[i-k >= 0?i-k:N+(i-k)]);
      sum += b[i][k+1];
    }
    ans = min(ans, sum+k*x);
  }

  printf("%lld\n", ans);
  
  return 0;
}