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: Wrong Answer)

#include<stdio.h>
int MIN(int a,int b){return a<b?a:b;}
int main(){
  int n,m,i,j,d[4010],max,s,min=1e9,k;
  scanf("%d %d",&n,&m);
  for(i=0;i<n;i++)scanf("%d",&d[i]);
  for(i=0;i<n;i++)d[i+n]=d[i];
  for(i=0;i<n;i++){
    for(j=max=s=0;j<n;j+=k){
      s+=d[i+j];
      for(k=1;k<n;k++){
	if(max>=k){
	  if(d[i+j]>d[i+j+k])break;
	  s+=d[i+j];
	}
	else{
	  if(d[i+j]+m>d[i+j+k])break;
	  s+=d[i+j]+m;
	}
      }//printf("%d ",s);
      if(max<k-1)max=k-1;
      //j+=k;
    }//printf("%d\n",s);
    if(min>s)min=s;
  }
  printf("%d\n",min);
  return 0;
}