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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <limits.h>

typedef struct{
    long long get;
    long long cost;
    long long change;
    long long base;
}slime_t;

int main(void){
    long long n,x;
    scanf("%lld%lld",&n,&x);
    long long ans=0,change=0;
    
    slime_t slime[n];
    for (int i=0; i<n; i++){
        scanf("%lld",&slime[i].get);
        slime[i].cost=slime[i].get;
        slime[i].change=0;
        slime[i].base=i;
    }
    
    for (int i=0; i<n; i++){
        for (int j=0; j<n; j++){
            if (i>=j){
                if (slime[i].cost>slime[j].get+x*(i-j)){
                slime[i].cost=slime[j].get+x*(i-j);
                slime[i].change=i-j;
                slime[i].base=j;
                }
            } else {
                if (slime[i].cost>slime[j].get+x*(n-j+i)){
                slime[i].cost=slime[j].get+x*(n-j+i+1);
                slime[i].change=n-j+i;
                slime[i].base=j;
                }
            }
        }
    }
    
    for (int i=0; i<n; i++){
        if (change<slime[i].change){
            change=slime[i].change;
        }
        ans+=slime[slime[i].base].get;
    }
    ans+=x*change;
    printf("%lld\n",ans);
	return 0 ;
}