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>

static int j,n,x,max,b[2001];

int gettime(int k);

int main(void){
    int c,i,t=0;
    scanf("%d %d",&n,&x);
    int a[n];
    for(i=0;i<n;i++){
        scanf("%d",&a[i]);
    }
    b[0]=a[0];
    c=0;
    for(i=1;i<n;i++){   
        if(b[0]>a[i]){
            b[0]=a[i];
            c=i;
        }
    }
    for(i=1;i<=n-c;i++){
        b[i]=a[c+i];
    }
    for(i=0;i<c;i++){
        b[c+i+1]=a[i];
    }
    for(i=0;i<n;i++){
        t+=gettime(i);
        j=0;
    }
    t+=(max*x);
    printf("%d\n",t);
    return 0;
}

int gettime(int k){
    int bt[k+1],bt2[k+1];
    if(k==0){
        return b[0];
    }
    else{
        bt2[k]=gettime(k-1);
        bt[k]=bt2[k]+x;
        j++;
        if(b[k]<bt[k]){
            return b[k];
        }
        else{
            if(max<j){
                max=j;
            }
            return b[k-j];
        }
    }
}