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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;


const int maxn = 2000+100;
typedef long long LL;
const LL INF = 0x3f3f3f3f3f3f3f3f;
LL A[maxn];
int n;
LL x;

LL Min[maxn][maxn];



int main()
{
   // freopen("./test.txt","r",stdin);
    scanf("%d %lld",&n,&x);

    for(int i = 0;i < n;++i)
    {
        scanf("%d",&A[i]);
    }



    for(int i = 0;i < n;++i)
        Min[i][0] = A[i];

    for(int len = 1;len < n;++len)
    {
        for(int i = 0;i < n;++i)
        {
            int reach;
            if(i >= len)
                reach = i-len;
            else
            {
                int lft = len-i;
                reach = n-lft;
            }


            Min[i][len] = min(Min[i][len-1],A[reach]);
        }
    }

    LL res = INF;
    for(int len = 0;len < n;++len)
    {
        LL now = len*x;
        for(int i = 0;i < n;++i)
            now += Min[i][len];

       // printf("**** %lld\n",now);
        res = min(res,now);
    }


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