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: Wrong Answer)

#include<iostream>
#include<vector>
#include<string>
#include<array>
#include<cmath>
#include<algorithm>
#include<map>
#include<set>
#include<queue>
#include<numeric>
#include<iomanip>
#include<utility>
#include<cstdlib>
#include<typeinfo>


using namespace std;
#define INF 1000000005
int main()
{
int n,x;
std::cin >> n >> x;
std::vector<int> a;
for(int i = 0; i < n; i++){
    int temp;
    std::cin >> temp;
    a.push_back(temp);
}
std::vector<std::vector<long long int>> small;

std::vector<long long int> smallf;
smallf.push_back(a[0]);
for(int i = 1; i < n; i++){
    smallf.push_back(a[i]);
}
small.push_back(smallf);

int flag = 0;
for(int j = 1; j < n; j++){
    std::vector<long long int> smallt;
    if(small[j - 1][0] >= x + small[j - 1][n - 1]){
        flag = j;
        smallt.push_back(x + small[j - 1][n - 1]);
    } else {
        smallt.push_back(small[j - 1][0]);
    }
    for(int i = 1; i < n; i++){
    if(small[j - 1][i] >= x + small[j - 1][i - 1]){
        flag = j;
        smallt.push_back(x + small[j - 1][i - 1]);
    } else {
        smallt.push_back(small[j - 1][i]);
    }
    }
small.push_back(smallt);
}
for(int j = 1; j <= flag; j++){
    if(small[j - 1][0] >=small[j - 1][n - 1]){
        small[j][0] = small[j - 1][n - 1];
    } else {
        small[j][0] = small[j - 1][0];
    }
    for(int i = 1; i < n; i++){
    if(small[j - 1][i] >= small[j - 1][i - 1]){
        small[j][i] = small[j - 1][i - 1];
    } else {
        small[j][i] = small[j - 1][i];
    }
    }
}

long long int sum = 0;
int count = 0;
int fsum = 0;
int same = 0;
for(int i = 0; i < n; i++){
    count = 0;
    int tf = 0;
    long long int min = small[0][i];
    for(int j = 1; j < n; j++){
        if(small[j][i] < min){
            tf = count;
            min = small[j][i];
        }
    }
    fsum += tf;
    sum += min;
}
std::cout << sum + flag * x<< std::endl;
return 0;
}