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>
using namespace std;

typedef long long ll;
typedef pair<ll,ll> P;
ll N,x;
ll A[2001];
ll C[2001][2001];
P D[2001][2001];

int main(){
	cin >> N >> x;
	for(int i=0;i<N;i++){
		cin >> A[i];
		C[i][0] = A[i];
		D[i][0] = P(i,0);
	}
	for(int j=1;j<N;j++){
		for(int i=0;i<N;i++){
			if(C[i][j-1]>C[(i+N-j)%N][0] + j*x){
				C[i][j] = C[(i+N-j)%N][0] + j*x;
				D[i][j] = P((i+N-j)%N,j);
			}else{
				C[i][j] = C[i][j-1];
				D[i][j] = D[i][j-1];
			}
		}
	}
	ll ans = 1e18;
	for(int j=0;j<N;j++){
		ll now = 0;
		ll magic = 0;
		for(int i=0;i<N;i++){
			now += A[D[i][j].first];
			magic = max(magic,D[i][j].second);
		}
		ans = min(now + magic*x,ans);
	}
	cout << ans << endl;
}