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 <bits/stdc++.h>

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)
#define POW(n) ((n)*(n))
#define ALL(a) (a).begin(),(a).end()
#define cerr if(false) cerr
 
using namespace std;
 
typedef long long ll;
typedef unsigned long long ull;
 
typedef vector<int> vi;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<unsigned long long> vull;

void solve(long long N, long long x, vector<long long> a){
	ll ans = 0;
	ll no_move = 0;
	ll move_max = 0;

	REP(i,N){
		ll min_cost = 1e9;
		ll moves = N*2;
		ll idd = 0;

		REP(j,N){
			if(i == j)continue;

			ll diff = i-j;
			if(diff < 0)diff += N;

			ll cost = a[j] + diff * x;

			if(min_cost == cost){
				moves = min(moves,diff);
				if(moves == diff)idd = j;
			}else{
				min_cost = min(min_cost,cost);
				if(min_cost == cost){
					moves = diff;
					idd = j;
				}	
			}

			// cout << i << " " << j << " " << cost << endl;
		}
		if(min_cost >= a[i]){
			no_move++;
			ans += a[i];
		}else{
			ans += a[idd];
			move_max = max(moves,move_max);
		}
	}

	ans += x*move_max;

	cout << ans << endl;
}



int main(){	
	ios::sync_with_stdio(false);
	long long N;
	long long x;
	cin >> N;
	vector<long long> a(N-1+1);
	cin >> x;
	for(int i = 0 ; i <= N-1 ; i++){
		cin >> a[i];
	}
	solve(N, x, a);
	return 0;
}