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 <iomanip>
#include <string>
#include <vector>
#include <queue>
#include <algorithm>
#include <utility>
#include <cmath>

#define INF_LL 9000000000000000000
#define INF 2000000000

#define REP(i, n) for(int i = 0;i < (n);i++)
#define FOR(i, a, b) for(int i = (a);i < (b);i++)

using namespace std;

typedef long long ll;
typedef pair<int, int> PII;

class Union_find{
private:
	vector<int> par;
	vector<int> rank;
	int n;

public:
	Union_find(int a){
		n = a;
		for(int i = 0;i < n;i++){
			par.push_back(i);
			rank.push_back(0);
		}
	}

	int find(int x){
		if(par[x] == x){
			return x;
		}else{
			return par[x] = find(par[x]);
		}
	}

	void unite(int x, int y){
		x = find(x);
		y = find(y);
		if(x == y) return;

		if(rank[x] < rank[y]){
			par[x] = y;
		}else{
			par[y] = x;
			if(rank[x] == rank[y]) rank[x]++;
		}
	}

	bool same(int x, int y){
		return find(x) == find(y);
	}
};

int main(void){
	int n;
	int a[2000];
	int x;
	int cost[2000];
	int max_c = 0;
	
	cin >> n >> x;
	REP(i, n){
		cost[i] = INF;
		cin >> a[i];
		cost[i] = a[i];
	}

	ll res = 0;
	REP(i, n){

		cost[i] = a[i];
		for(int j = 0;a[i] > j*x;j++){
			int index = i-j;
			if(index < 0){
				index = n + index;
			}
			if(cost[i] > a[index]+x*j){
				cost[i] = a[index];
				if(j > max_c)
					max_c = j;
			}
		}
		res += cost[i];
	}
	cout << res+x*max_c << endl;
}