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.

Examples

Input

2 10
1 100


Output

12


Input

3 10
100 1 100


Output

23


Input

4 10
1 2 3 4


Output

10
#include <iostream>
#include <queue>
#include <set>
#include <cassert>
#include <map>
#include <reverse>
#include <sstream>
using namespace std;

long long a[2010];
int mn[4010][4010];
int main(){
	int N,x;
	cin >> N >> x;
	for(int i = 0 ; i < N ; i++)
		cin >> a[i];
	reverse(a,a+N);

	for(int i = 0 ; i < 4010 ; i++)
		for(int j = 0 ; j < 4010 ; j++)
			mn[i][j] = 2e9;

	for(int i = 0 ;i < N ; i++) cin >> a[i], mn[i][i] = a[i], mn[i+N][i+N] = a[i];
	for(int i = 0 ; i < 2*N ; i++){
		for(int j = i+1 ; j < 2*N ; j++){
			mn[i][j] = min(mn[i][j],min(mn[j][j],mn[i][j-1]));
		}
	}
	long long ans = 1e18;
	//cout << mn[0][0] << endl;
	for(int s = 0 ; s <= N ; s++){	
		long long sub = 0;
		for(int k = 0 ; k < N ; k++){
			sub += mn[k][k+s];
		}
		//cout << s << " " << sub << endl;
		ans = min(ans,sub+s*x);
	}
	cout << ans << endl;
}