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 <vector>
#define ll long long
using namespace std;

int main() {
	int N;
	ll x, ans=0;
	cin >> N >> x;
	vector<ll> a(N), mn(N);
	for(int i=0; i<N; ++i){
	    cin >> a[i];
	    mn[i]=a[i];
	    ans += a[i];
	}
	for(int i=1; i<N; ++i){
	    ll now=0;
	    for(int j=0; j<N; ++j){
	        mn[j]=min(mn[j], a[(j+N-i)%N]);
	        now += mn[j];
	    }
	    ans=min(ans, now+x*i);
	}
	cout << ans << endl;
	return 0;
}
