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<bits/stdc++.h>
using namespace std;
typedef pair<int, int> P;
typedef long long ll;

int main(){
	ll N, x; cin >> N >> x;
	ll a[N];
	for(int i=0; i<N; i++) cin >> a[i];
	int min_cost[N][N];
	for(int i=0; i<N; i++){
		for(int j=0; j<N; j++){
			if(i==0) min_cost[j][i] = a[j];
			else{
				if(min_cost[j][i-1] > a[(j+N-i)%N]) time[j][i] = a[(j+N-i)%N];
			}
		}
	}
	ll ans = 1e18;
	for(int i=0; i<N; i++){
		ll cnt = x*i;
		for(int j=0; j<N; j++){
			cnt += time[j][i];
		}
		if(ans > cnt) ans = cnt;
	}
	cout << ans << endl;
	return 0;
}