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 <cmath>
using namespace std;

typedef long long ll;
typedef pair<ll,ll> P;
ll N,x;
ll A[2001];
ll C[2001][2001];
P D[2001][2001];

int main(){
	cin >> N >> x;
	for(int i=0;i<N;i++){
		cin >> A[i];
		C[0][i] = A[i];
	}
	for(int k=1;k<N;k++){
		for(int i=0;i<N;i++){
			C[k][i] = min(A[(i-k+N)%N],C[k-1][i]);
		}
	}
	ll ans = 1e18;
	for(int k=0;k<N;k++){
		ll now = 0;
		for(int i=0;i<N;i++){
			now += C[k][i];
		}
		ans = min(ans,x*k + now);
	}
	cout << ans << endl;
}