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 unsigned long long ull;
typedef long long ll;

int main(){
	int n;
	ll x;
	cin >> n >> x;
	ll a[n];
	for(int i=0; i<n; i++) cin >> a[i];

	ll b[n][n];
	for(int i=0; i<n; i++){
		b[i][0]=a[i];
		for(int j=0; j<n-1; j++){
			b[i][j+1]=min(b[i][j], a[(i-j-1+n)%n]);
		}
	}

	ll ans=20000*(ll)(1e9);
	for(int k=0; k<=n-1; k++){
		ll tmp=k*x;
		for(int j=0; j<n; j++){
			tmp+=b[j][k];
		}
		ans=min(ans, tmp);
	}
	cout << ans << endl;
	return 0;
}