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>
#include <map>
#include <algorithm>
#include <math.h>
using namespace std;
typedef long long int ll;

int main(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	ll n,x; cin >> n >> x;
	vector<ll> a(n),b(n);
	for(int i=0;i<n;i++){
		cin >> a[i];
	}
	b=a;
	ll ans=1e18;
	for(int i=0;i<n;i++){
		// 色変する回数の最大値
		ll res=x*i;
		for(int j=0;j<n;j++){
			res+=b[j];
		}
		ans=min(ans,res);
		for(int j=0;j<n;j++){
			b[j]=min(b[j],a[(j-i-1+n)%n]);
		}
	}
	cout << ans << endl;
}