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>
#define fi first
#define se second
#define ll long long
//priority_queue<int, vector<int>, greater<int> > pq;
#define _CRT_SECURE_NO_DEPRECATE
const int N = 33003;
#define rep(i, begin, end) for (__typeof(end) i = (begin) - ((begin) > (end)); i != (end) - ((begin) > (end)); i += 1 - 2 * ((begin) > (end)))
const ll mod =  1e9+7;
using namespace std;
//ll n,s;
multiset<long long> m;
int main(){
ll n;
ll x;
cin>>n>>x;
ans=1e18;
ll a[n];
rep(i,0,n)
cin>>a[i];
rep(i,0,n)
{
	ll y=i*x;
	m.clear();
	rep(j,0,i+1)
	m.insert(a[j]);
	rep(j,0,n)
	{
		y+=*m.begin();
		m.erase(m.find(a[j]));
		m.insert(a[(i+j+1)%n]);
	}
	ans=min(ans,y);
}
cout<<ans;
}