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 long long ll;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
const ll INF = 1LL << 60; //MAX 9223372036854775807
ll ans = INF;

int main()
{
ll n , x ;
cin >> n >> x ;
vector<ll> a(n);
rep(i, n){
  cin >> a[i];
}
vector<vector<ll>> v(n, vector<ll>(n,0) );
rep(i,n){
  ll mi;
  rep(j,n){
    mi=min(mi,a[(i-j+n)%n]);
    v[i][j]=mi;
  }
}
rep(i,n){
  ll sum=0;
  rep(j,n){
    sum+=v[j][i];
  }
  ans=min(ans,sum+i*x);
}
cout << ans << endl;

return 0;
}