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;

using ll = long long;

#define rep(i, n) for (int i = 0; i < (int) n; i++)

ll n, x;
vector<ll> a, mi;

ll calc(int pos)
{
  ll res = 0;
  rep(i, n) mi[i] = min(mi[i], a[(i+pos)%n]);
  rep(i, n) res+= mi[i];
  return res + pos * x;
}

int main()
{
  cin >> n >> x;
  rep(i, n) {
    ll t;
    cin >> t;
    a.push_back(t);
    mi.push_back(t);
  }
  ll res = INF;
  rep(i, n) {
    res = min(res, calc(i));
  }
  cout << res << endl;
}