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;
const ll MOD = (ll)1e9 + 7;
int main() {
  int N, x;
  cin >> N >> x;
  vector<int> a(N);
  for (int i = 0; i < N; ++i) {
    cin >> a[i];
  }
  vector<vector<ll>> t(N, vector<ll>(N, 0));
  for (int i = 0; i < N; ++i) {
    t[i][i] = a[i];
    int times = 1;
    int j = i - 1;
    while (j != i) {
      if (j < 0) j = N - 1;
      t[i][j] = a[j];
      if (j == i) break;
      times++;
      j--;
    }
  }
  vector<ll> mini(N);
  ll ans = 0ll;
  for (int i = 0; i < N; ++i) {
    mini[i] = t[i][i];
    ans += mini[i];
  }
  for (int i = 1; i < N; ++i) {
    ll tmp = 0ll;
    for (int j = 0; j < N; ++j) {
      int ref = j - i;
      if (ref < 0) ref = N - ref;
      mini[j] = min(mini[j], t[j][ref]);
      tmp += mini[j];
    }
    ans = min(ans, tmp + (ll)x * i);
  }
  cout << ans << endl;
  return 0;
}
