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;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
bool state[100] = {};
ll N;
ll x;
ll ans = 0;
void magic() {
  ans += x;
  for (int i = N; i > 0; i--) {
    state[i] = state[i - 1];
  }
  state[0] = state[N];
}
bool isfin() {
  bool ret = true;
  for (int i = 0; i < N; i++) {
    if (!state[i]) {
      ret = false;
      break;
    }
  }
  return ret;
}
signed main() {
  cin >> N;
  cin >> x;
  vector<ll> a(N);
  for (int i = 0; i < N; i++) {
    cin >> a[i];
  }
  bool ischanged = true;
  ;
  while (!isfin()) {
    ischanged = false;
    for (int i = 0; i < N; i++) {
      if (a[i] < x && !state[i]) {
        ans += a[i];
        state[i] = true;
        ischanged = true;
      }
    }
    if (!ischanged) magic();
  }
  cout << ans << endl;
  return 0;
}
