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;
int main() {
  int N, x;
  cin >> N >> x;
  vector<ll> a(N);
  for (int i = 0; i < N; ++i) {
    cin >> a[i];
  }
  ll ret = 0;
  vector<bool> used(N, false);
  for (int j = 0; j < N; ++j) {
    ll min_a = 1e9 + 1;
    int idx = 0;
    bool rot = false;
    int prev = 0;
    for (int i = N - 1; i >= 0; --i) {
      if (!used[i]) {
        prev = i;
        break;
      }
    }
    for (int i = 0; i < N; ++i) {
      if (used[i]) {
        int dist = 0;
        if (prev > i) {
          dist = N - prev + i;
        } else {
          dist = i - prev;
        }
        if (min_a > a[i] + dist * x) {
          min_a = a[i] + dist * x;
          idx = i;
          rot = true;
        }
      } else {
        if (min_a > a[i]) {
          idx = i;
          min_a = a[i];
          rot = false;
          prev = i;
        }
      }
    }
    if (rot) {
      rotate(used.rbegin(), used.rbegin() + 1, used.rend());
    }
    used[idx] = true;
    ret += min_a;
    if (find(used.begin(), used.end(), false) == used.end()) {
      break;
    }
  }
  cout << ret << endl;
}
