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;
int main() {
  int N;
  long long x;
  cin >> N >> x;
  vector<long long> a(N * 2);
  for (auto i = 0; i < N; ++i) {
    cin >> a[i];
    a[i + N] = a[i];
  }
  auto maxX = 0;
  auto ans = 0ll;
  for (auto i = 0; i < N; ++i) {
    auto minSec = LLONG_MAX;
    auto count = 0;
    auto val = 0ll;
    for (auto j = 0; j < N; ++j) {
      auto next = i - j + N;
      if (minSec > a[next] + x * j) {
        minSec = a[next] + x * j;
        count = j;
        val = a[next];
      }
    }
    ans += val;
    maxX = max(count, maxX);
  }
  ans += x * maxX;
  cout << ans << endl;
  return 0;
}
