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;
const double PI = 3.14159265358979323846;
const double EPS = 1e-12;
const int INF = numeric_limits<int>::max() / 2;
const int NEG_INF = numeric_limits<int>::min() / 2;
int N, x;
const int MAX_N = 2000;
int A[MAX_N];
int moved[MAX_N];
void solve() {
  for (int i = 0; i < (N); i++) {
    int tmp = A[i];
    for (int j = (1); j < (N); j++) {
      int pos = i - j;
      if (pos < 0) pos += N;
      if (A[pos] + j * x < tmp) {
        tmp = A[pos] + j * x;
        moved[i] = j;
      }
    }
  }
  int max_v = 0;
  for (int i = 0; i < (N); i++) max_v = max(max_v, moved[i]);
  long long ans = max_v * x;
  for (int i = 0; i < (N); i++) {
    int pos = i - moved[i];
    if (pos < 0) pos += N;
    ans += A[pos];
  }
  cout << ans << endl;
}
int main(int argc, char const* argv[]) {
  cin >> N >> x;
  for (int i = 0; i < (N); i++) cin >> A[i];
  solve();
  return 0;
}
