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 N, x;
long long d[100001];
long long A[100001];
int parent[100001];
void input() {
  cin >> N >> x;
  for (int i = 1; i <= N; i++) cin >> A[i];
}
void solve() {
  for (int i = 1; i <= N; i++) d[i] = 1LL << 60;
  for (int i = 1; i <= N; i++) {
    for (int j = 1; j <= N; j++) {
      int dif = (i - j + N) % N;
      if (d[i] >= A[j] + dif * x) {
        d[i] = A[j] + dif * x;
        parent[i] = j;
      }
    }
  }
  long long ans = 0;
  for (int i = 1; i <= N; i++) ans += A[parent[i]];
  long long max_magic = 0;
  for (int i = 1; i <= N; i++) {
    max_magic = max(max_magic, (d[i] - A[parent[i]]) / x);
  }
  ans += max_magic * x;
  cout << ans << endl;
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  input();
  solve();
  return 0;
}
