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;
int a[2000];
int dp[2000][2];
void solve() {
  long long ans = 0;
  cin >> N >> x;
  for (int i = 0; i < (N); i++) {
    cin >> a[i];
    dp[i][0] = 0;
    dp[i][1] = a[i];
  }
  long long max_m = 0;
  for (int i = 0; i < (N); i++) {
    int n = N;
    for (int j = (i + 1); j < (i + N); j++) {
      n--;
      int d = n * 10;
      int b = a[j % N];
      if (dp[i][0] + dp[i][1] > d + b) {
        dp[i][0] = d;
        dp[i][1] = b;
        max_m = (dp[i][0] > max_m ? dp[i][0] : max_m);
      }
    }
  }
  for (int i = 0; i < (N); i++) {
    ans += dp[i][1];
  }
  cout << ans + max_m << endl;
}
int main(void) {
  cin.tie(0);
  ios::sync_with_stdio(false);
  solve();
  return 0;
}
