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>
const long long INF = (1LL << 59);
using namespace std;
int main() {
  int n, x;
  cin >> n >> x;
  long long dp[2000][2] = {0};
  long long a[2000];
  for (int i = 0; i < (n); i++) cin >> a[i];
  for (int i = 0; i < (n); i++) dp[i][0] = INF;
  for (int i = 0; i < (n); i++) {
    int parent;
    for (int j = 0; j < (n); j++) {
      int diff;
      if (i <= j)
        diff = j - i;
      else if (i > j)
        diff = n - (i - j);
      if (dp[i][0] > diff * x + a[j]) {
        dp[i][0] = diff * x + a[j];
        parent = j;
      }
    }
    assert(parent < 2000);
    assert(parent >= 0);
    dp[parent][1]++;
  }
  long long sum = 0;
  for (int i = 0; i < (n); i++) sum += dp[i][1] * a[i];
  long long maxi = 0;
  for (int i = 0; i < (n); i++) maxi = max(maxi, dp[i][1]);
  if (maxi) sum += (maxi - 1) * x;
  cout << sum << endl;
}
