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;
long long cost[2000];
long long nx[2000];
long long from[2000];
long long ai[2000];
int main() {
  int n, x;
  cin >> n >> x;
  for (int i = 0; i < n; i++) {
    cin >> ai[i];
    cost[i] = ai[i];
    nx[i] = 0;
    from[i] = i;
  }
  for (int i = 0; i < n; i++) {
    for (int j = 1; j < n; j++) {
      int pos = (i + j) % n;
      if (cost[pos] > ai[i] + x * j) {
        cost[pos] = ai[i] + x * j;
        nx[pos] = j;
        from[pos] = i;
      }
    }
  }
  int nxmax = 0;
  long long ret = 0;
  for (int i = 0; i < n; i++)
    if (nx[i] > nxmax) nxmax = nx[i];
  for (int inx = nxmax; inx >= 0; inx--) {
    for (int i = 0; i < n; i++) {
      if (inx == nx[i]) {
        ret += ai[from[i]];
      }
    }
    ret += x;
  }
  ret -= x;
  cout << ret << endl;
}
