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>
static std::istream& ip = std::cin;
static std::ostream& op = std::cout;
using namespace std;
int main(int argc, char* argv[]) {
  ;
  int n;
  long long a[2010 + 1];
  long long x;
  bool has1[2010 + 1];
  bool has2[2010 + 1];
  bool* has = has1;
  bool* has_new = has2;
  ip >> n >> x;
  for (int i = 1; i <= n; ++i) {
    ip >> a[i];
    has[i] = false;
  }
  a[0] = 0x1FFFFFFFFFL;
  long long rst = 0;
  for (int i = 1; i <= n; ++i) {
    int jm = 0, jnm = 0;
    for (int j = 2; j <= n; ++j) has_new[j] = has[j - 1];
    has_new[1] = has[n];
    for (int j = 1; j <= n; ++j) {
      if (!has[j]) {
        if (a[j] < a[jm]) jm = j;
      }
      if (!has_new[j]) {
        if (a[j] < a[jnm]) jnm = j;
      }
    }
    if (a[jm] < a[jnm] + x) {
      rst += a[jm];
      has[jm] = true;
    } else {
      swap(has, has_new);
    }
  }
  cout << rst << endl;
  return 0;
}
