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;
bool allTypeExists(bool a[2000], int n) {
  for (int i = 0; i < (n); i++) {
    if (a[i] == 0) return 0;
  }
  return 1;
}
void useMagical(bool a[2000], int n) {
  bool copy[2000];
  for (int i = 0; i < (n - 1); i++) {
    copy[i + 1] = a[i];
  }
  copy[0] = a[n - 1];
  for (int i = 0; i < (n); i++) a[i] = copy[i];
}
int main() {
  int n, x, a[2000];
  long long time = 0;
  bool isCaught[2000] = {0};
  cin >> n >> x;
  for (int i = 0; i < (n); i++) cin >> a[i];
  while (not allTypeExists(isCaught, n)) {
    int smallest = (1 << 29), p;
    bool check = 0;
    for (int i = 0; i < (n); i++) {
      if (smallest > a[i]) {
        smallest = a[i];
        p = i;
      }
      if (a[i] <= x && isCaught[i] == 0) {
        check = 1;
        isCaught[i] = 1;
        time += a[i];
      }
    }
    if (not check) {
      isCaught[p] = 1;
      time += smallest;
    }
    if (allTypeExists(isCaught, n)) break;
    useMagical(isCaught, n);
    time += x;
  }
  cout << time << endl;
}
