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>
long long int N, x, a[2123], which[2123] = {-1}, how[2123] = {-1}, cou = 0,
                             ans = 0;
int main() {
  scanf("%lld%lld", &N, &x);
  for (int i = 0; i < N; i++) {
    scanf("%lld", &a[i]);
  }
  for (int i = 0; i < N; i++) {
    if (a[i] > x) {
      which[i] = 1;
    }
    if (a[i] <= x) {
      which[i] = 0;
    }
  }
  for (int i = 0; i < N; i++) {
    if (which[i] == 0) {
      for (int j = i + 1; j < N; j++) {
        if (which[j] == 0) {
          break;
        } else {
          cou++;
        }
        if (j == N - 1) {
          j = -1;
        }
      }
      how[i] = cou;
      cou = 0;
    }
  }
  for (int i = 0; i < N; i++) {
    if (how[i] != -1) {
      ans += x * how[i];
      ans += a[i] * how[i];
    }
  }
  for (int i = 0; i < N; i++) {
    if (a[i] <= x) {
      ans += a[i];
    }
  }
  printf("%lld", ans);
  return 0;
}
