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;
int main() {
  int n, x;
  scanf("%d %d", &n, &x);
  vector<int> a(n);
  for (int i = 0; n > i; i++) {
    scanf("%d", &a[i]);
  }
  long long int ans;
  long long int hokaku_time = 0;
  int Magic_time = 0;
  for (int i = 0; n > i; i++) {
    long long int Mintime = LLONG_MAX;
    pair<int, int> hm;
    for (int j = 0; n > j; j++) {
      long long int guru;
      if (j > i)
        guru = n - j + i;
      else
        guru = i - j;
      if (Mintime >= (a[j] + guru * x)) {
        Mintime = a[j] + guru * x;
        hm.first = a[j];
        hm.second = guru;
      }
    }
    hokaku_time += hm.first;
    Magic_time = max(Magic_time, hm.second);
  }
  ans = hokaku_time + Magic_time * x;
  for (int ccou = Magic_time - 1; 0 <= ccou; ccou--) {
    long long int bufans = 0;
    int guru = 0;
    for (int i = 0; n > i; i++) {
      int Minhok = INT_MAX;
      for (int j = 0; ccou > j; j++) {
        int num = i - j;
        if (num < 0) num = n - num;
        if (Minhok > a[j]) guru = max(guru, ccou);
        Minhok = min(Minhok, a[j]);
      }
      bufans += Minhok;
    }
    bufans += (long long int)ccou * guru;
    ans = min(ans, bufans);
  }
  printf("%lld\n", ans);
  return 0;
}
