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 N;
long long cost[(2010LL)];
long long x;
long long a[(2010LL)];
long long co[(2010LL)];
int main() {
  long long ans = 0;
  long long max_m = 0;
  scanf("%d %lld", &N, &x);
  for (int i = 0; i < N; i++) scanf("%lld", &a[i]);
  for (int i = 0; i < N; i++) {
    long long min_cost = ((2010LL) * (1000000010LL));
    long long min_index = i;
    long long tmp = 0;
    for (long long j = 0; j < N; j++) {
      int index = (i - j + N) % N;
      long long cost = a[index] + j * x;
      if (min_cost > cost) {
        min_cost = cost;
        min_index = index;
        tmp = j;
      }
    }
    co[min_index]++;
    max_m = max(max_m, tmp);
  }
  ans = max_m * x;
  for (int i = 0; i < N; i++) {
    ans += a[i] * co[i];
  }
  printf("%lld\n", ans);
  return 0;
}
