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>
const int MAXN = 2000 + 10;
long long answer;
long long N, x;
long long a[MAXN];
long long min[MAXN], pos[MAXN];
int main() {
  scanf("%lld%lld", &N, &x);
  for (int i = 1; i <= N; i++)
    scanf("%lld", &a[i]), min[i] = a[i], pos[i] = i, answer += a[i];
  for (int i = 1; i <= N; i++) {
    long long tans(0);
    for (int j = 1; j <= N; j++) {
      pos[j]--;
      if (pos[j] <= 0) pos[j] = N;
      min[i] = std::min(min[i], a[pos[i]]);
      tans += min[i];
    }
    answer = std::min(answer, tans + x * i);
  }
  printf("%lld\n", answer);
  fclose(stdin), fclose(stdout);
  return 0;
}
