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() {
  long long unsigned int n, x;
  long long unsigned int a[3777] = {};
  scanf("%llu%llu", &n, &x);
  for (int i = 0; i < n; i++) {
    scanf("%llu", &a[i]);
  }
  long long unsigned int ans[3334] = {};
  long long unsigned int trans = 0;
  fill(ans, ans + n, (1e9) * 66661111);
  long long unsigned int answer = 0;
  for (int i = 0; i < n; i++) {
    for (int j = i + n; j > i; j--) {
      if (ans[i] > a[j % n] + x * ((j - i + n) % n)) {
        ans[i] = a[j % n];
        trans = max<long long unsigned int>((j - i + n) % n, trans);
      }
    }
    answer += ans[i];
  }
  printf("%llu\n", answer + trans * x);
  return 0;
}
