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;
mt19937 rnd;
const int N = 2e3 + 10;
int a[N];
long long calc(int i, int j, int n, int x) {
  if (i >= j) {
    return 1ll * (i - j) * x + a[j];
  } else {
    return 1ll * (n - j + i) * x + a[j];
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n, x;
  cin >> n >> x;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  long long ans = 0;
  int cnt = 0;
  for (int i = 1; i <= n; i++) {
    int mem = i;
    for (int j = 1; j <= n; j++) {
      if (calc(i, mem, n, x) > calc(i, j, n, x)) {
        mem = j;
      }
    }
    ans += a[mem];
    if (i >= mem) {
      cnt = max(cnt, i - mem);
    } else {
      cnt = max(cnt, n - mem + i);
    }
  }
  ans += 1ll * x * cnt;
  cout << ans << "\n";
  return 0;
}
