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;
const int N = 4e3 + 5;
int n, start;
long long f[N], x, a[N], ans;
long long A(int mx) {
  memset(f, 0x7f, sizeof(f));
  f[start - 1] = 0;
  for (int i = start; i < start + n; i++)
    for (int j = i; j >= i - mx && j >= start; j--)
      f[i] = min(f[i], f[j - 1] + a[j] * (i - j + 1));
  return f[n + start - 1] + mx * x;
}
int main() {
  cin >> n >> x;
  a[0] = 1e9;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    a[i + n] = a[i];
    if (a[start] > a[i]) start = i;
    ans += a[i];
  }
  for (int i = 1; i < n; i++) ans = min(ans, A(i));
  cout << ans << endl;
}
