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 MOD = 1000000007;
const int MAX = 510000;
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  long long n, x, a[3999], d[3999][3999], ans = 0, sec = 0;
  cin >> n >> x;
  for (long long i = 0; i < n; i++) cin >> a[i];
  for (long long i = 0; i < n; i++) {
    for (long long j = 0; j < n; j++) {
      long long cnt = j - i;
      if (cnt < 0) cnt += n;
      d[i][j] = a[i] + cnt * x;
    }
  }
  for (long long i = 0; i < n; i++) {
    long long m = (1 << 30) - 1, s = (1 << 30) - 1, A;
    for (long long j = 0; j < n; j++) {
      if (m >= d[j][i]) {
        A = a[j];
        s = (d[j][i] - a[j]) / x;
        m = min(m, d[j][i]);
      }
    }
    sec = max(s, sec);
    ans += A;
  }
  cout << ans + sec * x << endl;
  return 0;
}
