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 long long MOD = 1000000007;
const int INF = 1e9;
const long long LINF = 1LL * INF * INF;
const int MAXN = 2007;
const double EPS = 1e-7;
long long A[MAXN], S[MAXN];
int main() {
  ios_base::sync_with_stdio(0);
  int n;
  long long x, ans = 0, maxs = 0;
  cin >> n >> x;
  for (int i = (0); i < (n); ++i) cin >> A[i];
  for (int i = (0); i < (n); ++i) {
    int b = 0;
    for (int j = (1); j < (n); ++j) {
      if (A[(i - j + n) % n] + x * max(maxs, S[(i - j + n) % n] + j) <
          A[(i - b + n) % n] + x * max(maxs, S[(i - b + n) % n] + b))
        b = j;
    }
    maxs = max(maxs, S[(i - b + n) % n] + b);
    ans += A[(i - b + n) % n];
  }
  cout << ans + x * maxs;
  return 0;
}
