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 INF = (1LL << 30) - 1;
int MOD = 1e9 + 7;
int main() {
  long long N, X;
  cin >> N >> X;
  vector<long long> V(N), minval(N), minidx(N);
  for (int i = int(0); i < int(N); ++i) {
    cin >> V[i];
    minval[i] = V[i];
    minidx[i] = i;
  }
  for (int i = int(0); i < int(N); ++i)
    for (int j = int(0); j < int(N); ++j) {
      if (minval[i] > V[(i - j + N) % N] + X * j) {
        minval[i] = V[(i - j + N) % N] + X * j;
        minidx[i] = (i - j + N) % N;
      }
    }
  long long ans = 0, maxi = 0;
  for (int i = int(0); i < int(N); ++i) {
    long long dif = (i - minidx[i] + N) % N;
    ans += V[minidx[i]];
    maxi = max(maxi, dif);
  }
  cout << ans + maxi * X << endl;
}
