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>
const int INF = (int)1e9;
const long long MOD = (long long)1e9 + 7;
const long long LINF = (long long)1e18;
const double PI = acos(-1.0);
const double EPS = 1e-9;
using namespace ::std;
void solve() {
  int N;
  long long X;
  cin >> N >> X;
  vector<long long> A(N);
  for (int i = 0; i < N; ++i) {
    cin >> A[i];
  }
  vector<long long> org(N);
  vector<long long> time(N, 0);
  for (int i = 0; i < N; ++i) {
    long long res = LINF;
    long long num = i;
    long long Xnum = 0;
    for (int x = 0; x < N; ++x) {
      long long No = (i - x + N) % N;
      long long temp = A[No] + x * X;
      if (temp < res) {
        res = temp;
        num = No;
        Xnum = x;
      }
    }
    org[i] = num;
    time[i] = Xnum;
  }
  long long ans = 0;
  long long maxX = 0;
  for (int i = 0; i < N; ++i) {
    ans += A[org[i]];
    maxX = max(maxX, time[i]);
  }
  ans = ans + maxX * X;
  cout << ans << endl;
}
signed main(void) {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);
  std::cout << std::fixed;
  cout << setprecision(16);
  solve();
}
