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;
void _main();
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  _main();
}
const int inf = INT_MAX / 2;
const long long infl = 1LL << 60;
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
void _main() {
  int N, x;
  cin >> N >> x;
  vector<int> a(N);
  for (int i = 0; i < N; i++) cin >> a[i];
  vector<int> b(N);
  int maxShift = 0;
  for (int i = 0; i < N; i++) {
    long long shortestTime = a[i] + 1;
    for (int shift = 0; shift < N; shift++) {
      const int j = ((i - shift) + N) % N;
      const long long time = a[j] + static_cast<long long>(x) * shift;
      if (chmin(shortestTime, time)) {
        b[i] = j;
        chmax(maxShift, shift);
      }
    }
  }
  long long ans = 0;
  for (int i = 0; i < N; i++) {
    ans += a[b[i]];
  }
  ans += static_cast<long long>(x) * maxShift;
  cout << ans << endl;
}
