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;
int64_t N, x;
int main() {
  cin >> N >> x;
  vector<int64_t> a(N);
  for (int i = 0; i < N; i++) {
    cin >> a[i];
  }
  vector<vector<int64_t>> min_value(N, vector<int64_t>(N, INT_MAX));
  for (int i = 0; i < N; i++) {
    int j = i;
    min_value[i][j] = a[i];
    for (int k = 0; k < N - 1; k++) {
      j = (j + 1) % N;
      min_value[i][j] = min(a[j], min_value[i][(j - 1 + N) % N]);
    }
  }
  uint64_t ans = INT_MAX;
  for (int i = 0; i < N; i++) {
    uint64_t tmp = i * x;
    priority_queue<pair<int, int>> pq;
    for (int j = 0; j < N; j++) {
      pq.push({a[j] - min_value[(j - i + N) % N][j], j});
    }
    auto copy = a;
    for (int j = 0; j < i; j++) {
      auto t = pq.top();
      pq.pop();
      copy[t.second] -= t.first;
    }
    tmp += accumulate(copy.begin(), copy.end(), 0LL);
    ans = min(ans, tmp);
  }
  cout << ans << endl;
}
