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;
int n, x;
int v[2001];
long long calc(int mn) {
  std::vector<int> adr;
  long long sum = 0;
  for (int i = 0; i < n; i++) {
    if (v[i] <= mn) {
      adr.push_back(i);
      sum += v[i];
    }
  }
  int mx = adr[0] + n - adr.back() - 1;
  sum += v[adr[0]] * mx;
  for (int i = 1; i < (int)adr.size(); i++) {
    int dd = adr[i] - adr[i - 1] - 1;
    mx = std::max(mx, dd);
    sum += v[i] * 1LL * dd;
  }
  sum += mx * 1LL * x;
  return sum;
}
int main() {
  scanf("%d %d", &n, &x);
  std::set<int> st;
  for (int i = 0; i < n; i++) {
    scanf("%d", &v[i]);
    st.insert(v[i]);
  }
  long long min = INF * 1LL * INF;
  for (auto &e : st) min = std::min(min, calc(e));
  std::cout << min << std::endl;
}
