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;
using ll = long long;
constexpr int mo = 1e9 + 7;
constexpr int mod = mo;
constexpr int inf = 1 << 30;
constexpr int mo2 = 998244353;
int main() {
  int n, x;
  cin >> n >> x;
  vector<int> v(n);
  for (auto &a : v) cin >> a;
  ll ret = 1ll * accumulate(v.begin(), v.end(), 0);
  for (int i = 1; i < n; ++i) {
    int tmp = v[n - 1];
    for (int j = n - 1; j > 0; j--) {
      v[j] = min(v[j - 1], v[j]);
    }
    v[0] = min(v[0], tmp);
    ret = min(ret, 1ll * accumulate(v.begin(), v.end(), 0) + 1ll * i * x);
  }
  cout << ret << endl;
  return 0;
}
