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;
template <typename T>
inline bool chkmin(T &a, const T &b) {
  return a > b ? a = b, 1 : 0;
}
template <typename T>
inline bool chkmax(T &a, const T &b) {
  return a < b ? a = b, 1 : 0;
}
const int oo = 0x3f3f3f3f;
const int maxn = 2000;
int n, first;
int a[maxn + 5];
int main() {
  long long ans = LLONG_MAX;
  scanf("%d%d", &n, &first);
  for (int i = (0), i_end_ = (n); i < i_end_; ++i) scanf("%d", a + i);
  for (int i = (1), i_end_ = (n + 1); i < i_end_; ++i) {
    long long tmp = (long long)(i - 1) * first;
    for (int j = (0), j_end_ = (n); j < j_end_; ++j) tmp += a[j];
    chkmin(ans, tmp);
    for (int j = (0), j_end_ = (n); j < j_end_; ++j)
      chkmin(a[j], a[(j - i + n) % n]);
  }
  cout << ans << endl;
  return 0;
}
