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;
const unsigned long long BASE = 107;
const long long LINF = 9e18 + 7;
const int N = 5e2 + 7;
const int INF = 1e9 + 7;
const int MOD = 1e9 + 7;
const double PI = acos(-1.0);
const double EPS = 1e-8;
int n, x, a[N], f[N][N];
void init() {
  for (int i = (0); i < (n); ++i) {
    f[i][0] = a[i];
    for (int j = (1); j < (n); ++j)
      f[i][j] = min(f[i][j - 1], a[(i - j + n) % n]);
  }
}
long long solve(long long d) {
  long long ret = x * d;
  for (int i = (0); i < (n); ++i) ret += f[i][d];
  return ret;
}
int main() {
  cin >> n >> x;
  for (int i = (0); i < (n); ++i) cin >> a[i];
  init();
  long long ans = solve(0);
  for (int i = (1); i < (n); ++i) ans = min(ans, solve(i));
  cout << ans;
  return 0;
}
