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 i32 = int32_t;
using i64 = int64_t;
using f64 = double_t;
using str = string;
template <typename T>
using vec = vector<T>;
template <typename T>
using heap = priority_queue<T, vec<T>, greater<T>>;
const i64 MOD = 1000000007;
i32 n, x;
i64 a[2000], b[2000];
i32 main() {
  cin >> n >> x;
  for (i32 i = 0; i < (n); ++i) {
    cin >> a[i];
    b[i] = a[i];
  }
  i64 ans = INT_MAX;
  for (i32 i = 0; i < (n); ++i) {
    i64 t = 0;
    for (i32 j = 0; j < (n); ++j) {
      b[j] = min(b[j], a[(j - i + n) % n]);
      t += b[j];
    }
    t += x * i;
    ans = min(ans, t);
  }
  cout << ans << endl;
  return 0;
}
