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;
int a[2010];
int b[2010];
int c[2010][2010];
int main(void) {
  int N, X, Min = 0;
  cin >> N >> X;
  for (int i = 0; i < N; i++) {
    cin >> a[i];
    if (a[Min] > a[i]) Min = i;
  }
  for (int i = 0; i < N; i++) {
    b[i] = a[(Min + i) % N];
  }
  c[0][0] = b[0];
  for (int i = 0; i < N; i++) c[0][i] = b[0];
  for (int i = 1; i < N; i++) {
    c[i][0] = b[i];
    for (int j = 1; j < N; j++) {
      c[i][j] = min(c[i - 1][j - 1], c[i][j - 1]);
    }
  }
  long long int res = 2010 * pow(10, 9);
  for (int i = 0; i < N; i++) {
    long long int tmp = 0;
    for (int j = 0; j < N; j++) {
      tmp += c[j][i];
    }
    tmp += X * i;
    res = min(res, tmp);
  }
  cout << res << endl;
}
