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;
long long int a[2000], b[2000];
long long int x;
int N;
int maxa[2000];
int mx = 0;
int main() {
  cin >> N >> x;
  for (int i = 0; i < N; i++) {
    a[i] = 2000000000001;
  }
  for (int i = 0; i < N; i++) {
    long long int ai = 0;
    cin >> ai;
    for (long long int j = 0; j < N; j++) {
      if (a[(i + j) % N] > ai + x * j) {
        maxa[(i + j) % N] = j;
        a[(i + j) % N] = ai + x * j;
        b[(i + j) % N] = ai;
      }
    }
  }
  long long int ret = 0;
  for (int i = 0; i < N; i++) {
    ret += b[i];
  }
  for (int i = 0; i < N; i++) {
    mx = max(mx, maxa[i]);
  }
  ret += mx * x;
  cout << ret << endl;
  return 0;
}
