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 long long MOD = pow(10, 9) + 7;
const long long LLINF = pow(2, 61) - 1;
const int INF = pow(2, 30) - 1;
int main() {
  int N;
  long long x;
  cin >> N >> x;
  long long a[N];
  for (int i = 0; i < (int)N; i++) cin >> a[i];
  int ms = 0;
  for (int i = 0; i < (int)N; i++)
    if (a[ms] > a[i]) ms = i;
  long long n = 0, mc = 0, count = 0, result = 0;
  for (int i = 0; i < (int)N; i++) {
    int now = (ms + i) % N;
    if (i == 0)
      n = a[ms];
    else if (n + x * count > a[now]) {
      mc = max(mc, count);
      count = 0;
      n = a[now];
    }
    result += n;
    count++;
  }
  mc = max(mc, count);
  result += (mc - 1) * x;
  cout << result << endl;
  return 0;
}
