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 int N = 2005;
int n, x, a[N], mn = 2e9, pos;
vector<int> v;
int main() {
  scanf("%d %d", &n, &x);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 1; i <= n; i++) {
    if (a[i] < mn) {
      mn = a[i];
      pos = i;
    }
  }
  for (int i = pos; i <= n; i++) v.push_back(a[i]);
  for (int i = 1; i < pos; i++) v.push_back(a[i]);
  long long ans = 0;
  int Max = 0;
  for (int i = 0; i < v.size(); i++) {
    long long cur = 1e18;
    pos = i;
    for (int j = 0; j <= i; j++) {
      if (1LL * x * max(Max, i - j) + v[j] < cur) {
        cur = 1LL * x * max(Max, i - j) + v[j];
        pos = j;
      }
    }
    Max = max(Max, i - pos);
    ans += v[pos];
  }
  printf("%lld", ans + 1LL * x * Max);
  return 0;
}
