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 f[4010];
long long a[2010][4010];
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) scanf("%lld", &f[i]), f[n + i] = f[i];
  for (int i = 1; i <= n; i++) {
    long long k = 2e9;
    for (int j = i; j <= 2 * n; j++) {
      k = min(k, f[j]);
      a[i][j] = k;
    }
  }
  long long maxn = 1e18;
  for (int l = 1; l <= n; l++) {
    long long ans = (l - 1) * m;
    for (int i = 1; i <= n; i++) {
      long long k = a[i][(i + l - 1)];
      ans += k;
    }
    maxn = min(ans, maxn);
  }
  printf("%lld\n", maxn);
}
