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;
const int M = 1000000007;
int n;
long long x;
long long a[N];
int cnt[N];
int from[N];
int main() {
  while (~scanf("%d%lld", &n, &x)) {
    memset(cnt, 0, sizeof(cnt));
    for (int i = 1; i <= n; i++) {
      scanf("%lld", &a[i]);
      from[i] = i;
    }
    for (int i = 1; i <= n; i++) {
      long long mn = a[i];
      for (int j = 1; j <= n; j++) {
        if (mn > a[j] + (j <= i ? i - j : n - j + i)) {
          mn = a[j] + (j <= i ? i - j : n - j + i);
          from[i] = j;
        }
      }
    }
    int mx = 0;
    for (int i = 1; i <= n; i++) {
      cnt[from[i]]++;
      mx = max(mx, from[i] <= i ? i - from[i] : n - from[i] + i);
    }
    long long ans = 0;
    for (int i = 1; i <= n; i++) {
      ans += cnt[i] * a[i];
    }
    ans += mx * x;
    printf("%lld\n", ans);
  }
}
