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 <stdio.h>
typedef long long ll;

int main(void) {
  ll i, j, k, n, x, ans = 0;
  scanf("%lld%lld", &n, &x);
  ll a[n], now[n];
  for(i = 0; i < n; ++i) scanf("%lld", &a[i]), now[i] = a[i], ans += a[i];
  for(i = 1; i < n; ++i) {
    ll sum = i * x;
    for(j = 0; j < n; ++j) {
      if(now[j] > a[(j + n - i) % n]) now[j] = a[(j + n - i) % n];
      sum += now[j];
    }
    if(sum < ans) ans = sum;
  }
  printf("%lld", ans);
  return 0;
}