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;
int n,m,i,j,a[2020];
long long c,r;
int main() {
  scanf("%d%d",&n,&m);
  for (i=0; i<n; i++) {
    scanf("%d",&a[i]);
    r+=a[i];
  }
  for (j=1; j<n; j++) if (1LL*m*j<r) {
    multiset<int> s;
    for (i=1; i<=j; i++) s.insert(a[n-i]);
    for (c=i=0; i<n; i++) {
      s.insert(a[i]);
      c+=*s.begin();
      s.erase(s.find(a[(n+i-j)%n]));
    }
    r=min(r,c+1LL*m*j);
  }
  printf("%lld\n",r);
  return 0;
}
