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 nlist[2010];
long long int data[2010];
int cnt[2010];
int main() {
  long long int N, x;
  cin >> N >> x;
  for (int(i) = (int)(0); i < (int)(N); ++i) cin >> nlist[i];
  long long int ans = 0;
  for (int(i) = (int)(0); i < (int)(N); ++i) {
    data[i] = nlist[i];
    int t = -1;
    for (int(j) = (int)(0); j < (int)(N); ++j) {
      if (data[i] > nlist[(i - j + N) % N] + x * j) {
        data[i] = nlist[(i - j + N) % N];
        t = (i - j + N) % N;
      }
    }
    if (t != -1 && t != i) cnt[t]++;
  }
  int m = 0;
  for (int(i) = (int)(0); i < (int)(N); ++i) m = max(m, cnt[i]);
  for (int(i) = (int)(0); i < (int)(N); ++i) ans += data[i];
  cout << ans + m * x << endl;
  return 0;
}
