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;
long long cost[(2010LL)][(2010LL)];
long long x;
long long a[(2010LL)];
int main() {
  long long ans = ((2010LL) * (1000000010LL));
  scanf("%d %lld", &N, &x);
  for (int i = 0; i < N; i++) {
    scanf("%lld", &a[i]);
    cost[i][0] = i;
  }
  for (int i = 0; i < N; i++) {
    for (long long j = 1; j < N; j++) {
      if (cost[i][j - 1] * x + a[cost[i][j - 1]] > j * x + a[(i - j + N) % N]) {
        cost[i][j] = (i - j + N) % N;
      } else {
        cost[i][j] = cost[i][j - 1];
      }
    }
  }
  for (long long i = 0; i < N; i++) {
    long long tmp = i * x;
    for (int j = 0; j < N; j++) {
      tmp += a[cost[j][i]];
    }
    ans = min(ans, tmp);
  }
  printf("%lld\n", ans);
  return 0;
}
