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 x;
long long a[2001][2001];
int main(void) {
  scanf("%d%lld", &n, &x);
  long long res = 0;
  for (int i = 0; i < n; i++) {
    scanf("%lld", &a[i][0]);
    res += a[i][0];
  }
  for (int i = 0; i < n; i++) {
    for (int j = 1; j < n; j++) {
      a[i][j] = a[i][0];
    }
  }
  for (int i = 0; i < n; i++) {
    for (long long j = 1; j < n; j++) {
      if (a[i][0] > a[(i - j + n) % n][0] + j * x) {
        a[i][j] = min(a[i][j], a[(i - j + n) % n][0]);
      }
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 1; j < n; j++) {
      a[i][j] = min(a[i][j], a[i][j - 1]);
    }
  }
  for (int i = 1; i < n; i++) {
    long long sum = 0;
    for (int j = 0; j < n; j++) {
      sum += a[j][i];
    }
    res = min(res, (long long)sum + i * x);
  }
  printf("%lld\n", res);
  return 0;
}
