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;
const int N = (int)1e6 + 123;
const long long INF = (long long)1e18 + 123;
const int inf = (int)1e9 + 123;
const int MOD = (int)1e9 + 7;
void megaRandom() {
  unsigned int FOR;
  asm("rdtsc" : "=A"(FOR));
  srand(FOR);
}
int n, x, a[N];
int opt[N];
int main() {
  megaRandom();
  cin >> n >> x;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) {
    long long mn = INF;
    int ps = -1;
    for (int j = i; j >= 1; j--)
      if (1ll * (i - j) * x + a[j] < mn) mn = 1ll * (i - j) * x + a[j], ps = j;
    int ptr = i;
    for (int j = n; j > i; j--) {
      if (1ll * ptr * x + a[j] < mn) mn = 1ll * ptr * x + a[j], ps = j;
      ptr++;
    }
    opt[i] = ps;
  }
  long long res = 0;
  for (int i = 1; i <= n; i++) {
    if (opt[i] == i) {
      int ps = i, cont = 1;
      for (int j = i + 1; j <= n; j++) {
        if (opt[j] != i) {
          ps = j - 1, cont = 0;
          break;
        }
      }
      if (cont) {
        for (int j = 1; j <= i; j++) {
          if (opt[j] != i || j == i) {
            ps = j - 1;
            break;
          }
        }
        if (!ps) ps = n;
      }
      if (ps < i) {
        res += 1ll * (n - i + ps) * x + 1ll * (n - i + ps + 1) * a[i];
      } else {
        res += 1ll * (ps - i) * x + 1ll * (ps - i + 1) * a[i];
      }
    }
  }
  cout << res;
  return 0;
}
