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;
bool shortesting(long long ary[][2], int n, int x) {
  bool changed = false;
  for (int i = 0; i < (n); i++) {
    int next = i + 1;
    if (next >= n) next = 0;
    if (ary[i][0] + x < ary[next][0]) {
      ary[next][0] = ary[i][0] + x;
      ary[next][1]++;
      changed = true;
    }
  }
  return changed;
}
int main() {
  string r = "";
  int n;
  int x;
  scanf("%d %d", &n, &x);
  long long ary[n][2];
  for (int i = 0; i < (n); i++) {
    scanf("%lld", &ary[i][0]);
    ary[i][1] = 0;
  }
  while (true) {
    if (shortesting(ary, n, x) == false) break;
  }
  long long sum = 0;
  long long times = 0;
  for (int i = 0; i < (n); i++) {
    int org;
    org = i - ary[i][1];
    if (org < 0) org += n;
    sum += ary[org][0];
    times = max(times, ary[i][1]);
  }
  sum += times * x;
  cout << sum << endl;
  return 0;
}
