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>
static int j, n, x, max, b[2001];
int gettime(int k);
int main(void) {
  int c, i, t = 0;
  scanf("%d %d", &n, &x);
  int a[n];
  for (i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  b[0] = a[0];
  c = 0;
  for (i = 1; i < n; i++) {
    if (b[0] > a[i]) {
      b[0] = a[i];
      c = i;
    }
  }
  for (i = 1; i <= n - c; i++) {
    b[i] = a[c + i];
  }
  for (i = 0; i < c; i++) {
    b[c + i + 1] = a[i];
  }
  for (i = 0; i < n; i++) {
    t += gettime(i);
    j = 0;
  }
  t += (max * x);
  printf("%d\n", t);
  return 0;
}
int gettime(int k) {
  int bt[k + 1], bt2[k + 1];
  if (k == 0) {
    return b[0];
  } else {
    bt2[k] = gettime(k - 1);
    bt[k] = bt2[k] + x;
    j++;
    if (b[k] < bt[k]) {
      return b[k];
    } else {
      if (max < j) {
        max = j;
      }
      return b[k - j];
    }
  }
}
