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