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 a[2010];
int n, x;
int main() {
  int i, j;
  while (~scanf("%d%d", &n, &x)) {
    for (i = 1; i <= n; i++) scanf("%d", &a[i]);
    sort(a + 1, a + 1 + n);
    int num = upper_bound(a + 1, a + 1 + n, x) - a - 1;
    int min_num = a[1], id = 1;
    for (i = 2; i <= num; i++)
      if (a[i] < min_num) {
        min_num = a[i];
        id = i;
      }
    long long ans = 0;
    for (i = 1; i <= num; i++) ans += (long long)a[i];
    for (i = num; i <= n; i++) {
      if ((long long)x + (long long)min_num < (long long)a[i])
        ans += (long long)x + (long long)min_num;
      else
        ans += (long long)a[i];
    }
    printf("%lld\n", ans);
  }
  return 0;
}
