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;
long long int ans = 1e18;
long long int cur;
long long int cost[2111];
long long int chk[2111];
int move, n, x;
int done(void) {
  int i;
  for (i = 1; i <= n; i++) {
    if (chk[i] == 0) {
      return 0;
    }
  }
  return 1;
}
void updatechk(void) {
  int i;
  int temp[2111];
  for (i = 1; i <= n; i++) {
    if (chk[i] == 1) {
      temp[i % n + 1] = 1;
    }
  }
  for (i = 1; i <= n; i++) {
    chk[i] = temp[i];
  }
}
int main(void) {
  cin >> n >> x;
  int i, j;
  for (i = 1; i <= n; i++) {
    scanf("%lld", &cost[i]);
  }
  for (i = 1; i <= n; i++) {
    for (j = 1; j <= n; j++) {
      if (cost[j] <= x) {
        chk[j] = 1;
        cur += cost[j];
      }
    }
    if (done() == 1) {
      ans = min(ans, cur);
      cout << ans << endl;
      return 0;
    } else {
      updatechk();
      cur += x;
    }
  }
  return 0;
}
