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;
const double EPS = 1e-11;
long long a[2005];
bool b[2005];
int main(void) {
  long long ret = 0;
  long long N, x;
  cin >> N >> x;
  for (int i = 0; i < (int)N; ++i) {
    cin >> a[i];
  }
  for (;;) {
    for (int i = 0; i < (int)N; ++i) {
      if (!b[i] && a[i] <= x) {
        ret += a[i];
        b[i] = true;
      }
    }
    bool ok = true;
    for (int i = 0; i < (int)N; ++i) {
      if (b[i] == false) {
        ok = false;
        break;
      }
    }
    if (ok) {
      cout << ret << endl;
      return 0;
    }
    bool copy[2005];
    copy[0] = b[N - 1];
    for (int i = 0; i < (int)N; ++i) {
      copy[i + 1] = b[i];
    }
    for (int i = 0; i < (int)N; ++i) {
      b[i] = copy[i];
    }
    ret += x;
  }
}
