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 getZero(vector<int> block) {
  for (int i = block.size() - 1; i >= 0; i--) {
    if (block[i] == 0) return i;
  }
  return 0;
}
int main() {
  int N, x;
  vector<int> a;
  int tmp;
  int ret = 0;
  vector<int> block;
  cin >> N >> x;
  for (int i = 0; i < N; i++) {
    cin >> tmp;
    a.push_back(tmp);
    block.push_back(0);
  }
  for (int i = 0; i < N; i++) {
    if (a[i] <= x) {
      ret += a[i];
      block[i] = 0;
    } else {
      int minVal = a[i];
      int ind = 1;
      int k = 0;
      int cind;
      for (int j = 1; j <= N; j++) {
        k = i - j;
        if (k < 0) {
          k = N + k;
        }
        if (minVal > a[k] + x * ind) {
          minVal = a[k] + x * ind;
          cind = ind;
        }
        ind++;
      }
      block[i] = cind;
    }
  }
  int zeroI = -1;
  int ind = 0;
  ret = 0;
  for (int i = 0; i < N; i++) {
    if (zeroI == -1) {
      zeroI = getZero(block);
    }
    if (block[i] == 0) {
      ind = i;
      if (i == 0) ind = N;
      ret += a[zeroI] * (block[ind - 1] + 1) + x * block[ind - 1];
      zeroI = i;
    }
  }
  cout << ret << endl;
  return 0;
}
