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 main() {
  int n;
  long long x, sum = 0;
  cin >> n >> x;
  long long dp[n], cnt[n], cntm = 0;
  for (int i = 0; i < n; i++) {
    cin >> dp[i];
    cnt[i] = 0;
  }
  for (int i = 1; i < n; i++) {
    if (dp[i] > dp[i - 1] + x) cnt[i] = cnt[i - 1] + 1;
    cntm = max(cntm, cnt[i]);
    dp[i] = min(dp[i], dp[i - 1] + x);
    if (i == n - 1) {
      if (dp[0] > dp[n - 1] + x) cnt[0] = cnt[n - 1] + 1;
      cntm = max(cntm, cnt[0]);
      dp[0] = min(dp[0], dp[n - 1] + x);
    }
  }
  for (int i = 0; i < n; i++) sum += (dp[i] - cnt[i] * x);
  cout << sum + cntm * x << endl;
  return 0;
}
