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() {
  long long int N, x;
  scanf("%lld%lld", &N, &x);
  vector<long long int> a(N, 0);
  int mincost = 1000000001;
  int minindex = 0;
  for (int i = 0; i < N; i++) {
    scanf("%lld", &(a[i]));
    if (a[i] < mincost) {
      mincost = a[i];
      minindex = i;
    }
  }
  vector<long long int> dp(N, 1000000000000000001);
  dp[0] = a[minindex];
  for (int i = 1; i < N; i++) {
    int j = (minindex + i) % N;
    if ((a[minindex] + x) < a[j]) {
      dp[i] = dp[i - 1] + a[minindex] + x;
    } else {
      dp[i] = dp[i - 1] + a[j];
    }
  }
  cout << dp[N - 1] << endl;
  return 0;
}
