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 int MAXN = 100007;
const int MOD = 1000000007;
const long long INF = 1000000000LL * 1000000000;
const long long LINF = INF * (long long)INF;
const long double PI = acos(-1.0);
int n, t;
long long ans = INF;
int a[2005];
int catched[2005];
int main() {
  cin >> n >> t;
  int minCost = MOD;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    minCost = min(minCost, a[i]);
  }
  long long curAns1 = 0, curAns2 = 0;
  for (int i = 0; i < n; i++) {
    curAns2 = 0;
    for (int j = 0; j < n; j++) {
      if (!catched[j] && a[(i + j) % n] == minCost) {
        catched[j] = 1;
        curAns1 += minCost;
        continue;
      }
      if (!catched[j]) {
        curAns2 += a[(i + j) % n];
      }
    }
    ans = min(ans, curAns1 + curAns2 + t * i);
  }
  cout << ans;
}
