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 = 2 * 1000 + 10;
const long long INF = 5000000000000000000;
long long x, ans, a[maxn], cost[maxn], M, X;
int n, tmp;
int main() {
  cin >> n >> x;
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) {
    M = INF;
    X = -1;
    for (int j = 0; j < n; j++) {
      if (M > cost[j] * x + a[j]) {
        M = cost[j] * x + a[j];
        X = j;
      }
    }
    tmp = cost[X];
    ans += M;
    for (int j = 0; j < n; j++) cost[j] = cost[(j + n - tmp) % n];
    cost[X] = 1 + cost[(X + n - 1) % n];
    for (int j = (X + 1) % n; cost[j] != 0; j = (j + 1) % n) cost[j] += cost[X];
  }
  cout << ans;
  return 0;
}
