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 = 2005;
int n, x, pos;
long long dat[MAXN], cnt[MAXN];
int main() {
  scanf("%d%d", &n, &x);
  pos = 0;
  for (int i = 0; i < n; i++) scanf("%d", &dat[i]);
  for (int i = 1; i < n; i++)
    if (dat[i] < dat[pos]) pos = i;
  for (int i = 0; i < n; i++) {
    int u = (pos + i) % n;
    for (int j = 1; j < n; j++) {
      int v = (u + j) % n;
      if (dat[v] + cnt[v] * x > dat[u] + (j + cnt[u]) * x)
        dat[v] = dat[u], cnt[v] = j + cnt[u];
    }
  }
  long long res = 0, mx = 0;
  for (int i = 0; i < n; i++) res += dat[i], mx = max(mx, cnt[i]);
  printf("%lld", res + mx * x);
  return 0;
}
