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>
long long slimes[2005];
int vis[2005];
int Search(int n) {
  for (int i = n; i >= 0; i--) {
    if (vis[i] == 1) return i;
  }
  return -1;
}
int main() {
  int N;
  long long x;
  while (~scanf("%d%lld", &N, &x)) {
    memset(slimes, 0, sizeof(slimes));
    memset(vis, 0, sizeof(vis));
    for (int i = 0; i < N; i++) {
      scanf("%lld", &slimes[i]);
      if (slimes[i] < x) vis[i] = 1;
    }
    for (int i = 0; i < N; i++) {
      if (vis[i] == 0) {
        int tmp = Search(i);
        if (tmp != -1) {
          int t = slimes[tmp] + (i - tmp) * x;
          slimes[i] = slimes[i] < t ? slimes[i] : t;
        } else {
          for (int j = N - 1; j >= 0; j--) {
            if (vis[j] == 1) {
              int t = (N - 1 - j) * x + (i + 1) * x;
              slimes[j] = slimes[j] < t ? slimes[j] : t;
            }
          }
        }
      }
    }
    if (slimes[N - 1] + x < slimes[0]) slimes[0] = slimes[N - 1] + x;
    long long ans = 0;
    for (int i = 0; i < N; i++) {
      ans += slimes[i];
    }
    printf("%lld\n", ans);
  }
}
