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 long long oo = 0x3f3f3f3f;
const int maxn = 2020;
long long Min[maxn][maxn];
long long s[maxn];
long long a[maxn];
int n, m, X;
int main() {
  ios::sync_with_stdio(0);
  cin >> n >> X;
  m = 1;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  for (int i = 1; i <= n; ++i) {
    Min[i][i] = a[i];
    for (int j = i + 1; j <= n; ++j) Min[i][j] = min(Min[i][j - 1], a[j]);
  }
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j <= n; ++j) {
      long long t;
      if (j < i)
        t = min(Min[1][j], Min[n + 1 + j - i][n]);
      else
        t = Min[j - i + 1][j];
      s[i - 1] += t;
    }
  while (m--) {
    long long ans = oo;
    for (int i = 0; i <= n; ++i) ans = min(1ll * X * i + s[i], ans);
    cout << ans << endl;
  }
  return 0;
}
