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>
int n, x, d[2005], f[2005][2005];
inline int min(int a, int b) { return a < b ? a : b; }
int main() {
  scanf("%d%d", &n, &x);
  int* const a = d + n;
  for (int i = 0; i < n; ++i) scanf("%d", d + i), a[i] = d[i];
  for (int i = 0; i < n; ++i) {
    f[i][0] = a[i];
    for (int j = 1; j < n; ++j) f[i][j] = min(f[i][j - 1], a[i - j]);
  }
  long long ans = 1LL << 60, tmp;
  for (int j = 0; j < n; ++j) {
    tmp = j * x;
    for (int i = 0; i < n; ++i) tmp += f[i][j];
    if (tmp < ans) ans = tmp;
  }
  printf("%lld", ans);
  return 0;
}
