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>
#pragma GCC optimize(2)
using namespace std;
inline long long read() {
  long long x = 0, w = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') w = -1;
    c = getchar();
  }
  while (c <= '9' && c >= '0') {
    x = (x << 1) + (x << 3) + c - '0';
    c = getchar();
  }
  return w == 1 ? x : -x;
}
long long n, a[2005], x, mn[2005][2005], ans;
int main() {
  n = read();
  x = read();
  for (int i = 1; i <= n; i++) a[i] = read(), a[n + i] = a[i], mn[i][i] = a[i];
  for (int i = (n + 1); i <= 2 * n; i++) mn[i][i] = a[i];
  for (int i = 1; i <= 2 * n; i++)
    for (int j = (i + 1); j <= 2 * n; j++) mn[i][j] = min(mn[i][j - 1], a[j]);
  ans = 1e18;
  for (int k = 0; k <= n - 1; k++) {
    long long tmp = k * x;
    for (int i = 1; i <= n; i++) tmp += mn[i - k + n][i + n];
    ans = min(ans, tmp);
  }
  cout << ans << endl;
  return 0;
}
