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;
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = (x << 3) + (x << 1) + ch - '0';
    ch = getchar();
  }
  return x * f;
}
long long n, x, a[2005 * 2], f[2005][2005 * 2];
long long ans = 0x3fffffff;
int main() {
  n = read(), x = read();
  register int i, j, k;
  memset(f, 0x3f, sizeof 0x3f);
  for (i = 1; i <= n; i++) a[i] = a[i + n] = f[0][i] = f[0][i + n] = read();
  for (i = n + 1; i <= n + n; i++)
    for (j = 1; j < n; j++) f[j][i] = min(f[j - 1][i], a[i - j]);
  for (k = 0; k < n; k++) {
    long long res = k * x;
    for (i = n + 1; i <= n + n; i++) res += f[k][i];
    ans = min(ans, res);
  }
  printf("%lld\n", ans);
  return 0;
}
