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() {
  char ch = getchar();
  int x = 0, f = 0;
  while (ch < '0' || ch > '9') {
    f |= ch == '-';
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return f ? -x : x;
}
int n, x;
int a[2005], minx[2005][2005];
int main() {
  n = read(), x = read();
  for (int i = 1; i <= n; i++) a[i] = read();
  memset(minx, 127, sizeof minx);
  long long ans = (long long)1 << 60;
  for (int i = 1; i <= n; i++) {
    minx[i][0] = a[i];
    for (int j = 1; j <= n; j++)
      minx[i][j] = min(minx[i][j - 1], a[(i - j - 1 + n) % n + 1]);
  }
  for (int i = 0; i <= n; i++) {
    long long sum = 0;
    for (int j = 1; j <= n; j++) sum += minx[j][i];
    sum += i * x;
    ans = min(ans, sum);
  }
  printf("%lld\n", ans);
}
