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>
long long int dp[2010][2010];
int N, change_count[2010];
long long int min(long long int a, long long int b) { return a < b ? a : b; }
int main(void) {
  int i, j, x, a[2010], max = 0, total = 0;
  long long int ans = 0;
  scanf("%d%d", &N, &x);
  for (i = 0; i < N; i++) {
    scanf("%d", &a[i]);
    dp[0][i] = a[i];
    change_count[i] = 0;
  }
  for (i = 1; i < N; i++) {
    for (j = 0; j < N; j++) {
      dp[i][j] =
          min(dp[i - 1][j], dp[i - 1][(N + j - i) % N] + (long long int)x * i);
      if (dp[i][j] != dp[i - 1][j])
        change_count[j] = change_count[(N + j - i) % N] + i;
    }
  }
  for (i = 0; i < N; i++) {
    ans += dp[N - 1][i];
    max = max > change_count[i] ? max : change_count[i];
    total += change_count[i];
  }
  ans -= (long long int)(total - max) * x;
  printf("%lld\n", ans);
  return 0;
}
