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 n, x, a[2005], dp[2005][2005];
long long dps(int i, int j) {
  if (i == j) return a[i];
  if (dp[i][j]) return dp[i][j];
  int ls = dps(i, j - 1);
  dp[i][j] = (ls + a[j] < ls + a[i] + x ? ls + a[j] : ls + a[i] + x);
  return dp[i][j];
}
int main() {
  scanf("%lld%lld", &n, &x);
  for (int i = 1; i <= n; i++) {
    scanf("%lld", &a[i]);
    a[i + n] = a[i];
  }
  long long mini = 1e15;
  for (int i = 1; i <= n; i++)
    mini = (mini < dps(i, i + n - 1) ? mini : dps(i, i + n - 1));
  printf("%lld\n", mini);
  return 0;
}
