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>
int data[2005], dp[2005][2005];
int main() {
  int n, x;
  long long ans = LLONG_MAX;
  scanf("%d%d", &n, &x);
  for (int c = 0; c < n; c++) scanf("%d", &data[c]), dp[0][c] = data[c];
  for (int c = 1; c < n; c++)
    for (int c2 = 0; c2 < n; c2++) {
      dp[c][c2] = std::min(dp[c - 1][c2], dp[c - 1][((c2 - 1) + n) % n]);
    }
  for (int c = 0; c < n; c++) {
    long long tmp = x * c;
    for (int c2 = 0; c2 < n; c2++) tmp += dp[c][c2];
    ans = std::min(ans, tmp);
  }
  printf("%lld\n", ans);
}
