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;
const int N = 2e3 + 5;
long long dp[N << 1][N << 1], a[N << 1];
int x, n;
int main() {
  scanf("%d%d", &n, &x);
  for (int i = 1; i <= n; ++i) scanf("%d", &a[i]), a[i + n] = a[i];
  for (int len = 0; len < n; ++len) {
    for (int i = 1; i + len <= 2 * n; ++i) {
      int j = i + len;
      if (j == i) {
        dp[i][i] = a[i];
        dp[i][i] = min(dp[i][i], dp[i - 1][i - 1] + x);
        continue;
      }
      if (i - 1 == 0)
        dp[i][j] = dp[i + 1][j] + a[i];
      else
        dp[i][j] = dp[i - 1][j - 1] + x;
      dp[i][j] = min(dp[i][j], dp[i + 1][j] + a[i]);
      dp[i][j] = min(dp[i][j], dp[i][j - 1] + a[j]);
    }
  }
  long long ret = -1;
  for (int i = 1; i <= n + 1; ++i) {
    if (ret == -1)
      ret = dp[i][i + n - 1];
    else
      ret = min(ret, dp[i][i + n - 1]);
  }
  printf("%lld\n", ret);
  return 0;
}
