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;
int f(int N, int i) {
  if (i >= 1)
    return i;
  else
    return N + i;
}
int main() {
  long long N, x;
  scanf("%lld%lld", &N, &x);
  long long a[2002];
  for (int i = (1); i <= (N); ++i) {
    scanf("%lld", &a[i]);
  }
  static long long dp[2002][2002];
  for (int i = (1); i <= (N); ++i) {
    dp[i][0] = a[i];
  }
  for (int k = (1); k <= (N - 1); ++k) {
    dp[1][k] = min(dp[1][k - 1], a[f(N, 1 - k)]);
  }
  for (int i = (2); i <= (N); ++i) {
    for (int k = (1); k <= (N - 1); ++k) {
      dp[i][k] = min(dp[i][k - 1], a[f(N, i - k)]);
    }
  }
  long long ans = 100000000000;
  for (int k = (0); k <= (N - 1); ++k) {
    long long msum = 0;
    for (int i = (1); i <= (N); ++i) {
      msum += dp[i][k];
    }
    ans = min(ans, k * x + msum);
  }
  printf("%lld\n", ans);
}
