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 getmin(long long int a[], long long int x, int N, int i) {
  long long int min = a[0] + i * x;
  for (int j = 1; j < N; j++) {
    long long int temp = a[j] + ((i - j + N) % N) * x;
    if (min > temp) min = temp;
  }
  std::cout << min << std::endl;
  return min;
}
long long int min_element(long long int *st, long long int *end) {
  long long int *now = st;
  long long int min = *now;
  now++;
  while (now != end) {
    if (min > *now) {
      min = *now;
    }
    now++;
  }
  return min;
}
int main(void) {
  int N;
  std::cin >> N;
  long long int x, a[2 * N];
  std::cin >> x;
  for (int i = 0; i < N; i++) {
    std::cin >> a[i];
    a[i + N] = a[i];
  }
  long long int total_min = 1000000000000000L;
  for (int k = 0; k < N; k++) {
    long long int total = 0;
    for (int i = 0; i < N; i++) {
      total += min_element(a + N - k + i, a + 1 + N + i);
    }
    total += k * x;
    if (total_min > total) {
      total_min = total;
    }
  }
  std::cout << total_min << std::endl;
  return 0;
}
