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>
typedef struct {
  long long cost;
  long long change;
  long long base;
} slime_t;
int main(void) {
  int n, x;
  scanf("%d%d", &n, &x);
  long long ans = 0, change = 0;
  slime_t slime[n];
  for (int i = 0; i < n; i++) {
    scanf("%lld", &slime[i].cost);
    slime[i].change = 0;
    slime[i].base = i;
  }
  for (int i = 0; i < n; i++) {
    int tmp = slime[i].cost;
    for (int j = 0; j < n; j++) {
      if (i >= j) {
        tmp = slime[j].cost + x * (i - j);
        if (slime[i].cost > tmp) {
          slime[i].cost = tmp;
          slime[i].change = i - j;
          slime[i].base = j;
        }
      } else {
        tmp = slime[j].cost + x * (n - j + i);
        if (slime[i].cost > tmp) {
          slime[i].cost = tmp;
          slime[i].change = n - j + i;
          slime[i].base = j;
        }
      }
    }
  }
  for (int i = 0; i < n; i++) {
    if (change < slime[i].change) {
      change = slime[i].change;
    }
  }
  for (int i = 0; i < n; i++) {
    ans += slime[slime[i].base].cost;
  }
  ans += x * change;
  printf("%lld\n", ans);
  return 0;
}
