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 num;
int magic;
int slime[2000];
int cost[2000];
long long int ans = LLONG_MAX;
long long box = 0;
int main() {
  scanf("%d %d", &num, &magic);
  for (int i = 0; i < num; i++) {
    scanf("%d", &slime[i]);
  }
  for (int i = 0; i < num; i++) {
    for (int j = 0; j < num; j++) {
      cost[j] = slime[j];
    }
    for (int j = 0; j < num; j++) {
      for (int k = 0; k <= i; k++) {
        if (cost[(j + k) % num] > slime[j]) cost[(j + k) % num] = slime[j];
      }
    }
    box = 0;
    for (int j = 0; j < num; j++) {
      box += cost[j];
    }
    if (ans > box + magic * i) ans = box + magic * i;
  }
  printf("%lld\n", ans);
  return 0;
}
