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;
struct node {
  int x, y;
} ans[2005];
bool comp(node a, node b) {
  return a.x < b.x;
  if (a.x == b.x) return a.y < b.y;
}
int main() {
  long long sum;
  int i, j, n, m;
  while (scanf("%d%d", &n, &m) != EOF) {
    sum = 0;
    for (i = 1; i <= n; i++) {
      scanf("%d", &ans[i].x);
      ans[i].y = i;
    }
    sort(ans + 1, ans + n + 1, comp);
    for (i = 1; i <= n; i++) {
      int mins = INT_MAX;
      for (j = 1; j < i; j++) {
        if ((ans[j].x * abs(ans[i].y - ans[j].y) * m + ans[j].x) < ans[i].x)
          mins = min(mins, ans[j].x * abs(ans[i].y - ans[j].y) * m + ans[j].x);
        else
          mins = min(ans[i].x, mins);
      }
      if (mins == INT_MAX) mins = ans[i].x;
      sum += mins;
    }
    printf("%lld\n", sum);
  }
}
