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 n, a[2020], X;
long long int ans = 9999987654321LL, dt[2020][2020];
long long int dp(int x, int d) {
  if (x == n) return 0;
  if (~dt[x][d]) return dt[x][d];
  long long int &ret = dt[x][d] = dp(x + 1, d) + a[x];
  for (int i = 1; i <= n / 2; i++) {
    ret = min(ret, (dp(x + 1, (d + i) % n) + X * i + a[(x + d + i) % n]));
    ret = min(ret, (dp(x + 1, (d + n - i) % n) + X * (n - i) +
                    a[(x + n + d - i) % n]));
  }
  return ret;
}
int main() {
  memset(dt, -1, sizeof(dt));
  scanf("%d%d", &n, &X);
  for (int i = 0; i < n; i++) scanf("%d", a + i);
  printf("%lld\n", dp(0, 0));
  return 0;
}
