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, X;
int v[2005];
long long ans;
int main() {
  scanf("%d%d", &N, &X);
  for (int i = 1; i <= N; i++) scanf("%d", &v[i]);
  ans = 1LL << 60;
  for (int st = 1; st <= N; st++) {
    long long sum = 0;
    for (int dr = st; dr <= N; dr++) {
      sum += v[dr];
      long long pans = sum + 1LL * (v[st] + X) * (N - (dr - st + 1));
      ans = min(ans, pans);
    }
  }
  printf("%lld\n", ans);
  return 0;
}
