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;
unsigned long long ans = -1;
unsigned long long N;
unsigned long long x;
vector<unsigned long long> vec;
bool flag[2001];
void func(unsigned long long memo, unsigned long long change, signed deep) {
  if (deep == N) {
    ans = min(memo, ans);
    return;
  };
  for (unsigned long long i = 0; i < N; i++) {
    unsigned long long p = (i - change + N) % N;
    if (flag[p]) {
      flag[i] = false;
      func(memo + vec[i], change, deep + 1);
      flag[i] = true;
    }
  }
  if (change < N - 1) {
    func(memo + x, change + 1, deep);
  }
}
signed main() {
  scanf("%llu %llu", &N, &x);
  for (unsigned long long a = 0; a < N; a++) {
    unsigned long long r;
    scanf("%llu", &r);
    vec.push_back(r);
  }
  for (unsigned long long n = 0; n < N; n++) {
    flag[n] = true;
  }
  func(0, 0, 0);
  printf("%llu\n", ans);
}
