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;
template <typename T>
int vector_finder(std::vector<T> vec, T number) {
  auto itr = std::find(vec.begin(), vec.end(), number);
  size_t index = std::distance(vec.begin(), itr);
  if (index != vec.size()) {
    return 1;
  } else {
    return 0;
  }
}
template <typename T>
T gcd(T a, T b) {
  if (b > 0) {
    return gcd(b, a % b);
  } else {
    return a;
  }
}
template <typename T>
T lcm(T a, T b) {
  T g = gcd(a, b);
  return a * b / g;
}
void clear(std::queue<pair<int, int> > &q) {
  std::queue<pair<int, int> > empty;
  std::swap(q, empty);
}
bool IsPrime(int num) {
  if (num < 2)
    return false;
  else if (num == 2)
    return true;
  else if (num % 2 == 0)
    return false;
  double sqrtNum = sqrt(num);
  for (int i = 3; i <= sqrtNum; i += 2) {
    if (num % i == 0) {
      return false;
    }
  }
  return true;
}
template <typename T>
std::vector<T> enum_div(T n) {
  std::vector<T> ret;
  for (T i = 1; i * i <= n; ++i) {
    if (n % i == 0) {
      ret.push_back(i);
      if (i != 1 && i * i != n) {
        ret.push_back(n / i);
      }
    }
  }
  return ret;
}
int main() {
  int N;
  long long unsigned int x;
  cin >> N >> x;
  long long unsigned int a[N];
  for (int i = 0; i < N; i++) {
    cin >> a[i];
  }
  long long unsigned int ans = 0;
  for (int i = 0; i < N; i++) {
    long long unsigned int mi = 1844674407370955161;
    for (int j = 0; j < N; j++) {
      if (j > i) {
        mi = min(mi, a[j] + (N - 1 + i - j) * x);
      } else {
        mi = min(mi, a[j] + x * (i - j));
      }
    }
    ans += mi;
  }
  cout << ans << endl;
  return 0;
}
