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 <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  ~debug() { cerr << endl; }
  template <class c>
  typename enable_if<sizeof dud<c>(0) != 1, debug&>::type operator<<(c i) {
    cerr << boolalpha << i;
    return *this;
  }
  template <class c>
  typename enable_if<sizeof dud<c>(0) == 1, debug&>::type operator<<(c i) {
    return *this << range(begin(i), end(i));
  }
  template <class c, class b>
  debug& operator<<(pair<b, c> d) {
    return *this << "(" << d.first << ", " << d.second << ")";
  }
  template <class c>
  debug& operator<<(rge<c> d) {
    *this << "[";
    for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it;
    return *this << "]";
  }
};
using int64 = long long;
const int64 INF = (1LL << 60);
vector<vector<int64> > dp;
void Update(int64& a, int64 b) {
  if (b < a) a = b;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int N;
  int64 X;
  vector<int64> A;
  cin >> N >> X;
  A.resize(N);
  for (int i = 0; i < N; i++) cin >> A[i];
  for (int i = 0; i < N; i++) A.push_back(A[i]);
  dp = vector<vector<int64> >(N + 1, vector<int64>(2 * N, INF));
  for (int i = 0; i < N; i++) {
    dp[1][i] = A[i];
  }
  for (int l = 1; l <= N; l++) {
    for (int i = 0; i < N; i++) {
      int j = i + l - 1;
      if (i) {
        Update(dp[l][i], dp[l - 1][i] + A[j]);
        Update(dp[l][i], dp[l - 1][i] + X + A[i]);
        Update(dp[l][i], dp[l][i - 1] + X);
      }
      Update(dp[l][i], dp[l - 1][i + 1] + A[i]);
    }
  }
  int64 result = INF;
  for (int i = 0; i < N; i++) Update(result, dp[N][i]);
  cout << result << "\n";
  return 0;
}
