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;
typedef struct {
  long long to;
  long long cost;
} Graphs;
const signed INF = (1LL << 30);
const long long MOD = (1e9 + 7);
const long long LINF = (1LL << 60);
const long long LMAX = LLONG_MAX;
void YN(bool b) { cout << (b ? "Yes" : "No") << endl; }
template <class tuple>
inline tuple gcd(tuple a, tuple b) {
  if (b == 0) return a;
  return (gcd(b, a % b));
}
template <class tuple>
inline tuple lcm(tuple a, tuple b) {
  return a / gcd(a, b) * b;
}
template <class tuple>
inline bool chmax(tuple &a, const tuple &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class tuple>
inline bool chmin(tuple &a, const tuple &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class tuple>
tuple center(tuple a, tuple b, tuple c) {
  if ((a <= b && b <= c) || (a >= b && b >= c)) return b;
  if ((b >= a && a >= c) || (b <= a && a <= c)) return a;
  return c;
}
void print() {}
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
  cout << head << endl;
  print(forward<Tail>(tail)...);
}
void input() {}
template <class Head, class... Tail>
void input(Head &&head, Tail &&...tail) {
  cin >> head;
  input(forward<Tail>(tail)...);
}
template <typename tuple>
ostream &operator<<(ostream &out, const vector<tuple> &v) {
  if (!v.empty()) {
    copy(v.begin(), v.end(), ostream_iterator<tuple>(out, ", "));
    out << "\b\b";
  }
  return out;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &out, const pair<T1, T2> &p) {
  out << p.first << ", " << p.second;
  return out;
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(10);
  long long n, x;
  cin >> n >> x;
  vector<long long> a(n);
  for (long long i = 0; i < (n); ++i) cin >> a[i];
  vector<long long> slime(n);
  slime[0] = a[0];
  for (long long i = 1; i <= (n - 1); ++i) {
    slime[i] = min(slime[i - 1] + x, a[i]);
  }
  long long sum = 0;
  for (long long i = 0; i < (n); ++i) sum += slime[i];
  cout << (sum) << endl;
  return 0;
}
