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;
long long N, M, K, a, b, c, d, e, H, W;
long long A[200005] = {};
long long B[200005] = {};
long long C[200005] = {};
bool f, ff;
string S;
set<long long> sll;
pair<long long, long long> bufpl;
vector<long long> vl[100005];
vector<pair<long long, long long> > vpl[20];
vector<string> vs[20];
set<long long> llset;
struct ST {
  long long Kati;
  int bangou;
  bool operator<(const ST& another) const { return Kati < another.Kati; };
};
vector<ST> vst;
ST st[200005];
ST bufst;
bitset<5000> bits;
int main() {
  cin >> N >> e;
  a = 0;
  b = 0;
  f = false;
  for (int i = 0; i < N; i++) {
    cin >> A[i];
    b += A[i];
  }
  for (int i = 1; i < N; i++) {
    a += max(A[i] - A[i - 1], (long long)0);
  }
  a += min(A[0] - A[N - 1], (long long)0);
  c = min(b - a + e, a);
  cout << c << endl;
  return 0;
}
