Cho mảng \(A\) gồm \(N\) số nguyên \(A_1, A_2, \dots, A_N\).

Cần chọn ra một tập hợp các phần tử (có thể không chọn phần tử nào) sao cho số lượng cặp phần tử kề nhau cùng được chọn (tức là cả \(A_i\) và \(A_{i+1}\) đều thuộc tập được chọn) không vượt quá \(K\).

Hãy tìm tổng lớn nhất của các phần tử trong tập hợp được chọn.

Input

• Dòng đầu tiên chứa hai số nguyên \(N\) và \(K\) (\(1 \le N \le 10^5, 0 \le K \le 100\)).
• Dòng thứ hai chứa \(N\) số nguyên \(A_1, A_2, \dots, A_N\) (\(-10^9 \le A_i \le 10^9\)).

Output

• In ra một số nguyên duy nhất là tổng lớn nhất có thể đạt được.

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Example

5 1
5 -2 4 3 6

15

Scoring

• Subtask 1 (100 điểm): Không có ràng buộc gì thêm.