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.

Cho \(N\) vật thể được đánh số từ \(1\) đến \(N\). Mỗi vật thể \(i\) có ba thông số:

• Trọng lượng \(w_i\)
• Thể tích \(a_i\)
• Giá trị \(v_i\)

Bạn có một cái túi có sức chứa tối đa về trọng lượng là \(W\) và sức chứa tối đa về thể tích là \(A\).

Hãy chọn một tập hợp các vật thể sao cho:

1. Tổng trọng lượng các vật thể được chọn không vượt quá \(W\).
2. Tổng thể tích các vật thể được chọn không vượt quá \(A\).
3. Tổng giá trị các vật thể được chọn là lớn nhất.

Input

• Dòng đầu tiên chứa hai số nguyên \(N\) và \(A\) (\(1 \le N \le 300\), \(0 \le A \le 300\)).
• Dòng thứ hai chứa số nguyên \(W\) (\(1 \le W \le 10^9\)).
• \(N\) dòng tiếp theo, dòng thứ \(i\) chứa ba số nguyên \(w_i, a_i, v_i\) (\(1 \le w_i \le 10^9\), \(0 \le a_i \le 300\), \(1 \le v_i \le 10\)).

Output

• In ra một số nguyên duy nhất là tổng giá trị lớn nhất đạt được.

Example

4 10
15
10 5 4
6 4 3
5 3 2
4 2 3

8

Scoring

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

Cho \(7\) số tự nhiên \(A, B, C, D, E, F, G\).
Yêu cầu: Hãy đếm số lượng số nguyên \(x\) thỏa mãn đồng thời tất cả các điều kiện sau:

1. \(A \le x \le B\)
2. \(x \le G\)
3. \(x \bmod C = D\)
4. \(x \bmod E = F\)

Input

• Một dòng duy nhất chứa \(7\) số tự nhiên \(A, B, C, D, E, F, G\) (\(0 \le A \le B \le 10^{18}\), \(1 \le C, E \le 10^9\), \(0 \le D < C\), \(0 \le F < E\), \(0 \le G \le 10^{18}\)).

Output

• In ra một số nguyên duy nhất là số lượng số \(x\) thỏa mãn đề bài.

Example

1 20 3 1 5 2 15

1

10 100 2 0 4 1 50

0

Bạn được cho một dãy các số tự nhiên từ \(1\) đến \(n\) và một số nguyên \(k\). Bạn sẽ thực hiện một hoặc nhiều thao tác để xóa các số khỏi dãy này.

Trong mỗi thao tác, bạn xét các số hiện còn lại theo thứ tự tăng dần và xóa đi mỗi số thứ \(k\) (tức là số thứ \(k\), thứ \(2k\), thứ \(3k\),... trong danh sách hiện tại). Quá trình này kết thúc khi tổng số lượng số còn lại nhỏ hơn \(k\).

Nhiệm vụ của bạn là xác định thứ tự (chỉ số) của thao tác mà tại đó số \(n\) bị xóa. Nếu số \(n\) không bao giờ bị xóa cho đến khi quá trình kết thúc, in ra 0.

Input

• Dòng đầu tiên chứa số nguyên \(n\) (\(3 \le n \le 10^{18}\)).
• Dòng thứ hai chứa số nguyên \(k\) (\(2 \le k \le 100\)).

Output

• In ra một số nguyên duy nhất: chỉ số của thao tác mà \(n\) bị xóa, hoặc 0 nếu \(n\) không bao giờ bị xóa.

Example

13
2

3