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Tắt Đèn Nhà Ngô Tất Tố hiện tại đang có N bóng đèn và có K khóa. Các khóa được nối vào các bóng đèn theo quy luật như sau: Khóa thứ K sẽ được nối vào các bóng đèn thứ K+n(K+1) (n>=0; 0<=K+n(K+1) <=N). Ví dụ: Khóa thứ 1 sẽ nối vào các bóng đèn số 1, 3, 5, 7,9… Khóa thứ 2 sẽ nối vào các bóng đèn số 2, 5, 8, 11,… Khóa thứ 3 sẽ nối vào các bóng đèn số 3, 7, 11, 15,… Nếu khóa thứ k được thay đổi trạng thái, tất cả các bóng đèn đang nối với khóa k sẽ chuyển trạng thái (Bật->Tắt, tắt->bật). Ngô Tất Tố mỗi lần ra khỏi nhà sẽ đóng khóa sao cho số lượng bóng đèn được tắt là lớn nhất. Anh ta phát hiện ra rằng sự thay đổi trạng thái các khóa khác nhau để tắt có thể có số lượng đèn khác nhau được tắt. Anh ta đang nghĩ đến làm sao nếu chỉ thay đổi trạng thái khóa tối đa 3 lần sẽ tắt được nhiều bóng điện nhất. Mặc dù là một nhà toán học nhưng anh ấy đang bận sáng tác thơ cho cho kỳ thi sắp tới. Nên anh ấy cần các bạn nhân viên tìm ra phương pháp tối ưu để tắt đèn với tối đa 3 lần tác động vào khóa^.^ Input: Dòng 1 chứa số T là số TC. Mỗi testcase bao gồm các thông tin sau: - Dòng đầu tiên chứa số lượng bóng đèn N và số Khóa K (10<=N<=100, 3<=K<=10); - Dòng tiếp theo là N bóng đèn, mỗi bóng đèn nhận 1 trong 2 trạng thái: 1 là bật, 0 là tắt. OutPut: In ra số lượng bóng đèn tối đa có thể tắt tại mỗi case. Đáp số của mỗi TC in ra trên 1 dòng theo định dạng: # TC Answer Ví dụ: Input 1 10 3 (10 bóng đèn và 3 khóa) 0 0 1 1 1 1 0 0 1 0 (lần lượt là 10 trạng thái của 10 bóng đèn, 1 là đang bật, 0 là đang tắt) // Input 500 100 9 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 96 5 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 1 89 3 1 1 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 0 1 14 3 1 1 0 1 0 1 0 0 1 1 1 0 1 0 84 6 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 1 0 1 1 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