Cinema Cashier

输入第一行为两个整数 $N,K$，表示一个大小为 $K^2$ 的电影院，会来 $N$ 波人，相同一波的人必须坐在同一排。 输入第二行有 $N$ 个数，表示每波的人数。 定义中心点 $(x_c,y_c),x_c=\lceil\frac{k}{2}\rceil,y_c=\lceil\frac{k}{2}\rceil$，每个人的花费为 $|x-x_c|+|y-y_c|$，要求总花费最少。如果总花费一样，尽量向靠左靠前的位置坐。 如果坐不下，输出 $-1$；否则，输出每一波人所在的行以及所在的列的起始和终止位置。

All cinema halls in Berland are rectangles with $ K $ rows of $ K $ seats each, and $ K $ is an odd number. Rows and seats are numbered from $ 1 $ to $ K $ . For safety reasons people, who come to the box office to buy tickets, are not allowed to choose seats themselves. Formerly the choice was made by a cashier, but now this is the responsibility of a special seating program. It was found out that the large majority of Berland's inhabitants go to the cinema in order to watch a movie, that's why they want to sit as close to the hall center as possible. Moreover, a company of $ M $ people, who come to watch a movie, want necessarily to occupy $ M $ successive seats in one row. Let's formulate the algorithm, according to which the program chooses seats and sells tickets. As the request for $ M $ seats comes, the program should determine the row number $ x $ and the segment $ [y_{l},y_{r}] $ of the seats numbers in this row, where $ y_{r}-y_{l}+1=M $ . From all such possible variants as a final result the program should choose the one with the minimum function value of total seats remoteness from the center. Say,  — the row and the seat numbers of the most "central" seat. Then the function value of seats remoteness from the hall center is . If the amount of minimum function values is more than one, the program should choose the one that is closer to the screen (i.e. the row number $ x $ is lower). If the variants are still multiple, it should choose the one with the minimum $ y_{l} $ . If you did not get yet, your task is to simulate the work of this program.

The first line contains two integers $ N $ and $ K $ ( $ 1<=N<=1000,1<=K<=99 $ ) — the amount of requests and the hall size respectively. The second line contains $ N $ space-separated integers $ M_{i} $ from the range $ [1,K] $ — requests to the program.

Output $ N $ lines. In the $ i $ -th line output «-1» (without quotes), if it is impossible to find $ M_{i} $ successive seats in one row, otherwise output three numbers $ x,y_{l},y_{r} $ . Separate the numbers with a space.

2 1
1 1

1 1 1
-1

4 3
1 2 3 1

2 2 2
1 1 2
3 1 3
2 1 1