CF10B.Cinema Cashier

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.