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.

伯兰的所有电影院影厅均为 $K$ 行 $\times$ $K$ 列的矩形，其中 $K$ 为奇数。行号与座位号均从 $1$ 编号至 $K$。出于安全原因，前往售票处购票的观众不得自行选择座位。过去由售票员人工选座，而如今该任务由一个专用的座位分配程序负责。研究发现，伯兰绝大多数居民去电影院是为了观看电影，因此他们希望尽可能坐得靠近影厅中心。此外，一个由 $M$ 人组成的观影团体，必须占据同一行中连续的 $M$ 个座位。

下面给出该程序在接到 $M$ 个座位请求时所采用的选座与售票算法：
程序需确定行号 $x$，以及该行中座位编号区间 $[y_l,\,y_r]$，满足 $y_r - y_l + 1 = M$。在所有满足条件的可行方案中，程序应选择使“所有被选座位到影厅中心的总距离”函数值最小的那个方案。设 为影厅最“中心”座位的行号与列号，则座位 $(i,j)$ 到影厅中心的距离函数值为：
。

若存在多个方案具有相同的最小距离函数值，则程序应从中选择更靠近银幕（即行号 $x$ 更小）的方案；若仍存在多个方案，则选择其中 $y_l$ 最小者。

若你尚未完全理解，请注意：你的任务就是模拟该程序的工作过程。

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.

第一行包含两个整数 $N$ 和 $K$（$1 \leq N \leq 1000$，$1 \leq K \leq 99$）—— 分别表示请求的数量和大厅的容量。
第二行包含 $N$ 个空格分隔的整数 $M_i$，每个 $M_i$ 均在区间 $[1, K]$ 内—— 表示对程序的请求。

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.

输出 N 行。在第 i 行中，若无法在某一行中找到 M__i 个连续的空座位，则输出 «-1»（不带引号）；否则输出三个数 x, y__l, y__r。各数之间用空格分隔。