[POI2009] LYZ-Ice Skates

滑冰俱乐部初始有 $[1,n]$ 号码溜冰鞋各 $k$ 双，已知 $x$ 号脚的人可以穿 $[x,x+d]$ 号码的鞋子。 现在有 $m$ 次操作，每次两个数 $r,x$，表示来了 $x$ 个 $r$ 号脚的人，$x$ 为负则表示离开。在每次操作之后，你需要判断溜冰鞋是否足够。 ### 输入格式： 第一行 $4$ 个整数 $n,m,k,d$。 接下来 $m$ 行，每行两个整数 $r_i,x_i$，代表一次操作。 ### 输出格式： $m$ 行，每行一个字符串，若此次操作后满足题意则输出 `TAK`，否则输出 `NIE`。 ### 数据范围： $n\le 2\times 10^5,m\le 5\times 10^5,k\le 10^9,1\le r_i\le n-d,-10^9\le x_i\le 10^9,0\le d<n$

Byteasar runs a skate club. Its members meet on a regular basis and train together, and they always use the club's ice-skates. The skate sizes are (by convention) numbered from  to . Naturally, each club member has some foot size, but that is not all to it! Skaters have skate size tolerance factor : a skater with foot size  can wear skates with sizes from  up to . It should be noted, though, that no skater ever wears two skates of different size simultaneously. To supply the club, Byteasar bought  pairs of ice-skates of each size, i.e. from  to . As time passes, some people join the club, just as some established members leave it. Byteasar worries if he will have enough skates of appropriate size for every member at each training. We assume that initially the club has no members at all. Byteasar will give you a sequence of  events of the following form:  (new) members with foot size  have joined/left the club. Right after each such event Byteasar wants to know whether he has enough skates of appropriate size for every club member. He asks you to write a programme that will check it for him.

The first line of the standard input contains four integers , ,  and  (, , , ), separated by single spaces, that denote, respectively: maximum skate size, number of events, number of skate pairs of each size Byteasar initially bought, and the skate size tolerance factor. The following  lines contain the sequence of  events, one per line. The -th line (for ![](http://main.edu.pl…

Your programme should print out  lines to the standard output. The -th line (for ) should either contain the word TAK (Polish for yes), or the word NIE (Polish for no), depending on whether Byteasar has the skates of appropriate size for every club member right after the -th event.

4 4 2 1
1 3
2 3
3 3
2 -1

TAK
TAK
NIE
TAK