P3586 [POI 2015 R2] Logistics

Maintain a sequence of length $n$, initially all $0$, supporting the following two operations: 1. `U k a`: set the $k$-th number in the sequence to $a$. 2. `Z c s`: on this sequence, each time choose $c$ positive numbers and subtract $1$ from each; ask whether it is possible to perform $s$ such operations. Each query is independent, i.e., each query does not modify the sequence.

The first line contains two positive integers $n, m$, denoting the length of the sequence and the number of operations. The next $m$ lines contain the $m$ operations.

Output several lines. For each `Z` query, print `TAK` if it is possible; otherwise, print `NIE`.

**Constraints** For $100\%$ of the testdata, $1\leq n,m\leq 10^6$, $1\leq k,c\leq n$, $0\leq a\leq 10^9$, $1\leq s\leq 10^9$. Original title: Logistyka. Translated by ChatGPT 5