P12013 [Ynoi April Fool's Round 2025] Lao Kua

 

Ai Hoshino Aiku Aimi gives you a sequence $a_1,\dots,a_n$ of length $n$, with a total of $m$ operations. There are two types of operations: 1. Given $l,r,x$, add $x$ to $a_l,\dots,a_r$. 2. Given $l,r$, query $\mathop{\max}\limits_{l\le L

The first line contains two integers $n,m$. The second line contains $n$ integers $a_1,\dots,a_n$. The next $m$ lines each contain either `1,l,r,x` or `2,l,r`, describing one operation.

For each operation of type 2, output one line containing the answer as an irreducible fraction (in the form `a/b` or `-a/b` or `0/1`; $a,b$ are coprime positive integers). For example, $\frac{5}{3},\;-\frac46,\;-1,\;0,\;2$ should be output as `5/3`, `-2/3`, `-1/1`, `0/1`, `2/1`, respectively.

Idea: nzhtl1477, Solution: ccz181078, Code: ccz181078, Data: ccz181078. For $25\%$ of the testdata, $n,m\le 100$. For $50\%$ of the testdata, $n,m\le 8000$. For the other $25\%$ of the testdata, there is no operation 1. For $100\%$ of the testdata, $1\le n,m\le 10^6$, $|a_i|,|x|\le 10^3$, and all values are integers. For operation 2, it is guaranteed that there is no case with $l=r$. Translated by ChatGPT 5