P5065 [Ynoi Easy Round 2014] The People Who Never Return and the People Who Wait in Vain.

【The First Fleet has sent a message】 【It is about the battle result of Floating Island No. 15】 【The defense operation of Floating Island No. 15...】 【Has failed...】      

Chtholly gives you a sequence. It supports point updates, and queries asking for the minimum possible length of an interval whose bitwise OR sum is **greater than or equal to** a given number. If there is no solution, output $-1$.

The first line contains two integers $n, m$. The next line contains $n$ integers, representing the sequence $a$. The next $m$ lines are in one of the following forms: * $1\ i\ x$: set $a_i$ to $x$. * $2\ k$: query the minimum length such that there exists an interval of that length whose bitwise OR sum is $\geq k$.

For every operation of type $2$, output one line containing an integer, the answer. If there is no solution, output $-1$.

Idea: kczno1. Solution: kczno1 ($O( m\sqrt n\log a )$ solution), liu_cheng_ao ($O( m\log^2 n\log^2 a )$ solution), 142857cs ($O( m\log n\log^2 a )$ solution). Code: kczno1 ($O( m\sqrt n\log a )$ code), liu_cheng_ao ($O( m\log^2 n\log^2a$ ) code). Data: kczno1. Constraints: For $100\%$ of the testdata, $0\leq a_i, k\leq 2^{30}$, $1\leq n, m\leq 5\times 10^4$. Translated by ChatGPT 5