brain

Let a canonical basis $(\alpha_1,\ldots,\alpha_t)$ be represented as an ordered $t$-tuple of distinct elements of ${1,\ldots,n}$.

We are given a tree for each test case, and we choose an arbitrary subset of vertices to delete. After deleting those vertices, the remaining vertices still form a forest, since we are only removing nodes from a tree.

Let $mathcal{A}$ be a family of $s$-combinations and $mathcal{B}$ a family of $t$-combinations, both subsets of $U={0,1,dots,n-1}$ with $nge s+t$.

I can’t reliably write a correct editorial for Codeforces 103148B - “Luna Likes Love” because the problem statement is missing from your prompt. Right now I don’t know: what the input describes, what needs to be computed, or even the core task (graph, strings, DP, etc.).

I can’t reliably reconstruct Codeforces 103148D - Lanterns from the title alone, and I shouldn’t guess the statement because the editorial would end up misleading. Please paste the full problem statement (or at least the input/output description and constraints).

I can’t write a correct editorial yet because the actual problem statement for Codeforces 103148A - Zeros is missing from your prompt.

Let the degree-$t$ combinatorial representation (57) of $N$ be written in the form $$N = binom{ct}{t} + binom{c{t-1}}{t-1} + cdots + binom{c1}{1},$$ where $$s+t ct cdots c1 ge 0.$$ Let $$M = binom{s+t}{t} - N.

Let the $2 \times 2 \times 3$ torus be the Cartesian product $C_2 \times C_2 \times C_3,$ so its elements are triples $(i,j,k)$ with $i \in {0,1}$, $j \in {0,1}$, $k \in {0,1,2}$, and addition is take...

Let the degree-$t$ combinatorial representation (57) of $N$ be written in the form $$N = binom{ct}{t} + binom{c{t-1}}{t-1} + cdots + binom{c1}{1},$$ where $$s+t ct cdots c1 ge 0.$$ Let $$M = binom{s+t}{t} - N.

We are given two integer arrays of equal length, and we are allowed to apply a single kind of operation: pick two positions and swap the elements at those positions in both arrays simultaneously.

I can absolutely write this editorial in the exact style you requested, but I’m missing the most important piece: the actual problem statement for Codeforces 103149B - Railway.

A configuration is a length-$n=s+t$ word over ${0,1,\ast}$ containing exactly $s$ digits $0,1$ and exactly $t$ asterisks $\ast$.

Codeforces 103388N: No Luck

Let $(a_{ij})$ be an $m\times n$ contingency table with fixed row sums $\sum_{j=1}^n a_{ij}=r_i \quad (1\le i\le m)$ and column sums $\sum_{i=1}^m a_{ij}=c_j \quad (1\le j\le n),$ where $\sum_i r_i=\s...

The binomial tree $Tn$ used in this section has $2^n$ nodes, each node corresponding to a binary string of length $n$, and $Tinfty$ is the limiting structure in which nodes correspond to all finite binary strings obtained by suppressing leading zeros.

Write $N$ in binary form $$N = (am a{m-1}dots a0)2 = sum{i=0}^m ai 2^i.$$ Let $kappat N$ denote the least integer $M ge N$ whose binary expansion contains exactly $t$ ones, i.e.

I can’t write a correct Codeforces-style editorial for this yet because the actual problem statement is missing. Right now I only have the title (“103388M - Monarchy in Vertigo”), but no description of the rules, input format, or what needs to be computed.

The operators in this exercise are those introduced earlier in Section 7.

I can’t reliably write a correct Codeforces editorial for 103388K - Kathmandu because the actual problem statement is missing from your prompt.

Algorithm L lists the $t$-combinations $ct dots c2 c1$ of ${0,1,dots,n-1}$ in lexicographic order, starting from $cj = j-1$ for $1 le j le t$.

The problem statement for Codeforces 103388J - Just Bootfall is not included in your prompt, so I don’t have the actual input/output definition, constraints, or operations the solution is based on.

The problem statement for Codeforces 103388H - Handling the Blocks is not included in your message, so I don’t have enough information to reconstruct the task, constraints, or required solution.

I don’t have the actual statement of Codeforces 103388F - Freedom from Prison, and without it I can’t reliably reconstruct the problem or produce a correct editorial. Anything I write would be guesswork, and that would defeat the purpose of a Codeforces-style explanation.

We are given a network of cities connected by undirected roads, where each road has a positive weight representing its “beauty.” The task is to split the set of cities into two groups.

The problem statement is missing, so I don’t have enough information to write a correct editorial. “Codeforces 103388E - Escalator” could correspond to several different tasks (there are multiple “escalator” style problems involving queues, probabilities, DP, or…

I don’t have the actual problem statement for Codeforces 103388B (“Beautiful Words”) in your prompt, and the rest of the editorial depends entirely on it.

I can’t reliably write a correct editorial for CF 103388C - Creating Multiples because the actual problem statement is missing.

The operators in this exercise are those introduced earlier in Section 7.

Algorithm L lists the $t$-combinations $ct dots c2 c1$ of ${0,1,dots,n-1}$ in lexicographic order, starting from $cj = j-1$ for $1 le j le t$.

We are given a long one-dimensional road and two types of moving entities on it: pedestrians who temporarily block a single fixed position during a time interval, and cars that continuously move along a segment from a starting position to an ending position starting at a given…

We are given a tree with weighted nodes and weighted edges. Each node contains some number of apples. Each edge has a length.

Algorithm L lists the $t$-combinations $ct dots c2 c1$ of ${0,1,dots,n-1}$ in lexicographic order, starting from $cj = j-1$ for $1 le j le t$.

I don’t have the actual statement for Codeforces 103295M - Ominous Chess, so I can’t responsibly derive an algorithm, complexity, or implementation details yet.

I can’t write a correct, detailed editorial without the actual problem statement. Right now “Codeforces 103295I - Sling Ring” is just a title, and there’s no information about what the input describes, what operations are allowed, or what needs to be computed.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now you’ve only provided the title (“Space Tourism”), but none of the inputs, outputs, constraints, or rules of the task.

Let the index set be ${0,1,\dots,s}$ with variables $r_s,\dots,r_0$ and constraints $0 \le r_j \le m_j$ for $s \ge j \ge 0$, together with r_s + \cdots + r_0 = t.

Let $A$ be a family of $t$-combinations, and let $partial A$ denote its shadow, the family of all $(t-1)$-combinations contained in members of $A$.

The problem statement section is empty, so there is no way to reconstruct the task, constraints, or required output. Without that, any editorial would be fabricated rather than derived from the actual problem structure, which defeats the purpose of a Codeforces-style explanation.

The input is a list of up to $N le 10^3$ integers, each at most $10^6$. These represent the “strength values” of heroes. We are not asked to reason about them individually after preprocessing; instead, the entire system is governed by what they share multiplicatively.

I can’t produce a correct editorial for this problem yet because the actual problem statement is missing from your prompt.

Let $A$ be a family of $t$-combinations, and let $partial A$ denote its shadow, the family of all $(t-1)$-combinations contained in members of $A$.

I can’t write a correct editorial for this yet because the actual problem statement is missing. “Codeforces 103218E - Rompepuertas” isn’t enough on its own to reconstruct the task reliably, and guessing would almost certainly produce the wrong solution and structure.

The problem statement for “Codeforces 103218D - Caballeros” is missing from your prompt, so there is no defined task, input format, or required output to base an editorial on.

The problem statement is missing from your prompt, so I can’t reliably reconstruct what “Codeforces 103218B - Xor” is asking.

I can’t produce a correct editorial for this yet because the actual problem statement (what “Organigramas” is asking us to compute) is missing.

Let $A$ be a family of $t$-combinations, and let $partial A$ denote its shadow, the family of all $(t-1)$-combinations contained in members of $A$.

I can’t write a correct editorial for “Codeforces 103214E - Objetos” without the actual problem statement. Right now, there is no information about what the input describes, what transformation or query is required, or what constraints we are operating under.

I can’t write a correct editorial for this yet because the actual problem statement for Codeforces 103214D - Bicoloracion is missing from your prompt.

Let $n = s + t$ as in equation (1) of Section 7.

I can’t write a correct editorial for “Codeforces 103214B - Scrabble” because the actual problem statement is missing from your prompt.

I’m missing the actual problem statement for Codeforces 103214C - Estatuas, so I can’t reliably derive the solution or write a correct editorial yet.

The problem statement for “Codeforces 103158L - Memable Ace” is missing from your message, so I don’t have enough information to derive the solution or write a correct editorial.

Let $A$ be a family of $t$-combinations, and let $partial A$ denote its shadow, the family of all $(t-1)$-combinations contained in members of $A$.

The problem statement for “Codeforces 103158J - 2wix+” is missing from your prompt, so there’s no way to reconstruct the intended input/output behavior, constraints, or even the underlying task.

I’m missing the actual problem statement for Codeforces 103158K - Helping Eagle (the input/output description is blank in your prompt).

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only see the title “Binary string”, but no definition of the operations, input format, or what is being asked.

The problem statement is missing, so there isn’t enough information to derive a correct solution or write a meaningful editorial.

The problem statement section is empty, so there’s not enough information to reconstruct the task or produce a correct Codeforces-style editorial.

I can’t write a correct editorial for Codeforces 103158F - Memeable String because the actual problem statement is missing from your prompt.

I can’t write a correct editorial for this yet because the actual problem statement is missing. “Codeforces 103158E - AKA AKA learns number theory” isn’t enough on its own to reconstruct the task reliably, and guessing would lead to a completely wrong solution and…

I can’t write a correct editorial yet because the actual problem statement for Codeforces 103158D - 2wix is missing from your prompt.

I can’t write a correct editorial for this yet because the actual problem statement is missing. “Codeforces 103158C - Topology vs Geometry” isn’t something I can reliably reconstruct from the title alone, and guessing would very likely produce the wrong solution.

I don’t have the actual problem statement for Codeforces 103158A - Sakally Soldier in your prompt, so I can’t correctly reconstruct the logic, constraints, or even the input/output format.

Let $n = s + t$ as in equation (1) of Section 7.

Let $T=\binom{2t-1}{t}$.

Let $T=\binom{2t-1}{t}$.

Let $T=\binom{2t-1}{t}$.

Let $S(n,t,r)$ denote the set of Ising configurations from Exercise 13, restricted to those binary strings $a{n-1}dots a1a0$ with $a0=0$ and with the fixed parameters $t$ and $r$ as in the exercise.

I can write the full editorial in exactly that format, but I’m missing the actual problem statement for Codeforces 103176I - Ice-cream Sampler. Right now the prompt includes no description of: - what the sampler does, - what the input represents, - what needs to be computed.

The proposed solution does not address the exercise.

Let $[n]={1,2,dots,n}$ and let $mathcal{A}$ be a family of $r$-subsets of $[n]$ such that for all $alpha,betainmathcal{A}$ one has $alphacapbetaneqvarnothing$. Assume $rle n/2$. The goal is to prove $$ Let $mathcal{B}={[n]setminus alpha : alphainmathcal{A}}$.

I don’t have the actual statement for Codeforces 103176K - Kth number in Byteland from what you provided, so I can’t reliably reconstruct the problem or derive a correct solution without guessing.

Fix $n,t,r$. We consider binary strings $a{n-1}cdots a1a0$ with $a0=0$, containing exactly $t$ ones and decomposable into exactly $r$ maximal alternating runs of $0$’s and $1$’s as in the Ising configurations of Exercise 13.

I can’t responsibly write a correct editorial yet because the actual problem statement for Codeforces 103176H - “Hacking” is not present in your prompt, and it is not recoverable from the standard Codeforces archive data I can access here.

The problem statement for Codeforces 103176G - Guessing Game is missing from your prompt, so I don’t have the actual rules of the game, input format, or what needs to be computed.

I can’t reliably write a correct editorial for Codeforces 103176F - Find the Base without the actual problem statement.

I’m missing the actual statement of Codeforces 103176E “Eat More”, so I can’t safely reconstruct the solution or write a correct editorial without guessing the problem. Please paste the full problem statement (or even a screenshot / text dump).

I can’t reliably write a correct editorial for “Codeforces 103176D - Drawing Circles” without the actual problem statement (or at least the input/output description and constraints).

I can’t write a correct Codeforces editorial for this yet because the actual problem statement for 103176B - Blokus Duo is missing from your prompt. Right now I don’t know: - what the input represents (grid, pieces, moves, graph, etc.

I can’t reliably reconstruct Codeforces 103176A (“A Billionaire”) from the title alone, and I don’t have the problem statement in the prompt.

Fix $n,t,r$. We consider binary strings $a{n-1}cdots a1a0$ with $a0=0$, containing exactly $t$ ones and decomposable into exactly $r$ maximal alternating runs of $0$’s and $1$’s as in the Ising configurations of Exercise 13.

We are given a connected undirected graph representing “Wonderland”, where each node is a tourist attraction with a fixed value $Hi$.

I’m missing the actual problem statement for Codeforces 103181L - Hard work. Right now the prompt only contains the template, so there’s no way to reconstruct: - what the input represents - what the output should compute - constraints (which drive the algorithm choice) -…

I can’t write a correct Codeforces editorial here because the actual problem statement for 103181J - Funny Tree is missing. Right now I only have the title, but no description of what the tree operations or required output are.

The problem statement for Codeforces 103181I - Starlight is not included in your prompt, so there is nothing concrete to restate, analyze, or derive an algorithm from.

Let $mathcal{C}$ be the set of all 5-card subsets of a standard 52-card deck, and for each $C in mathcal{C}$ let the starter be a distinguished choice $k in C$.

I can’t reliably write an editorial for CF 103181H - Similarities because the actual problem statement is missing from your prompt. Without the statement, I don’t know what the inputs represent, what “similarities” refers to (strings, arrays, graphs, bitmasks, etc.

I can’t write a correct Codeforces editorial without the actual problem statement. Right now I only see the title “103181F - Relay Race”, but no description of what the relay race rules are, what the input represents, or what needs to be computed.

The function $\tau(x)$ in Section 7.

The problem statement for “Codeforces 103181E - Metrix” is not included in your message, so there isn’t enough information to write a correct editorial.

I can absolutely write this editorial in the exact format you want, but I’m missing one critical piece: the actual statement of Codeforces 103181D - Markat.

I’m missing the actual problem statement for Codeforces 103181A - Crop Circles. Without it, I can’t correctly reconstruct the task, constraints, or solution structure, and any attempt to write a full editorial would be guesswork.

I can write the full editorial in exactly that format, but I’m missing the actual problem statement for Codeforces 103181B - Convoluted Fraction.

A canonical basis $(alpha1,ldots,alphat)$ in Exercise 12 is represented in this section as a selection of $t$ distinguished positions among $n$, equivalently as an $(s,t)$-combination with $n=s+t$, encoded by a binary string $a{n-1}ldots a1a0$ satisfying $sum ai=t$.

I can write the full editorial in exactly that format, but I’m missing the actual problem statement for Codeforces 103182L - XorAnd.

I don’t have the actual statement of Codeforces 103182J - Strategy in your prompt, so I can’t reliably reconstruct the problem, constraints, or solution. Writing a correct editorial without that would require guessing, which would very likely produce a wrong algorithm.

I’m missing the actual problem statement for Codeforces 103182I - Number Spiral, and I can’t reliably reconstruct it from the title alone without risking writing the wrong editorial. Please paste the full statement (or at least input/output format + constraints + a sample).

A canonical basis $(alpha1,ldots,alphat)$ in Exercise 12 is represented in this section as a selection of $t$ distinguished positions among $n$, equivalently as an $(s,t)$-combination with $n=s+t$, encoded by a binary string $a{n-1}ldots a1a0$ satisfying $sum ai=t$.

I’m missing the actual problem statement for Codeforces 103182H - Spies. Without the description of what the “spies” are doing, what the input represents, and what needs to be computed, any editorial would be guesswork and would very likely be wrong.

The problem statement for Codeforces 103182G - SigSegv is missing from your prompt, so there isn’t enough information to reconstruct the task, constraints, or required algorithm.