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app_data_2500 | You are given a positive integer N.
Find the number of the pairs of integers u and v (0≦u,v≦N) such that there exist two non-negative integers a and b satisfying a xor b=u and a+b=v.
Here, xor denotes the bitwise exclusive OR.
Since it can be extremely large, compute the answer modulo 10^9+7.
-----Constraints-----
- ... |
app_data_2501 | You are the top spy of AtCoder Kingdom. To prevent the stolen secret from being handed to AlDebaran Kingdom, you have sneaked into the party where the transaction happens.
There are N attendees in the party, and they are given attendee numbers from 1 through N. The height of Attendee i is A_i.
According to an examinati... |
app_data_2502 | Given are two strings s and t consisting of lowercase English letters. Determine if the number of non-negative integers i satisfying the following condition is finite, and find the maximum value of such i if the number is finite.
- There exists a non-negative integer j such that the concatenation of i copies of t is a... |
app_data_2503 | AtCoDeer is thinking of painting an infinite two-dimensional grid in a checked pattern of side K.
Here, a checked pattern of side K is a pattern where each square is painted black or white so that each connected component of each color is a K × K square.
Below is an example of a checked pattern of side 3:
AtCoDeer has ... |
app_data_2504 | There are N towns numbered 1 to N and M roads. The i-th road connects Town A_i and Town B_i bidirectionally and has a length of C_i.
Takahashi will travel between these towns by car, passing through these roads. The fuel tank of his car can contain at most L liters of fuel, and one liter of fuel is consumed for each un... |
app_data_2505 | We have a set S of N points in a two-dimensional plane. The coordinates of the i-th point are (x_i, y_i). The N points have distinct x-coordinates and distinct y-coordinates.
For a non-empty subset T of S, let f(T) be the number of points contained in the smallest rectangle, whose sides are parallel to the coordinate a... |
app_data_2506 | Takahashi has come to a party as a special guest.
There are N ordinary guests at the party. The i-th ordinary guest has a power of A_i.
Takahashi has decided to perform M handshakes to increase the happiness of the party (let the current happiness be 0).
A handshake will be performed as follows:
- Takahashi chooses on... |
app_data_2507 | Takahashi will take part in an eating contest. Teams of N members will compete in this contest, and Takahashi's team consists of N players numbered 1 through N from youngest to oldest. The consumption coefficient of Member i is A_i.
In the contest, N foods numbered 1 through N will be presented, and the difficulty of F... |
app_data_2508 | Snuke, a water strider, lives in a rectangular pond that can be seen as a grid with H east-west rows and W north-south columns. Let (i,j) be the square at the i-th row from the north and j-th column from the west.
Some of the squares have a lotus leaf on it and cannot be entered.
The square (i,j) has a lotus leaf on it... |
app_data_2509 | Takahashi had a pair of two positive integers not exceeding N, (a,b), which he has forgotten.
He remembers that the remainder of a divided by b was greater than or equal to K.
Find the number of possible pairs that he may have had.
-----Constraints-----
- 1 \leq N \leq 10^5
- 0 \leq K \leq N-1
- All input values ar... |
app_data_2510 | There are N persons called Person 1 through Person N.
You are given M facts that "Person A_i and Person B_i are friends." The same fact may be given multiple times.
If X and Y are friends, and Y and Z are friends, then X and Z are also friends. There is no friendship that cannot be derived from the M given facts.
Takah... |
app_data_2511 | You are given a tree with N vertices and N-1 edges. The vertices are numbered 1 to N, and the i-th edge connects Vertex a_i and b_i.
You have coloring materials of K colors.
For each vertex in the tree, you will choose one of the K colors to paint it, so that the following condition is satisfied:
- If the distance bet... |
app_data_2512 | There are K items placed on a grid of squares with R rows and C columns. Let (i, j) denote the square at the i-th row (1 \leq i \leq R) and the j-th column (1 \leq j \leq C). The i-th item is at (r_i, c_i) and has the value v_i.
Takahashi will begin at (1, 1), the start, and get to (R, C), the goal. When he is at (i, j... |
app_data_2513 | Snuke, who loves animals, built a zoo.
There are N animals in this zoo. They are conveniently numbered 1 through N, and arranged in a circle.
The animal numbered i (2≤i≤N-1) is adjacent to the animals numbered i-1 and i+1. Also, the animal numbered 1 is adjacent to the animals numbered 2 and N, and the animal numbered ... |
app_data_2514 | You have a sequence A composed of N positive integers: A_{1}, A_{2}, \cdots, A_{N}.
You will now successively do the following Q operations:
- In the i-th operation, you replace every element whose value is B_{i} with C_{i}.
For each i (1 \leq i \leq Q), find S_{i}: the sum of all elements in A just after the i-th ope... |
app_data_2515 | We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.
-----Constraints-----
- 1≤Q≤10^5
- 1≤l_i≤r_i≤10^5
- l_i and r_i are odd.
- All in... |
app_data_2516 | Takahashi has a string S of length N consisting of digits from 0 through 9.
He loves the prime number P. He wants to know how many non-empty (contiguous) substrings of S - there are N \times (N + 1) / 2 of them - are divisible by P when regarded as integers written in base ten.
Here substrings starting with a 0 also co... |
app_data_2517 | There are N towns in the State of Atcoder, connected by M bidirectional roads.
The i-th road connects Town A_i and B_i and has a length of C_i.
Joisino is visiting R towns in the state, r_1,r_2,..,r_R (not necessarily in this order).
She will fly to the first town she visits, and fly back from the last town she visits,... |
app_data_2518 | You are going out for a walk, when you suddenly encounter N monsters. Each monster has a parameter called health, and the health of the i-th monster is h_i at the moment of encounter. A monster will vanish immediately when its health drops to 0 or below.
Fortunately, you are a skilled magician, capable of causing explo... |
app_data_2519 | We have N dice arranged in a line from left to right. The i-th die from the left shows p_i numbers from 1 to p_i with equal probability when thrown.
We will choose K adjacent dice, throw each of them independently, and compute the sum of the numbers shown. Find the maximum possible value of the expected value of this s... |
app_data_2520 | An SNS has N users - User 1, User 2, \cdots, User N.
Between these N users, there are some relationships - M friendships and K blockships.
For each i = 1, 2, \cdots, M, there is a bidirectional friendship between User A_i and User B_i.
For each i = 1, 2, \cdots, K, there is a bidirectional blockship between User C_i an... |
app_data_2521 | Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}).
Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements.
Here, the score of a' is defined as follows: (the sum of the elements i... |
app_data_2522 | Given are two sequences A and B, both of length N.
A and B are each sorted in the ascending order.
Check if it is possible to reorder the terms of B so that for each i (1 \leq i \leq N) A_i \neq B_i holds, and if it is possible, output any of the reorderings that achieve it.
-----Constraints-----
- 1\leq N \leq 2 \ti... |
app_data_2523 | You are given a string S consisting of 0 and 1.
Find the maximum integer K not greater than |S| such that we can turn all the characters of S into 0 by repeating the following operation some number of times.
- Choose a contiguous segment [l,r] in S whose length is at least K (that is, r-l+1\geq K must be satisfied). F... |
app_data_2524 | We have N integers. The i-th integer is A_i.
Find \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \mbox{ XOR } A_j), modulo (10^9+7).What is \mbox{ XOR }?
The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:
- When A \mbox{ XOR } B is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if either... |
app_data_2525 | Takahashi has a string S consisting of lowercase English letters.
Starting with this string, he will produce a new one in the procedure given as follows.
The procedure consists of Q operations. In Operation i (1 \leq i \leq Q), an integer T_i is provided, which means the following:
- If T_i = 1: reverse the string S.
... |
app_data_2526 | You are going to eat X red apples and Y green apples.
You have A red apples of deliciousness p_1,p_2, \dots, p_A, B green apples of deliciousness q_1,q_2, \dots, q_B, and C colorless apples of deliciousness r_1,r_2, \dots, r_C.
Before eating a colorless apple, you can paint it red or green, and it will count as a red... |
app_data_2527 | Dilku and Bhopu live in Artland. Dilku loves Bhopu and he writes a message : “iloveyou”
on paper and wishes to send it to Bhopu. As Dilku is busy making an artwork, he asks his friend Raj to send the message to Bhopu. However Raj has a condition that he may add/remove some characters and jumble the letters of the mess... |
app_data_2528 | Chef loves research! Now he is looking for subarray of maximal length with non-zero product.
Chef has an array A with N elements: A1, A2, ..., AN.
Subarray Aij of array A is elements from index i to index j: Ai, Ai+1, ..., Aj.
Product of subarray Aij is product of all its elements (from ith to jth).
-----Input----... |
app_data_2529 | Pooja would like to withdraw X $US from an ATM. The cash machine will only accept the transaction if X is a multiple of 5, and Pooja's account balance has enough cash to perform the withdrawal transaction (including bank charges). For each successful withdrawal the bank charges 0.50 $US.
Calculate Pooja's account bal... |
app_data_2530 | Chefs from all over the globe gather each year for an international convention. Each chef represents some country. Please, note that more than one chef can represent a country.
Each of them presents their best dish to the audience. The audience then sends emails to a secret and secure mail server, with the subject bein... |
app_data_2531 | You are given a sequence of integers $a_1, a_2, ..., a_N$. An element ak is said to be an average element if there are indices $i, j$ (with $i \neq j$) such that $a_k = \frac{a_i + a_j}{2}$.
In the sequence
371022171537102217153 \quad 7 \quad 10 \quad 22 \quad 17 \quad 15
for $i=1, j=5$ and $k=3$, we get $a_k = \frac{... |
app_data_2532 | Ram has invented a magic sequence. Each element of the sequence is defined by the same recursive definition - take some linear combination of previous elements (whose coefficients are fixed) and add to them the n-th powers of some integers. Formally: Xn = Xn-1*a1 + ... + Xn-i*ai + b1*d1^n + ... + bj*dj^n, for some inte... |
app_data_2533 | The grand kingdom of Mancunia is famous for its tourist attractions and visitors flock to it throughout the year. King Mancunian is the benevolent ruler of the prosperous country whose main source of revenue is, of course, tourism.
The country can be represented by a network of unidirectional roads between the cities.... |
app_data_2534 | Our Chef is very happy that his son was selected for training in one of the finest culinary schools of the world.
So he and his wife decide to buy a gift for the kid as a token of appreciation.
Unfortunately, the Chef hasn't been doing good business lately, and is in no mood on splurging money.
On the other hand, the b... |
app_data_2535 | A daily train consists of N cars. Let's consider one particular car. It has 54 places numbered consecutively from 1 to 54, some of which are already booked and some are still free. The places are numbered in the following fashion:
The car is separated into 9 compartments of 6 places each, as shown in the picture. So, ... |
app_data_2536 | Mike is given a matrix A, N and M are numbers of rows and columns respectively. A1, 1 is the number in the top left corner. All the numbers in A are non-negative integers. He also has L pairs of integers (ik, jk). His task is to calculate Ai1, j1 + Ai2, j2 + ... + AiL, jL.
Unfortunately, Mike forgot if Ai, j was a num... |
app_data_2537 | You are given three strings $s$, $t$ and $p$ consisting of lowercase Latin letters. You may perform any number (possibly, zero) operations on these strings.
During each operation you choose any character from $p$, erase it from $p$ and insert it into string $s$ (you may insert this character anywhere you want: in the ... |
app_data_2538 | You play your favourite game yet another time. You chose the character you didn't play before. It has $str$ points of strength and $int$ points of intelligence. Also, at start, the character has $exp$ free experience points you can invest either in strength or in intelligence (by investing one point you can either rais... |
app_data_2539 | Let's denote as L(x, p) an infinite sequence of integers y such that gcd(p, y) = 1 and y > x (where gcd is the greatest common divisor of two integer numbers), sorted in ascending order. The elements of L(x, p) are 1-indexed; for example, 9, 13 and 15 are the first, the second and the third elements of L(7, 22), respec... |
app_data_2540 | You are given a rooted tree with root in vertex 1. Each vertex is coloured in some colour.
Let's call colour c dominating in the subtree of vertex v if there are no other colours that appear in the subtree of vertex v more times than colour c. So it's possible that two or more colours will be dominating in the subtree... |
app_data_2541 | You're given Q queries of the form (L, R).
For each query you have to find the number of such x that L ≤ x ≤ R and there exist integer numbers a > 0, p > 1 such that x = a^{p}.
-----Input-----
The first line contains the number of queries Q (1 ≤ Q ≤ 10^5).
The next Q lines contains two integers L, R each (1 ≤ L ≤... |
app_data_2542 | Let's call left cyclic shift of some string $t_1 t_2 t_3 \dots t_{n - 1} t_n$ as string $t_2 t_3 \dots t_{n - 1} t_n t_1$.
Analogically, let's call right cyclic shift of string $t$ as string $t_n t_1 t_2 t_3 \dots t_{n - 1}$.
Let's say string $t$ is good if its left cyclic shift is equal to its right cyclic shift.
Y... |
app_data_2543 | Dr. Evil is interested in math and functions, so he gave Mahmoud and Ehab array a of length n and array b of length m. He introduced a function f(j) which is defined for integers j, which satisfy 0 ≤ j ≤ m - n. Suppose, c_{i} = a_{i} - b_{i} + j. Then f(j) = |c_1 - c_2 + c_3 - c_4... c_{n}|. More formally, $f(j) =|\sum... |
app_data_2544 | Fishing Prince loves trees, and he especially loves trees with only one centroid. The tree is a connected graph without cycles.
A vertex is a centroid of a tree only when you cut this vertex (remove it and remove all edges from this vertex), the size of the largest connected component of the remaining graph is the sma... |
app_data_2545 | You are given two integers $a$ and $b$. You may perform any number of operations on them (possibly zero).
During each operation you should choose any positive integer $x$ and set $a := a - x$, $b := b - 2x$ or $a := a - 2x$, $b := b - x$. Note that you may choose different values of $x$ in different operations.
Is it... |
app_data_2546 | You are the head of a large enterprise. $n$ people work at you, and $n$ is odd (i. e. $n$ is not divisible by $2$).
You have to distribute salaries to your employees. Initially, you have $s$ dollars for it, and the $i$-th employee should get a salary from $l_i$ to $r_i$ dollars. You have to distribute salaries in such... |
app_data_2547 | Easy and hard versions are actually different problems, so read statements of both problems completely and carefully.
Summer vacation has started so Alice and Bob want to play and joy, but... Their mom doesn't think so. She says that they have to read exactly $m$ books before all entertainments. Alice and Bob will rea... |
app_data_2548 | You are given an array $a_1, a_2, \dots , a_n$ consisting of integers from $0$ to $9$. A subarray $a_l, a_{l+1}, a_{l+2}, \dots , a_{r-1}, a_r$ is good if the sum of elements of this subarray is equal to the length of this subarray ($\sum\limits_{i=l}^{r} a_i = r - l + 1$).
For example, if $a = [1, 2, 0]$, then there ... |
app_data_2549 | You are playing a computer game. In this game, you have to fight $n$ monsters.
To defend from monsters, you need a shield. Each shield has two parameters: its current durability $a$ and its defence rating $b$. Each monster has only one parameter: its strength $d$.
When you fight a monster with strength $d$ while havi... |
app_data_2550 | $n$ students are taking an exam. The highest possible score at this exam is $m$. Let $a_{i}$ be the score of the $i$-th student. You have access to the school database which stores the results of all students.
You can change each student's score as long as the following conditions are satisfied: All scores are integ... |
app_data_2551 | You are given two strings $s$ and $t$ consisting of lowercase Latin letters. Also you have a string $z$ which is initially empty. You want string $z$ to be equal to string $t$. You can perform the following operation to achieve this: append any subsequence of $s$ at the end of string $z$. A subsequence is a sequence th... |
app_data_2552 | Uncle Bogdan is in captain Flint's crew for a long time and sometimes gets nostalgic for his homeland. Today he told you how his country introduced a happiness index.
There are $n$ cities and $n−1$ undirected roads connecting pairs of cities. Citizens of any city can reach any other city traveling by these roads. Citi... |
app_data_2553 | Shubham has an array $a$ of size $n$, and wants to select exactly $x$ elements from it, such that their sum is odd. These elements do not have to be consecutive. The elements of the array are not guaranteed to be distinct.
Tell him whether he can do so.
-----Input-----
The first line of the input contains a single ... |
app_data_2554 | You are given an array $a$ consisting of $n$ integers. Indices of the array start from zero (i. e. the first element is $a_0$, the second one is $a_1$, and so on).
You can reverse at most one subarray (continuous subsegment) of this array. Recall that the subarray of $a$ with borders $l$ and $r$ is $a[l; r] = a_l, a_{... |
app_data_2555 | This is the hard version of the problem. The difference between the versions is that the easy version has no swap operations. You can make hacks only if all versions of the problem are solved.
Pikachu is a cute and friendly pokémon living in the wild pikachu herd.
But it has become known recently that infamous team R... |
app_data_2556 | Several days ago you bought a new house and now you are planning to start a renovation. Since winters in your region can be very cold you need to decide how to heat rooms in your house.
Your house has $n$ rooms. In the $i$-th room you can install at most $c_i$ heating radiators. Each radiator can have several sections... |
app_data_2557 | Shuseki Kingdom is the world's leading nation for innovation and technology. There are n cities in the kingdom, numbered from 1 to n.
Thanks to Mr. Kitayuta's research, it has finally become possible to construct teleportation pipes between two cities. A teleportation pipe will connect two cities unidirectionally, tha... |
app_data_2558 | Meka-Naruto plays a computer game. His character has the following ability: given an enemy hero, deal $a$ instant damage to him, and then heal that enemy $b$ health points at the end of every second, for exactly $c$ seconds, starting one second after the ability is used. That means that if the ability is used at time $... |
app_data_2559 | Welcome! Everything is fine.
You have arrived in The Medium Place, the place between The Good Place and The Bad Place. You are assigned a task that will either make people happier or torture them for eternity.
You have a list of $k$ pairs of people who have arrived in a new inhabited neighborhood. You need to assign ... |
app_data_2560 | Alexey, a merry Berland entrant, got sick of the gray reality and he zealously wants to go to university. There are a lot of universities nowadays, so Alexey is getting lost in the diversity — he has not yet decided what profession he wants to get. At school, he had bad grades in all subjects, and it's only thanks to w... |
app_data_2561 | Colossal! — exclaimed Hawk-nose. — A programmer! That's exactly what we are looking for.Arkadi and Boris Strugatsky. Monday starts on Saturday
Reading the book "Equations of Mathematical Magic" Roman Oira-Oira and Cristobal Junta found an interesting equation: $a - (a \oplus x) - x = 0$ for some given $a$, where $\opl... |
app_data_2562 | Winter is here at the North and the White Walkers are close. John Snow has an army consisting of n soldiers. While the rest of the world is fighting for the Iron Throne, he is going to get ready for the attack of the White Walkers.
He has created a method to know how strong his army is. Let the i-th soldier’s strength... |
app_data_2563 | You are given a huge integer $a$ consisting of $n$ digits ($n$ is between $1$ and $3 \cdot 10^5$, inclusive). It may contain leading zeros.
You can swap two digits on adjacent (neighboring) positions if the swapping digits are of different parity (that is, they have different remainders when divided by $2$).
For exa... |
app_data_2564 | Leo has developed a new programming language C+=. In C+=, integer variables can only be changed with a "+=" operation that adds the right-hand side value to the left-hand side variable. For example, performing "a += b" when a = $2$, b = $3$ changes the value of a to $5$ (the value of b does not change).
In a prototype... |
app_data_2565 | You are given two sequences $a_1, a_2, \dots, a_n$ and $b_1, b_2, \dots, b_n$. Each element of both sequences is either $0$, $1$ or $2$. The number of elements $0$, $1$, $2$ in the sequence $a$ is $x_1$, $y_1$, $z_1$ respectively, and the number of elements $0$, $1$, $2$ in the sequence $b$ is $x_2$, $y_2$, $z_2$ respe... |
app_data_2566 | Berland State University invites people from all over the world as guest students. You can come to the capital of Berland and study with the best teachers in the country.
Berland State University works every day of the week, but classes for guest students are held on the following schedule. You know the sequence of se... |
app_data_2567 | A binary string is a string where each character is either 0 or 1. Two binary strings $a$ and $b$ of equal length are similar, if they have the same character in some position (there exists an integer $i$ such that $a_i = b_i$). For example: 10010 and 01111 are similar (they have the same character in position $4$); ... |
app_data_2568 | You are given a string $s$ consisting only of characters + and -. You perform some process with this string. This process can be described by the following pseudocode: res = 0
for init = 0 to inf
cur = init
ok = true
for i = 1 to |s|
res = res + 1
if s[i] == '+'
cur = cur ... |
app_data_2569 | Lee tried so hard to make a good div.2 D problem to balance his recent contest, but it still doesn't feel good at all. Lee invented it so tediously slow that he managed to develop a phobia about div.2 D problem setting instead. And now he is hiding behind the bushes...
Let's define a Rooted Dead Bush (RDB) of level $n... |
app_data_2570 | You are given two arrays $a$ and $b$, each consisting of $n$ positive integers, and an integer $x$. Please determine if one can rearrange the elements of $b$ so that $a_i + b_i \leq x$ holds for each $i$ ($1 \le i \le n$).
-----Input-----
The first line of input contains one integer $t$ ($1 \leq t \leq 100$) — the n... |
app_data_2571 | Naruto has sneaked into the Orochimaru's lair and is now looking for Sasuke. There are $T$ rooms there. Every room has a door into it, each door can be described by the number $n$ of seals on it and their integer energies $a_1$, $a_2$, ..., $a_n$. All energies $a_i$ are nonzero and do not exceed $100$ by absolute value... |
app_data_2572 | A matrix of size $n \times m$ is called nice, if all rows and columns of the matrix are palindromes. A sequence of integers $(a_1, a_2, \dots , a_k)$ is a palindrome, if for any integer $i$ ($1 \le i \le k$) the equality $a_i = a_{k - i + 1}$ holds.
Sasha owns a matrix $a$ of size $n \times m$. In one operation he can... |
app_data_2573 | You are given a chessboard consisting of $n$ rows and $n$ columns. Rows are numbered from bottom to top from $1$ to $n$. Columns are numbered from left to right from $1$ to $n$. The cell at the intersection of the $x$-th column and the $y$-th row is denoted as $(x, y)$. Furthermore, the $k$-th column is a special colum... |
app_data_2574 | You are given an array of integers $a_1,a_2,\ldots,a_n$. Find the maximum possible value of $a_ia_ja_ka_la_t$ among all five indices $(i, j, k, l, t)$ ($i<j<k<l<t$).
-----Input-----
The input consists of multiple test cases. The first line contains an integer $t$ ($1\le t\le 2 \cdot 10^4$) — the number of test cases... |
app_data_2575 | Emuskald needs a fence around his farm, but he is too lazy to build it himself. So he purchased a fence-building robot.
He wants the fence to be a regular polygon. The robot builds the fence along a single path, but it can only make fence corners at a single angle a.
Will the robot be able to build the fence Emuskald... |
app_data_2576 | There is a famous olympiad, which has more than a hundred participants. The Olympiad consists of two stages: the elimination stage, and the final stage. At least a hundred participants will advance to the final stage. The elimination stage in turn consists of two contests.
A result of the elimination stage is the tota... |
app_data_2577 | Artem is building a new robot. He has a matrix $a$ consisting of $n$ rows and $m$ columns. The cell located on the $i$-th row from the top and the $j$-th column from the left has a value $a_{i,j}$ written in it.
If two adjacent cells contain the same value, the robot will break. A matrix is called good if no two adja... |
app_data_2578 | In some social network, there are $n$ users communicating with each other in $m$ groups of friends. Let's analyze the process of distributing some news between users.
Initially, some user $x$ receives the news from some source. Then he or she sends the news to his or her friends (two users are friends if there is at l... |
app_data_2579 | Kirill plays a new computer game. He came to the potion store where he can buy any potion. Each potion is characterized by two integers — amount of experience and cost. The efficiency of a potion is the ratio of the amount of experience to the cost. Efficiency may be a non-integer number.
For each two integer numbers ... |
app_data_2580 | You are given a tree that consists of $n$ nodes. You should label each of its $n-1$ edges with an integer in such way that satisfies the following conditions: each integer must be greater than $0$; the product of all $n-1$ numbers should be equal to $k$; the number of $1$-s among all $n-1$ integers must be minimum ... |
app_data_2581 | Gargari is jealous that his friend Caisa won the game from the previous problem. He wants to prove that he is a genius.
He has a n × n chessboard. Each cell of the chessboard has a number written on it. Gargari wants to place two bishops on the chessboard in such a way that there is no cell that is attacked by both of... |
app_data_2582 | You are given a permutation $p$ of $n$ integers $1$, $2$, ..., $n$ (a permutation is an array where each element from $1$ to $n$ occurs exactly once).
Let's call some subsegment $p[l, r]$ of this permutation special if $p_l + p_r = \max \limits_{i = l}^{r} p_i$. Please calculate the number of special subsegments.
--... |
app_data_2583 | Ashishgup and FastestFinger play a game.
They start with a number $n$ and play in turns. In each turn, a player can make any one of the following moves: Divide $n$ by any of its odd divisors greater than $1$. Subtract $1$ from $n$ if $n$ is greater than $1$.
Divisors of a number include the number itself.
The pl... |
app_data_2584 | This is the easy version of this problem. The only difference is the constraint on $k$ — the number of gifts in the offer. In this version: $k=2$.
Vasya came to the store to buy goods for his friends for the New Year. It turned out that he was very lucky — today the offer "$k$ of goods for the price of one" is held in... |
app_data_2585 | Let's consider all integers in the range from $1$ to $n$ (inclusive).
Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of $\mathrm{gcd}(a, b)$, where $1 \leq a < b \leq n$.
The greatest common divisor, $\mathrm{... |
app_data_2586 | Young boy Artem tries to paint a picture, and he asks his mother Medina to help him. Medina is very busy, that's why she asked for your help.
Artem wants to paint an $n \times m$ board. Each cell of the board should be colored in white or black.
Lets $B$ be the number of black cells that have at least one white neig... |
app_data_2587 | Captain Flint and his crew keep heading to a savage shore of Byteland for several months already, drinking rum and telling stories. In such moments uncle Bogdan often remembers his nephew Denis. Today, he has told a story about how Denis helped him to come up with an interesting problem and asked the crew to solve it.
... |
app_data_2588 | You are responsible for installing a gas pipeline along a road. Let's consider the road (for simplicity) as a segment $[0, n]$ on $OX$ axis. The road can have several crossroads, but for simplicity, we'll denote each crossroad as an interval $(x, x + 1)$ with integer $x$. So we can represent the road as a binary string... |
app_data_2589 | Ehab loves number theory, but for some reason he hates the number $x$. Given an array $a$, find the length of its longest subarray such that the sum of its elements isn't divisible by $x$, or determine that such subarray doesn't exist.
An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by delet... |
app_data_2590 | Many years ago Berland was a small country where only $n$ people lived. Each person had some savings: the $i$-th one had $a_i$ burles.
The government considered a person as wealthy if he had at least $x$ burles. To increase the number of wealthy people Berland decided to carry out several reforms. Each reform looked l... |
app_data_2591 | You have array of $n$ numbers $a_{1}, a_{2}, \ldots, a_{n}$.
Rearrange these numbers to satisfy $|a_{1} - a_{2}| \le |a_{2} - a_{3}| \le \ldots \le |a_{n-1} - a_{n}|$, where $|x|$ denotes absolute value of $x$. It's always possible to find such rearrangement.
Note that all numbers in $a$ are not necessarily differen... |
app_data_2592 | Tired of boring office work, Denis decided to open a fast food restaurant.
On the first day he made $a$ portions of dumplings, $b$ portions of cranberry juice and $c$ pancakes with condensed milk.
The peculiarity of Denis's restaurant is the procedure of ordering food. For each visitor Denis himself chooses a set of ... |
app_data_2593 | "You must lift the dam. With a lever. I will give it to you.
You must block the canal. With a rock. I will not give the rock to you."
Danik urgently needs rock and lever! Obviously, the easiest way to get these things is to ask Hermit Lizard for them.
Hermit Lizard agreed to give Danik the lever. But to get a stone... |
app_data_2594 | Due to the coronavirus pandemic, city authorities obligated citizens to keep a social distance. The mayor of the city Semyon wants to light up Gluharniki park so that people could see each other even at night to keep the social distance.
The park is a rectangular table with $n$ rows and $m$ columns, where the cells of... |
app_data_2595 | Johnny has recently found an ancient, broken computer. The machine has only one register, which allows one to put in there one variable. Then in one operation, you can shift its bits left or right by at most three positions. The right shift is forbidden if it cuts off some ones. So, in fact, in one operation, you can m... |
app_data_2596 | The Third Doctor Who once correctly said that travel between parallel universes is "like travelling sideways". However, he incorrectly thought that there were infinite parallel universes, whereas in fact, as we now all know, there will never be more than 250.
Heidi recently got her hands on a multiverse observation to... |
app_data_2597 | Ujan decided to make a new wooden roof for the house. He has $n$ rectangular planks numbered from $1$ to $n$. The $i$-th plank has size $a_i \times 1$ (that is, the width is $1$ and the height is $a_i$).
Now, Ujan wants to make a square roof. He will first choose some of the planks and place them side by side in some ... |
app_data_2598 | You are given an undirected graph that consists of n vertices and m edges. Initially, each edge is colored either red or blue. Each turn a player picks a single vertex and switches the color of all edges incident to it. That is, all red edges with an endpoint in this vertex change the color to blue, while all blue edge... |
app_data_2599 | Let $f(x)$ be the sum of digits of a decimal number $x$.
Find the smallest non-negative integer $x$ such that $f(x) + f(x + 1) + \dots + f(x + k) = n$.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 150$) — the number of test cases.
Each test case consists of one line containing two integers... |
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