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When Masha came to math classes today, she saw two integer sequences of length $n - 1$ on the blackboard. Let's denote the elements of the first sequence as $a_i$ ($0 \le a_i \le 3$), and the elements of the second sequence as $b_i$ ($0 \le b_i \le 3$).... |
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Om Nom is the main character of a game "Cut the Rope". He is a bright little monster who likes visiting friends living at the other side of the park. However the dark old parks can scare even somebody as fearless as Om Nom, so he asks you to help him. [... |
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Everybody knows that the Berland citizens are keen on health, especially students. Berland students are so tough that all they drink is orange juice!
Yesterday one student, Vasya and his mates made some barbecue and they drank this healthy drink only. ... |
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This task will exclusively concentrate only on the arrays where all elements equal 1 and/or 2.
Array a is k-period if its length is divisible by k and there is such array b of length k, that a is represented by array b written exactly $\frac{n}{k}$ tim... |
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Manao is trying to open a rather challenging lock. The lock has n buttons on it and to open it, you should press the buttons in a certain order to open the lock. When you push some button, it either stays pressed into the lock (that means that you've gu... |
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You are given a set of n elements indexed from 1 to n. The weight of i-th element is w_{i}. The weight of some subset of a given set is denoted as $W(S) =|S|\cdot \sum_{i \in S} w_{i}$. The weight of some partition R of a given set into k subsets is $W(... |
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Little Elephant loves magic squares very much.
A magic square is a 3 × 3 table, each cell contains some positive integer. At that the sums of integers in all rows, columns and diagonals of the table are equal. The figure below shows the magic square, t... |
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Initially Ildar has an empty array. He performs $n$ steps. On each step he takes a subset of integers already added to the array and appends the mex of this subset to the array.
The mex of an multiset of integers is the smallest non-negative integer n... |
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Pasha is participating in a contest on one well-known website. This time he wants to win the contest and will do anything to get to the first place!
This contest consists of n problems, and Pasha solves ith problem in a_{i} time units (his solutions ar... |
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You are a rebel leader and you are planning to start a revolution in your country. But the evil Government found out about your plans and set your punishment in the form of correctional labor.
You must paint a fence which consists of $10^{100}$ planks ... |
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Yet another Armageddon is coming! This time the culprit is the Julya tribe calendar.
The beavers in this tribe knew math very well. Smart Beaver, an archaeologist, got a sacred plate with a magic integer on it. The translation from Old Beaverish is as... |
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You are going to hold a competition of one-to-one game called AtCoder Janken. (Janken is the Japanese name for Rock-paper-scissors.)N players will participate in this competition, and they are given distinct integers from 1 through N.
The arena has M pl... |
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Consider sequences \{A_1,...,A_N\} of length N consisting of integers between 1 and K (inclusive).
There are K^N such sequences. Find the sum of \gcd(A_1, ..., A_N) over all of them.
Since this sum can be enormous, print the value modulo (10^9+7).
Here ... |
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Snuke had N cards numbered 1 through N.
Each card has an integer written on it; written on Card i is a_i.
Snuke did the following procedure:
- Let X and x be the maximum and minimum values written on Snuke's cards, respectively.
- If X = x, terminate ... |
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There are N piles of stones. The i-th pile has A_i stones.
Aoki and Takahashi are about to use them to play the following game:
- Starting with Aoki, the two players alternately do the following operation:
- Operation: Choose one pile of stones, and r... |
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Let us denote by f(x, m) the remainder of the Euclidean division of x by m.
Let A be the sequence that is defined by the initial value A_1=X and the recurrence relation A_{n+1} = f(A_n^2, M).
Find \displaystyle{\sum_{i=1}^N A_i}.
-----Constraints-----
... |
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Everyone knows that agents in Valorant decide, who will play as attackers, and who will play as defenders. To do that Raze and Breach decided to play $t$ matches of a digit game...
In each of $t$ matches of the digit game, a positive integer is generat... |
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One industrial factory is reforming working plan. The director suggested to set a mythical detail production norm. If at the beginning of the day there were x details in the factory storage, then by the end of the day the factory has to produce $x \oper... |
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You are given n points on a line with their coordinates x_{i}. Find the point x so the sum of distances to the given points is minimal.
-----Input-----
The first line contains integer n (1 ≤ n ≤ 3·10^5) — the number of points on the line.
The second... |
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Ivan is a student at Berland State University (BSU). There are n days in Berland week, and each of these days Ivan might have some classes at the university.
There are m working hours during each Berland day, and each lesson at the university lasts exa... |
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Arthur and Alexander are number busters. Today they've got a competition.
Arthur took a group of four integers a, b, w, x (0 ≤ b < w, 0 < x < w) and Alexander took integer с. Arthur and Alexander use distinct approaches to number bustings. Alexander i... |
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This problem uses a simplified network topology model, please read the problem statement carefully and use it as a formal document as you develop the solution.
Polycarpus continues working as a system administrator in a large corporation. The computer ... |
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Andrew often reads articles in his favorite magazine 2Char. The main feature of these articles is that each of them uses at most two distinct letters. Andrew decided to send an article to the magazine, but as he hasn't written any article, he just decid... |
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Arkady decides to observe a river for n consecutive days. The river's water level on each day is equal to some real value.
Arkady goes to the riverside each day and makes a mark on the side of the channel at the height of the water level, but if it coi... |
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Polycarp is mad about coding, that is why he writes Sveta encoded messages. He calls the median letter in a word the letter which is in the middle of the word. If the word's length is even, the median letter is the left of the two middle letters. In the... |
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Calculate the value of the sum: n mod 1 + n mod 2 + n mod 3 + ... + n mod m. As the result can be very large, you should print the value modulo 10^9 + 7 (the remainder when divided by 10^9 + 7).
The modulo operator a mod b stands for the remainder afte... |
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After returned from forest, Alyona started reading a book. She noticed strings s and t, lengths of which are n and m respectively. As usual, reading bored Alyona and she decided to pay her attention to strings s and t, which she considered very similar.... |
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Memory is performing a walk on the two-dimensional plane, starting at the origin. He is given a string s with his directions for motion: An 'L' indicates he should move one unit left. An 'R' indicates he should move one unit right. A 'U' indicates he ... |
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Omkar is building a house. He wants to decide how to make the floor plan for the last floor.
Omkar's floor starts out as $n$ rows of $m$ zeros ($1 \le n,m \le 100$). Every row is divided into intervals such that every $0$ in the row is in exactly $1$ i... |
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Are you going to Scarborough Fair?
Parsley, sage, rosemary and thyme.
Remember me to one who lives there.
He once was the true love of mine.
Willem is taking the girl to the highest building in island No.28, however, neither of them knows how to get... |
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Recently you've discovered a new shooter. They say it has realistic game mechanics.
Your character has a gun with magazine size equal to $k$ and should exterminate $n$ waves of monsters. The $i$-th wave consists of $a_i$ monsters and happens from the $... |
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In 2013, the writers of Berland State University should prepare problems for n Olympiads. We will assume that the Olympiads are numbered with consecutive integers from 1 to n. For each Olympiad we know how many members of the jury must be involved in it... |
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Vasya wrote down two strings s of length n and t of length m consisting of small English letters 'a' and 'b'. What is more, he knows that string t has a form "abab...", namely there are letters 'a' on odd positions and letters 'b' on even positions.
Su... |
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Colonel has n badges. He wants to give one badge to every of his n soldiers. Each badge has a coolness factor, which shows how much it's owner reached. Coolness factor can be increased by one for the cost of one coin.
For every pair of soldiers one of... |
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Vasya wants to turn on Christmas lights consisting of m bulbs. Initially, all bulbs are turned off. There are n buttons, each of them is connected to some set of bulbs. Vasya can press any of these buttons. When the button is pressed, it turns on all th... |
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While Vasya finished eating his piece of pizza, the lesson has already started. For being late for the lesson, the teacher suggested Vasya to solve one interesting problem. Vasya has an array a and integer x. He should find the number of different order... |
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Captain Marmot wants to prepare a huge and important battle against his enemy, Captain Snake. For this battle he has n regiments, each consisting of 4 moles.
Initially, each mole i (1 ≤ i ≤ 4n) is placed at some position (x_{i}, y_{i}) in the Cartesian... |
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An atom of element X can exist in n distinct states with energies E_1 < E_2 < ... < E_{n}. Arkady wants to build a laser on this element, using a three-level scheme. Here is a simplified description of the scheme.
Three distinct states i, j and k are ... |
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Ramesses came to university to algorithms practice, and his professor, who is a fairly known programmer, gave him the following task.
You are given two matrices $A$ and $B$ of size $n \times m$, each of which consists of $0$ and $1$ only. You can apply... |
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Hacker Zhorik wants to decipher two secret messages he intercepted yesterday. Yeah message is a sequence of encrypted blocks, each of them consists of several bytes of information.
Zhorik knows that each of the messages is an archive containing one or ... |
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Vanya smashes potato in a vertical food processor. At each moment of time the height of the potato in the processor doesn't exceed h and the processor smashes k centimeters of potato each second. If there are less than k centimeters remaining, than duri... |
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We often go to supermarkets to buy some fruits or vegetables, and on the tag there prints the price for a kilo. But in some supermarkets, when asked how much the items are, the clerk will say that $a$ yuan for $b$ kilos (You don't need to care about wha... |
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"We've tried solitary confinement, waterboarding and listening to Just In Beaver, to no avail. We need something extreme."
"Little Alena got an array as a birthday present..."
The array b of length n is obtained from the array a of length n and two in... |
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You are given a sequence $a_1, a_2, \dots, a_n$ consisting of $n$ non-zero integers (i.e. $a_i \ne 0$).
You have to calculate two following values: the number of pairs of indices $(l, r)$ $(l \le r)$ such that $a_l \cdot a_{l + 1} \dots a_{r - 1} \cd... |
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The king's birthday dinner was attended by $k$ guests. The dinner was quite a success: every person has eaten several dishes (though the number of dishes was the same for every person) and every dish was served alongside with a new set of kitchen utensi... |
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Every person likes prime numbers. Alice is a person, thus she also shares the love for them. Bob wanted to give her an affectionate gift but couldn't think of anything inventive. Hence, he will be giving her a graph. How original, Bob! Alice will surely... |
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You are given string s consists of opening and closing brackets of four kinds <>, {}, [], (). There are two types of brackets: opening and closing. You can replace any bracket by another of the same type. For example, you can replace < by the bracket {,... |
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Hasan loves playing games and has recently discovered a game called TopScore. In this soccer-like game there are $p$ players doing penalty shoot-outs. Winner is the one who scores the most. In case of ties, one of the top-scorers will be declared as the... |
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Vasily exited from a store and now he wants to recheck the total price of all purchases in his bill. The bill is a string in which the names of the purchases and their prices are printed in a row without any spaces. Check has the format "name_1price_1na... |
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You are given array a with n integers and m queries. The i-th query is given with three integers l_{i}, r_{i}, x_{i}.
For the i-th query find any position p_{i} (l_{i} ≤ p_{i} ≤ r_{i}) so that a_{p}_{i} ≠ x_{i}.
-----Input-----
The first line contai... |
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After a long day, Alice and Bob decided to play a little game. The game board consists of $n$ cells in a straight line, numbered from $1$ to $n$, where each cell contains a number $a_i$ between $1$ and $n$. Furthermore, no two cells contain the same num... |
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Tomorrow is a difficult day for Polycarp: he has to attend $a$ lectures and $b$ practical classes at the university! Since Polycarp is a diligent student, he is going to attend all of them.
While preparing for the university, Polycarp wonders whether h... |
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Disclaimer: there are lots of untranslateable puns in the Russian version of the statement, so there is one more reason for you to learn Russian :)
Rick and Morty like to go to the ridge High Cry for crying loudly — there is an extraordinary echo. Rece... |
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Vasya has got an undirected graph consisting of $n$ vertices and $m$ edges. This graph doesn't contain any self-loops or multiple edges. Self-loop is an edge connecting a vertex to itself. Multiple edges are a pair of edges such that they connect the sa... |
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Your friend gave you a dequeue D as a birthday present.
D is a horizontal cylinder that contains a row of N jewels.
The values of the jewels are V_1, V_2, ..., V_N from left to right. There may be jewels with negative values.
In the beginning, you have ... |
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N players will participate in a tennis tournament. We will call them Player 1, Player 2, \ldots, Player N.
The tournament is round-robin format, and there will be N(N-1)/2 matches in total.
Is it possible to schedule these matches so that all of the fol... |
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Given are a sequence of N integers A_1, A_2, \ldots, A_N and a positive integer S.
For a pair of integers (L, R) such that 1\leq L \leq R \leq N, let us define f(L, R) as follows:
- f(L, R) is the number of sequences of integers (x_1, x_2, \ldots , x... |
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We will create an artwork by painting black some squares in a white square grid with 10^9 rows and N columns.
The current plan is as follows: for the i-th column from the left, we will paint the H_i bottommost squares and will not paint the other squar... |
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In late autumn evening n robots gathered in the cheerful company of friends. Each robot has a unique identifier — an integer from 1 to 10^9.
At some moment, robots decided to play the game "Snowball". Below there are the rules of this game. First, all ... |
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Vasya is sitting on an extremely boring math class. To have fun, he took a piece of paper and wrote out n numbers on a single line. After that, Vasya began to write out different ways to put pluses ("+") in the line between certain digits in the line so... |
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Ryouko is an extremely forgetful girl, she could even forget something that has just happened. So in order to remember, she takes a notebook with her, called Ryouko's Memory Note. She writes what she sees and what she hears on the notebook, and the note... |
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Paul is at the orchestra. The string section is arranged in an r × c rectangular grid and is filled with violinists with the exception of n violists. Paul really likes violas, so he would like to take a picture including at least k of them. Paul can tak... |
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Dreamoon is a big fan of the Codeforces contests.
One day, he claimed that he will collect all the places from $1$ to $54$ after two more rated contests. It's amazing!
Based on this, you come up with the following problem:
There is a person who parti... |
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Recently, Anton has found a set. The set consists of small English letters. Anton carefully wrote out all the letters from the set in one line, separated by a comma. He also added an opening curved bracket at the beginning of the line and a closing curv... |
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The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p_1... |
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Given an integer N, find two permutations: Permutation p of numbers from 1 to N such that p_{i} ≠ i and p_{i} & i = 0 for all i = 1, 2, ..., N. Permutation q of numbers from 1 to N such that q_{i} ≠ i and q_{i} & i ≠ 0 for all i = 1, 2, ..., N.
& is... |
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Heidi the Cow is aghast: cracks in the northern Wall? Zombies gathering outside, forming groups, preparing their assault? This must not happen! Quickly, she fetches her HC^2 (Handbook of Crazy Constructions) and looks for the right chapter:
How to buil... |
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In order to make the "Sea Battle" game more interesting, Boris decided to add a new ship type to it. The ship consists of two rectangles. The first rectangle has a width of $w_1$ and a height of $h_1$, while the second rectangle has a width of $w_2$ and... |
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Unlike Knights of a Round Table, Knights of a Polygonal Table deprived of nobility and happy to kill each other. But each knight has some power and a knight can kill another knight if and only if his power is greater than the power of victim. However, e... |
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You are given a permutation of n numbers p_1, p_2, ..., p_{n}. We perform k operations of the following type: choose uniformly at random two indices l and r (l ≤ r) and reverse the order of the elements p_{l}, p_{l} + 1, ..., p_{r}. Your task is to find... |
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The R1 company wants to hold a web search championship. There were n computers given for the competition, each of them is connected to the Internet. The organizers believe that the data transfer speed directly affects the result. The higher the speed of... |
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Let's define the sum of two permutations p and q of numbers 0, 1, ..., (n - 1) as permutation [Image], where Perm(x) is the x-th lexicographically permutation of numbers 0, 1, ..., (n - 1) (counting from zero), and Ord(p) is the number of permutation p ... |
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From "ftying rats" to urban saniwation workers - can synthetic biology tronsform how we think of pigeons?
The upiquitous pigeon has long been viewed as vermin - spleading disease, scavenging through trush, and defecating in populous urban spases. Yet ... |
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Each employee of the "Blake Techologies" company uses a special messaging app "Blake Messenger". All the stuff likes this app and uses it constantly. However, some important futures are missing. For example, many users want to be able to search through ... |
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Game "Minesweeper 1D" is played on a line of squares, the line's height is 1 square, the line's width is n squares. Some of the squares contain bombs. If a square doesn't contain a bomb, then it contains a number from 0 to 2 — the total number of bombs ... |
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Since you are the best Wraith King, Nizhniy Magazin «Mir» at the centre of Vinnytsia is offering you a discount.
You are given an array a of length n and an integer c.
The value of some array b of length k is the sum of its elements except for the $\... |
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A Christmas party in city S. had n children. All children came in mittens. The mittens can be of different colors, but each child had the left and the right mitten of the same color. Let's say that the colors of the mittens are numbered with integers fr... |
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There are n points on a straight line, and the i-th point among them is located at x_{i}. All these coordinates are distinct.
Determine the number m — the smallest number of points you should add on the line to make the distances between all neighborin... |
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Polycarp is in really serious trouble — his house is on fire! It's time to save the most valuable items. Polycarp estimated that it would take t_{i} seconds to save i-th item. In addition, for each item, he estimated the value of d_{i} — the moment afte... |
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Two semifinals have just been in the running tournament. Each semifinal had n participants. There are n participants advancing to the finals, they are chosen as follows: from each semifinal, we choose k people (0 ≤ 2k ≤ n) who showed the best result in ... |
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While sailing on a boat, Inessa noticed a beautiful water lily flower above the lake's surface. She came closer and it turned out that the lily was exactly $H$ centimeters above the water surface. Inessa grabbed the flower and sailed the distance of $L$... |
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You are given a set of n points on the plane. A line containing the origin is called good, if projection of the given set to this line forms a symmetric multiset of points. Find the total number of good lines.
Multiset is a set where equal elements are... |
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Nowadays, most of the internet advertisements are not statically linked to a web page. Instead, what will be shown to the person opening a web page is determined within 100 milliseconds after the web page is opened. Usually, multiple companies compete f... |
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While Farmer John rebuilds his farm in an unfamiliar portion of Bovinia, Bessie is out trying some alternative jobs. In her new gig as a reporter, Bessie needs to know about programming competition results as quickly as possible. When she covers the 201... |
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Berland National Library has recently been built in the capital of Berland. In addition, in the library you can take any of the collected works of Berland leaders, the library has a reading room.
Today was the pilot launch of an automated reading room ... |
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Vus the Cossack has $n$ real numbers $a_i$. It is known that the sum of all numbers is equal to $0$. He wants to choose a sequence $b$ the size of which is $n$ such that the sum of all numbers is $0$ and each $b_i$ is either $\lfloor a_i \rfloor$ or $\l... |
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There are n sharks who grow flowers for Wet Shark. They are all sitting around the table, such that sharks i and i + 1 are neighbours for all i from 1 to n - 1. Sharks n and 1 are neighbours too.
Each shark will grow some number of flowers s_{i}. For i... |
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Dima has a hamsters farm. Soon N hamsters will grow up on it and Dima will sell them in a city nearby.
Hamsters should be transported in boxes. If some box is not completely full, the hamsters in it are bored, that's why each box should be completely f... |
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The R1 company has recently bought a high rise building in the centre of Moscow for its main office. It's time to decorate the new office, and the first thing to do is to write the company's slogan above the main entrance to the building.
The slogan of... |
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Chouti is working on a strange math problem.
There was a sequence of $n$ positive integers $x_1, x_2, \ldots, x_n$, where $n$ is even. The sequence was very special, namely for every integer $t$ from $1$ to $n$, $x_1+x_2+...+x_t$ is a square of some in... |
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You have a given integer $n$. Find the number of ways to fill all $3 \times n$ tiles with the shape described in the picture below. Upon filling, no empty spaces are allowed. Shapes cannot overlap. $\square$ This picture describes when $n = 4$. The left... |
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Stepan likes to repeat vowel letters when he writes words. For example, instead of the word "pobeda" he can write "pobeeeedaaaaa".
Sergey does not like such behavior, so he wants to write a program to format the words written by Stepan. This program mu... |
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You are given two arrays of integers a and b. For each element of the second array b_{j} you should find the number of elements in array a that are less than or equal to the value b_{j}.
-----Input-----
The first line contains two integers n, m (1 ≤ ... |
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Vova, the Ultimate Thule new shaman, wants to build a pipeline. As there are exactly n houses in Ultimate Thule, Vova wants the city to have exactly n pipes, each such pipe should be connected to the water supply. A pipe can be connected to the water su... |
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While playing yet another strategy game, Mans has recruited $n$ Swedish heroes, whose powers which can be represented as an array $a$.
Unfortunately, not all of those mighty heroes were created as capable as he wanted, so that he decided to do somethin... |
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You are given an undirected graph consisting of n vertices and $\frac{n(n - 1)}{2} - m$ edges. Instead of giving you the edges that exist in the graph, we give you m unordered pairs (x, y) such that there is no edge between x and y, and if some pair of ... |
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Nian is a monster which lives deep in the oceans. Once a year, it shows up on the land, devouring livestock and even people. In order to keep the monster away, people fill their villages with red colour, light, and cracking noise, all of which frighten ... |
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A positive integer X is said to be a lunlun number if and only if the following condition is satisfied:
- In the base ten representation of X (without leading zeros), for every pair of two adjacent digits, the absolute difference of those digits is at ... |
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Given is a permutation P of \{1, 2, \ldots, N\}.
For a pair (L, R) (1 \le L \lt R \le N), let X_{L, R} be the second largest value among P_L, P_{L+1}, \ldots, P_R.
Find \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.
-----Constraints-----
- ... |
Solve the programming task below in a Python markdown code block.
Given is an integer N.
Determine whether there is a pair of positive integers (A, B) such that 3^A + 5^B = N, and find one such pair if it exists.
-----Constraints-----
- 1 \leq N \leq 10^{18}
- All values in input are integers.
-----Input-----
Inpu... |
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