contestId int64 0 1.01k | name stringlengths 2 58 | tags listlengths 0 11 | title stringclasses 523
values | time-limit stringclasses 8
values | memory-limit stringclasses 8
values | problem-description stringlengths 0 7.15k | input-specification stringlengths 0 2.05k | output-specification stringlengths 0 1.5k | demo-input listlengths 0 7 | demo-output listlengths 0 7 | note stringlengths 0 5.24k | test_cases listlengths 0 402 | timeConsumedMillis int64 0 8k | memoryConsumedBytes int64 0 537M | score float64 -1 3.99 | __index_level_0__ int64 0 621k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
557 | Arthur and Table | [
"brute force",
"data structures",
"dp",
"greedy",
"math",
"sortings"
] | null | null | Arthur has bought a beautiful big table into his new flat. When he came home, Arthur noticed that the new table is unstable.
In total the table Arthur bought has *n* legs, the length of the *i*-th leg is *l**i*.
Arthur decided to make the table stable and remove some legs. For each of them Arthur determined number *d**i* — the amount of energy that he spends to remove the *i*-th leg.
A table with *k* legs is assumed to be stable if there are more than half legs of the maximum length. For example, to make a table with 5 legs stable, you need to make sure it has at least three (out of these five) legs of the maximum length. Also, a table with one leg is always stable and a table with two legs is stable if and only if they have the same lengths.
Your task is to help Arthur and count the minimum number of energy units Arthur should spend on making the table stable. | The first line of the input contains integer *n* (1<=≤<=*n*<=≤<=105) — the initial number of legs in the table Arthur bought.
The second line of the input contains a sequence of *n* integers *l**i* (1<=≤<=*l**i*<=≤<=105), where *l**i* is equal to the length of the *i*-th leg of the table.
The third line of the input contains a sequence of *n* integers *d**i* (1<=≤<=*d**i*<=≤<=200), where *d**i* is the number of energy units that Arthur spends on removing the *i*-th leg off the table. | Print a single integer — the minimum number of energy units that Arthur needs to spend in order to make the table stable. | [
"2\n1 5\n3 2\n",
"3\n2 4 4\n1 1 1\n",
"6\n2 2 1 1 3 3\n4 3 5 5 2 1\n"
] | [
"2\n",
"0\n",
"8\n"
] | none | [
{
"input": "2\n1 5\n3 2",
"output": "2"
},
{
"input": "3\n2 4 4\n1 1 1",
"output": "0"
},
{
"input": "6\n2 2 1 1 3 3\n4 3 5 5 2 1",
"output": "8"
},
{
"input": "10\n20 1 15 17 11 2 15 3 16 3\n129 114 183 94 169 16 18 104 49 146",
"output": "652"
},
{
"input": "10\... | 92 | 20,172,800 | 0 | 4,190 | |
652 | Gabriel and Caterpillar | [
"implementation",
"math"
] | null | null | The 9-th grade student Gabriel noticed a caterpillar on a tree when walking around in a forest after the classes. The caterpillar was on the height *h*1 cm from the ground. On the height *h*2 cm (*h*2<=><=*h*1) on the same tree hung an apple and the caterpillar was crawling to the apple.
Gabriel is interested when the caterpillar gets the apple. He noted that the caterpillar goes up by *a* cm per hour by day and slips down by *b* cm per hour by night.
In how many days Gabriel should return to the forest to see the caterpillar get the apple. You can consider that the day starts at 10 am and finishes at 10 pm. Gabriel's classes finish at 2 pm. You can consider that Gabriel noticed the caterpillar just after the classes at 2 pm.
Note that the forest is magic so the caterpillar can slip down under the ground and then lift to the apple. | The first line contains two integers *h*1,<=*h*2 (1<=≤<=*h*1<=<<=*h*2<=≤<=105) — the heights of the position of the caterpillar and the apple in centimeters.
The second line contains two integers *a*,<=*b* (1<=≤<=*a*,<=*b*<=≤<=105) — the distance the caterpillar goes up by day and slips down by night, in centimeters per hour. | Print the only integer *k* — the number of days Gabriel should wait to return to the forest and see the caterpillar getting the apple.
If the caterpillar can't get the apple print the only integer <=-<=1. | [
"10 30\n2 1\n",
"10 13\n1 1\n",
"10 19\n1 2\n",
"1 50\n5 4\n"
] | [
"1\n",
"0\n",
"-1\n",
"1\n"
] | In the first example at 10 pm of the first day the caterpillar gets the height 26. At 10 am of the next day it slips down to the height 14. And finally at 6 pm of the same day the caterpillar gets the apple.
Note that in the last example the caterpillar was slipping down under the ground and getting the apple on the next day. | [
{
"input": "10 30\n2 1",
"output": "1"
},
{
"input": "10 13\n1 1",
"output": "0"
},
{
"input": "10 19\n1 2",
"output": "-1"
},
{
"input": "1 50\n5 4",
"output": "1"
},
{
"input": "1 1000\n2 1",
"output": "82"
},
{
"input": "999 1000\n1 1",
"output"... | 62 | 0 | 3 | 4,196 | |
886 | Petya and Catacombs | [
"dsu",
"greedy",
"implementation",
"trees"
] | null | null | A very brave explorer Petya once decided to explore Paris catacombs. Since Petya is not really experienced, his exploration is just walking through the catacombs.
Catacombs consist of several rooms and bidirectional passages between some pairs of them. Some passages can connect a room to itself and since the passages are built on different depths they do not intersect each other. Every minute Petya arbitrary chooses a passage from the room he is currently in and then reaches the room on the other end of the passage in exactly one minute. When he enters a room at minute *i*, he makes a note in his logbook with number *t**i*:
- If Petya has visited this room before, he writes down the minute he was in this room last time; - Otherwise, Petya writes down an arbitrary non-negative integer strictly less than current minute *i*.
Initially, Petya was in one of the rooms at minute 0, he didn't write down number *t*0.
At some point during his wandering Petya got tired, threw out his logbook and went home. Vasya found his logbook and now he is curious: what is the minimum possible number of rooms in Paris catacombs according to Petya's logbook? | The first line contains a single integer *n* (1<=≤<=*n*<=≤<=2·105) — then number of notes in Petya's logbook.
The second line contains *n* non-negative integers *t*1,<=*t*2,<=...,<=*t**n* (0<=≤<=*t**i*<=<<=*i*) — notes in the logbook. | In the only line print a single integer — the minimum possible number of rooms in Paris catacombs. | [
"2\n0 0\n",
"5\n0 1 0 1 3\n"
] | [
"2\n",
"3\n"
] | In the first sample, sequence of rooms Petya visited could be, for example 1 → 1 → 2, 1 → 2 → 1 or 1 → 2 → 3. The minimum possible number of rooms is 2.
In the second sample, the sequence could be 1 → 2 → 3 → 1 → 2 → 1. | [
{
"input": "2\n0 0",
"output": "2"
},
{
"input": "5\n0 1 0 1 3",
"output": "3"
},
{
"input": "7\n0 1 0 0 0 0 0",
"output": "6"
},
{
"input": "100\n0 0 0 0 0 0 1 4 4 0 2 2 4 1 7 1 11 0 8 4 12 12 3 0 3 2 2 4 3 9 1 5 4 6 9 14 6 2 4 18 7 7 19 11 20 13 17 16 0 34 2 6 12 27 9 4 29 ... | 218 | 14,643,200 | 3 | 4,201 | |
629 | Famil Door and Brackets | [
"dp",
"strings"
] | null | null | As Famil Door’s birthday is coming, some of his friends (like Gabi) decided to buy a present for him. His friends are going to buy a string consisted of round brackets since Famil Door loves string of brackets of length *n* more than any other strings!
The sequence of round brackets is called valid if and only if:
1. the total number of opening brackets is equal to the total number of closing brackets; 1. for any prefix of the sequence, the number of opening brackets is greater or equal than the number of closing brackets.
Gabi bought a string *s* of length *m* (*m*<=≤<=*n*) and want to complete it to obtain a valid sequence of brackets of length *n*. He is going to pick some strings *p* and *q* consisting of round brackets and merge them in a string *p*<=+<=*s*<=+<=*q*, that is add the string *p* at the beginning of the string *s* and string *q* at the end of the string *s*.
Now he wonders, how many pairs of strings *p* and *q* exists, such that the string *p*<=+<=*s*<=+<=*q* is a valid sequence of round brackets. As this number may be pretty large, he wants to calculate it modulo 109<=+<=7. | First line contains *n* and *m* (1<=≤<=*m*<=≤<=*n*<=≤<=100<=000,<=*n*<=-<=*m*<=≤<=2000) — the desired length of the string and the length of the string bought by Gabi, respectively.
The second line contains string *s* of length *m* consisting of characters '(' and ')' only. | Print the number of pairs of string *p* and *q* such that *p*<=+<=*s*<=+<=*q* is a valid sequence of round brackets modulo 109<=+<=7. | [
"4 1\n(\n",
"4 4\n(())\n",
"4 3\n(((\n"
] | [
"4\n",
"1\n",
"0\n"
] | In the first sample there are four different valid pairs:
1. *p* = "(", *q* = "))" 1. *p* = "()", *q* = ")" 1. *p* = "", *q* = "())" 1. *p* = "", *q* = ")()"
In the second sample the only way to obtain a desired string is choose empty *p* and *q*.
In the third sample there is no way to get a valid sequence of brackets. | [
{
"input": "4 1\n(",
"output": "4"
},
{
"input": "4 4\n(())",
"output": "1"
},
{
"input": "4 3\n(((",
"output": "0"
},
{
"input": "875 50\n)))((())()))((()(())))))())))((((((()))))))()(((((",
"output": "0"
},
{
"input": "1980 464\n))(()()))(((((((((()))))))(()((((... | 327 | 37,273,600 | 0 | 4,202 | |
98 | Help King | [
"implementation",
"probabilities",
"trees"
] | B. Help King | 2 | 256 | This is the modification of the problem used during the official round. Unfortunately, author's solution of the original problem appeared wrong, so the problem was changed specially for the archive.
Once upon a time in a far away kingdom lived the King. The King had a beautiful daughter, Victoria. They lived happily, but not happily ever after: one day a vicious dragon attacked the kingdom and stole Victoria. The King was full of grief, yet he gathered his noble knights and promised half of his kingdom and Victoria's hand in marriage to the one who will save the girl from the infernal beast.
Having travelled for some time, the knights found the dragon's lair and all of them rushed there to save Victoria. Each knight spat on the dragon once and, as the dragon had quite a fragile and frail heart, his heart broke and poor beast died. As for the noble knights, they got Victoria right to the King and started brawling as each one wanted the girl's hand in marriage.
The problem was that all the noble knights were equally noble and equally handsome, and Victoria didn't want to marry any of them anyway. Then the King (and he was a very wise man and didn't want to hurt anybody's feelings) decided to find out who will get his daughter randomly, i.e. tossing a coin. However, there turned out to be *n* noble knights and the coin only has two sides. The good thing is that when a coin is tossed, the coin falls on each side with equal probability. The King got interested how to pick one noble knight using this coin so that all knights had equal probability of being chosen (the probability in that case should always be equal to 1<=/<=*n*). First the King wants to know the expected number of times he will need to toss a coin to determine the winner. Besides, while tossing the coin, the King should follow the optimal tossing strategy (i.e. the strategy that minimizes the expected number of tosses). Help the King in this challenging task. | The first line contains a single integer *n* from the problem's statement (1<=≤<=*n*<=≤<=10000). | Print the sought expected number of tosses as an irreducible fraction in the following form: "*a*/*b*" (without the quotes) without leading zeroes. | [
"2\n",
"3\n",
"4\n"
] | [
"1/1\n",
"8/3\n",
"2/1\n"
] | none | [
{
"input": "2",
"output": "1/1"
},
{
"input": "3",
"output": "8/3"
},
{
"input": "4",
"output": "2/1"
},
{
"input": "8",
"output": "3/1"
},
{
"input": "7",
"output": "24/7"
},
{
"input": "6",
"output": "11/3"
},
{
"input": "1",
"output"... | 0 | 0 | -1 | 4,209 |
190 | Non-Secret Cypher | [
"two pointers"
] | null | null | Berland starts to seize the initiative on the war with Flatland. To drive the enemy from their native land, the berlanders need to know exactly how many more flatland soldiers are left in the enemy's reserve. Fortunately, the scouts captured an enemy in the morning, who had a secret encrypted message with the information the berlanders needed so much.
The captured enemy had an array of positive integers. Berland intelligence have long been aware of the flatland code: to convey the message, which contained a number *m*, the enemies use an array of integers *a*. The number of its subarrays, in which there are at least *k* equal numbers, equals *m*. The number *k* has long been known in the Berland army so General Touristov has once again asked Corporal Vasya to perform a simple task: to decipher the flatlanders' message.
Help Vasya, given an array of integers *a* and number *k*, find the number of subarrays of the array of numbers *a*, which has at least *k* equal numbers.
Subarray *a*[*i*... *j*] (1<=≤<=*i*<=≤<=*j*<=≤<=*n*) of array *a*<==<=(*a*1,<=*a*2,<=...,<=*a**n*) is an array, made from its consecutive elements, starting from the *i*-th one and ending with the *j*-th one: *a*[*i*... *j*]<==<=(*a**i*,<=*a**i*<=+<=1,<=...,<=*a**j*). | The first line contains two space-separated integers *n*, *k* (1<=≤<=*k*<=≤<=*n*<=≤<=4·105), showing how many numbers an array has and how many equal numbers the subarrays are required to have, correspondingly.
The second line contains *n* space-separated integers *a**i* (1<=≤<=*a**i*<=≤<=109) — elements of the array. | Print the single number — the number of such subarrays of array *a*, that they have at least *k* equal integers.
Please do not use the %lld specifier to read or write 64-bit integers in С++. In is preferred to use the cin, cout streams or the %I64d specifier. | [
"4 2\n1 2 1 2\n",
"5 3\n1 2 1 1 3\n",
"3 1\n1 1 1\n"
] | [
"3",
"2",
"6"
] | In the first sample are three subarrays, containing at least two equal numbers: (1,2,1), (2,1,2) and (1,2,1,2).
In the second sample are two subarrays, containing three equal numbers: (1,2,1,1,3) and (1,2,1,1).
In the third sample any subarray contains at least one 1 number. Overall they are 6: (1), (1), (1), (1,1), (1,1) and (1,1,1). | [
{
"input": "4 2\n1 2 1 2",
"output": "3"
},
{
"input": "5 3\n1 2 1 1 3",
"output": "2"
},
{
"input": "3 1\n1 1 1",
"output": "6"
},
{
"input": "20 2\n6 7 2 4 6 8 4 3 10 5 3 5 7 9 1 2 8 1 9 10",
"output": "131"
},
{
"input": "63 2\n1 2 1 2 4 5 1 1 1 1 1 2 3 1 2 3 3... | 3,000 | 2,355,200 | 0 | 4,210 | |
460 | Little Dima and Equation | [
"brute force",
"implementation",
"math",
"number theory"
] | null | null | Little Dima misbehaved during a math lesson a lot and the nasty teacher Mr. Pickles gave him the following problem as a punishment.
Find all integer solutions *x* (0<=<<=*x*<=<<=109) of the equation:
where *a*, *b*, *c* are some predetermined constant values and function *s*(*x*) determines the sum of all digits in the decimal representation of number *x*.
The teacher gives this problem to Dima for each lesson. He changes only the parameters of the equation: *a*, *b*, *c*. Dima got sick of getting bad marks and he asks you to help him solve this challenging problem. | The first line contains three space-separated integers: *a*,<=*b*,<=*c* (1<=≤<=*a*<=≤<=5; 1<=≤<=*b*<=≤<=10000; <=-<=10000<=≤<=*c*<=≤<=10000). | Print integer *n* — the number of the solutions that you've found. Next print *n* integers in the increasing order — the solutions of the given equation. Print only integer solutions that are larger than zero and strictly less than 109. | [
"3 2 8\n",
"1 2 -18\n",
"2 2 -1\n"
] | [
"3\n10 2008 13726 ",
"0\n",
"4\n1 31 337 967 "
] | none | [
{
"input": "3 2 8",
"output": "3\n10 2008 13726 "
},
{
"input": "1 2 -18",
"output": "0"
},
{
"input": "2 2 -1",
"output": "4\n1 31 337 967 "
},
{
"input": "1 1 0",
"output": "9\n1 2 3 4 5 6 7 8 9 "
},
{
"input": "1 37 963",
"output": "16\n1000 1111 1222 1333 ... | 139 | 6,041,600 | 0 | 4,214 | |
612 | HDD is Outdated Technology | [
"implementation",
"math"
] | null | null | HDD hard drives group data by sectors. All files are split to fragments and each of them are written in some sector of hard drive. Note the fragments can be written in sectors in arbitrary order.
One of the problems of HDD hard drives is the following: the magnetic head should move from one sector to another to read some file.
Find the time need to read file split to *n* fragments. The *i*-th sector contains the *f**i*-th fragment of the file (1<=≤<=*f**i*<=≤<=*n*). Note different sectors contains the different fragments. At the start the magnetic head is in the position that contains the first fragment. The file are reading in the following manner: at first the first fragment is read, then the magnetic head moves to the sector that contains the second fragment, then the second fragment is read and so on until the *n*-th fragment is read. The fragments are read in the order from the first to the *n*-th.
It takes |*a*<=-<=*b*| time units to move the magnetic head from the sector *a* to the sector *b*. Reading a fragment takes no time. | The first line contains a positive integer *n* (1<=≤<=*n*<=≤<=2·105) — the number of fragments.
The second line contains *n* different integers *f**i* (1<=≤<=*f**i*<=≤<=*n*) — the number of the fragment written in the *i*-th sector. | Print the only integer — the number of time units needed to read the file. | [
"3\n3 1 2\n",
"5\n1 3 5 4 2\n"
] | [
"3\n",
"10\n"
] | In the second example the head moves in the following way:
- 1->2 means movement from the sector 1 to the sector 5, i.e. it takes 4 time units - 2->3 means movement from the sector 5 to the sector 2, i.e. it takes 3 time units - 3->4 means movement from the sector 2 to the sector 4, i.e. it takes 2 time units - 4->5 means movement from the sector 4 to the sector 3, i.e. it takes 1 time units
So the answer to the second example is 4 + 3 + 2 + 1 = 10. | [
{
"input": "3\n3 1 2",
"output": "3"
},
{
"input": "5\n1 3 5 4 2",
"output": "10"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "10\n8 2 10 3 4 6 1 7 9 5",
"output": "40"
... | 187 | 716,800 | -1 | 4,218 | |
78 | Beaver Game | [
"dp",
"games",
"number theory"
] | C. Beaver Game | 1 | 256 | Two beavers, Timur and Marsel, play the following game.
There are *n* logs, each of exactly *m* meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than *k* meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.
Timur makes the first move. The players play in the optimal way. Determine the winner. | The first line contains three integers *n*, *m*, *k* (1<=≤<=*n*,<=*m*,<=*k*<=≤<=109). | Print "Timur", if Timur wins, or "Marsel", if Marsel wins. You should print everything without the quotes. | [
"1 15 4\n",
"4 9 5\n"
] | [
"Timur",
"Marsel"
] | In the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as *k* = 4. Thus, the winner is Timur.
In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly. | [
{
"input": "1 15 4",
"output": "Timur"
},
{
"input": "4 9 5",
"output": "Marsel"
},
{
"input": "14 30 9",
"output": "Marsel"
},
{
"input": "81 180 53",
"output": "Timur"
},
{
"input": "225 187 20",
"output": "Marsel"
},
{
"input": "501 840 11",
"ou... | 46 | 4,608,000 | 0 | 4,222 |
186 | Growing Mushrooms | [
"greedy",
"sortings"
] | null | null | Each year in the castle of Dwarven King there is a competition in growing mushrooms among the dwarves. The competition is one of the most prestigious ones, and the winner gets a wooden salad bowl. This year's event brought together the best mushroom growers from around the world, so we had to slightly change the rules so that the event gets more interesting to watch.
Each mushroom grower has a mushroom that he will grow on the competition. Under the new rules, the competition consists of two parts. The first part lasts *t*1 seconds and the second part lasts *t*2 seconds. The first and the second part are separated by a little break.
After the starting whistle the first part of the contest starts, and all mushroom growers start growing mushrooms at once, each at his individual speed of *v**i* meters per second. After *t*1 seconds, the mushroom growers stop growing mushrooms and go to have a break. During the break, for unexplained reasons, the growth of all mushrooms is reduced by *k* percent. After the break the second part of the contest starts and all mushrooms growers at the same time continue to grow mushrooms, each at his individual speed of *u**i* meters per second. After a *t*2 seconds after the end of the break, the competition ends. Note that the speeds before and after the break may vary.
Before the match dwarf Pasha learned from all participants, what two speeds they have chosen. However, the participants did not want to disclose to him all their strategy and therefore, did not say in what order they will be using these speeds. That is, if a participant chose speeds *a**i* and *b**i*, then there are two strategies: he either uses speed *a**i* before the break and speed *b**i* after it, or vice versa.
Dwarf Pasha really wants to win the totalizer. He knows that each participant chooses the strategy that maximizes the height of the mushroom. Help Dwarf Pasha make the final table of competition results.
The participants are sorted in the result table by the mushroom height (the participants with higher mushrooms follow earlier in the table). In case of equal mushroom heights, the participants are sorted by their numbers (the participants with a smaller number follow earlier). | The first input line contains four integer numbers *n*, *t*1, *t*2, *k* (1<=≤<=*n*,<=*t*1,<=*t*2<=≤<=1000; 1<=≤<=*k*<=≤<=100) — the number of participants, the time before the break, the time after the break and the percentage, by which the mushroom growth drops during the break, correspondingly.
Each of the following *n* lines contains two integers. The *i*-th (1<=≤<=*i*<=≤<=*n*) line contains space-separated integers *a**i*, *b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=1000) — the speeds which the participant number *i* chose. | Print the final results' table: *n* lines, each line should contain the number of the corresponding dwarf and the final maximum height of his mushroom with exactly two digits after the decimal point. The answer will be considered correct if it is absolutely accurate. | [
"2 3 3 50\n2 4\n4 2\n",
"4 1 1 1\n544 397\n280 101\n280 101\n693 970\n"
] | [
"1 15.00\n2 15.00\n",
"4 1656.07\n1 937.03\n2 379.99\n3 379.99\n"
] | - First example: for each contestant it is optimal to use firstly speed 2 and afterwards speed 4, because 2·3·0.5 + 4·3 > 4·3·0.5 + 2·3. | [
{
"input": "2 3 3 50\n2 4\n4 2",
"output": "1 15.00\n2 15.00"
},
{
"input": "4 1 1 1\n544 397\n280 101\n280 101\n693 970",
"output": "4 1656.07\n1 937.03\n2 379.99\n3 379.99"
},
{
"input": "10 1 1 25\n981 1\n352 276\n164 691\n203 853\n599 97\n901 688\n934 579\n910 959\n317 624\n440 737",... | 278 | 22,835,200 | 3 | 4,227 | |
441 | Valera and Tubes | [
"constructive algorithms",
"dfs and similar",
"implementation"
] | null | null | Valera has got a rectangle table consisting of *n* rows and *m* columns. Valera numbered the table rows starting from one, from top to bottom and the columns – starting from one, from left to right. We will represent cell that is on the intersection of row *x* and column *y* by a pair of integers (*x*,<=*y*).
Valera wants to place exactly *k* tubes on his rectangle table. A tube is such sequence of table cells (*x*1,<=*y*1), (*x*2,<=*y*2), ..., (*x**r*,<=*y**r*), that:
- *r*<=≥<=2; - for any integer *i* (1<=≤<=*i*<=≤<=*r*<=-<=1) the following equation |*x**i*<=-<=*x**i*<=+<=1|<=+<=|*y**i*<=-<=*y**i*<=+<=1|<==<=1 holds; - each table cell, which belongs to the tube, must occur exactly once in the sequence.
Valera thinks that the tubes are arranged in a fancy manner if the following conditions are fulfilled:
- no pair of tubes has common cells; - each cell of the table belongs to some tube.
Help Valera to arrange *k* tubes on his rectangle table in a fancy manner. | The first line contains three space-separated integers *n*,<=*m*,<=*k* (2<=≤<=*n*,<=*m*<=≤<=300; 2<=≤<=2*k*<=≤<=*n*·*m*) — the number of rows, the number of columns and the number of tubes, correspondingly. | Print *k* lines. In the *i*-th line print the description of the *i*-th tube: first print integer *r**i* (the number of tube cells), then print 2*r**i* integers *x**i*1,<=*y**i*1,<=*x**i*2,<=*y**i*2,<=...,<=*x**ir**i*,<=*y**ir**i* (the sequence of table cells).
If there are multiple solutions, you can print any of them. It is guaranteed that at least one solution exists. | [
"3 3 3\n",
"2 3 1\n"
] | [
"3 1 1 1 2 1 3\n3 2 1 2 2 2 3\n3 3 1 3 2 3 3\n",
"6 1 1 1 2 1 3 2 3 2 2 2 1\n"
] | Picture for the first sample:
Picture for the second sample: | [
{
"input": "3 3 3",
"output": "3 1 1 1 2 1 3\n3 2 1 2 2 2 3\n3 3 1 3 2 3 3"
},
{
"input": "2 3 1",
"output": "6 1 1 1 2 1 3 2 3 2 2 2 1"
},
{
"input": "2 3 1",
"output": "6 1 1 1 2 1 3 2 3 2 2 2 1"
},
{
"input": "300 300 2",
"output": "2 1 1 1 2\n89998 1 3 1 4 1 5 1 6 1 7... | 607 | 16,486,400 | 3 | 4,230 | |
680 | Bear and Five Cards | [
"constructive algorithms",
"implementation"
] | null | null | A little bear Limak plays a game. He has five cards. There is one number written on each card. Each number is a positive integer.
Limak can discard (throw out) some cards. His goal is to minimize the sum of numbers written on remaining (not discarded) cards.
He is allowed to at most once discard two or three cards with the same number. Of course, he won't discard cards if it's impossible to choose two or three cards with the same number.
Given five numbers written on cards, cay you find the minimum sum of numbers on remaining cards? | The only line of the input contains five integers *t*1, *t*2, *t*3, *t*4 and *t*5 (1<=≤<=*t**i*<=≤<=100) — numbers written on cards. | Print the minimum possible sum of numbers written on remaining cards. | [
"7 3 7 3 20\n",
"7 9 3 1 8\n",
"10 10 10 10 10\n"
] | [
"26\n",
"28\n",
"20\n"
] | In the first sample, Limak has cards with numbers 7, 3, 7, 3 and 20. Limak can do one of the following.
- Do nothing and the sum would be 7 + 3 + 7 + 3 + 20 = 40. - Remove two cards with a number 7. The remaining sum would be 3 + 3 + 20 = 26. - Remove two cards with a number 3. The remaining sum would be 7 + 7 + 20 = 34.
You are asked to minimize the sum so the answer is 26.
In the second sample, it's impossible to find two or three cards with the same number. Hence, Limak does nothing and the sum is 7 + 9 + 1 + 3 + 8 = 28.
In the third sample, all cards have the same number. It's optimal to discard any three cards. The sum of two remaining numbers is 10 + 10 = 20. | [
{
"input": "7 3 7 3 20",
"output": "26"
},
{
"input": "7 9 3 1 8",
"output": "28"
},
{
"input": "10 10 10 10 10",
"output": "20"
},
{
"input": "8 7 1 8 7",
"output": "15"
},
{
"input": "7 7 7 8 8",
"output": "16"
},
{
"input": "8 8 8 2 2",
"output"... | 46 | 0 | 3 | 4,232 | |
784 | Numbers Joke | [
"*special"
] | null | null | The input contains a single integer *a* (1<=≤<=*a*<=≤<=30).
Output a single integer. | The input contains a single integer *a* (1<=≤<=*a*<=≤<=30). | Output a single integer. | [
"3\n"
] | [
"27\n"
] | none | [
{
"input": "3",
"output": "27"
},
{
"input": "1",
"output": "4"
},
{
"input": "2",
"output": "22"
},
{
"input": "4",
"output": "58"
},
{
"input": "5",
"output": "85"
},
{
"input": "6",
"output": "94"
},
{
"input": "7",
"output": "121"
... | 0 | 0 | -1 | 4,246 | |
142 | Help Greg the Dwarf 2 | [
"geometry"
] | null | null | Greg the Dwarf has been really busy recently with excavations by the Neverland Mountain. However for the well-known reasons (as you probably remember he is a very unusual dwarf and he cannot stand sunlight) Greg can only excavate at night. And in the morning he should be in his crypt before the first sun ray strikes. That's why he wants to find the shortest route from the excavation point to his crypt. Greg has recollected how the Codeforces participants successfully solved the problem of transporting his coffin to a crypt. So, in some miraculous way Greg appeared in your bedroom and asks you to help him in a highly persuasive manner. As usual, you didn't feel like turning him down.
After some thought, you formalized the task as follows: as the Neverland mountain has a regular shape and ends with a rather sharp peak, it can be represented as a cone whose base radius equals *r* and whose height equals *h*. The graveyard where Greg is busy excavating and his crypt can be represented by two points on the cone's surface. All you've got to do is find the distance between points on the cone's surface.
The task is complicated by the fact that the mountain's base on the ground level and even everything below the mountain has been dug through by gnome (one may wonder whether they've been looking for the same stuff as Greg...). So, one can consider the shortest way to pass not only along the side surface, but also along the cone's base (and in a specific case both points can lie on the cone's base — see the first sample test)
Greg will be satisfied with the problem solution represented as the length of the shortest path between two points — he can find his way pretty well on his own. He gave you two hours to solve the problem and the time is ticking! | The first input line contains space-separated integers *r* and *h* (1<=≤<=*r*,<=*h*<=≤<=1000) — the base radius and the cone height correspondingly. The second and third lines contain coordinates of two points on the cone surface, groups of three space-separated real numbers. The coordinates of the points are given in the systems of coordinates where the origin of coordinates is located in the centre of the cone's base and its rotation axis matches the *OZ* axis. In this coordinate system the vertex of the cone is located at the point (0,<=0,<=*h*), the base of the cone is a circle whose center is at the point (0,<=0,<=0), lying on the *XOY* plane, and all points on the cone surface have a non-negative coordinate *z*. It is guaranteed that the distances from the points to the cone surface do not exceed 10<=-<=12. All real numbers in the input have no more than 16 digits after decimal point. | Print the length of the shortest path between the points given in the input, with absolute or relative error not exceeding 10<=-<=6. | [
"2 2\n1.0 0.0 0.0\n-1.0 0.0 0.0\n",
"2 2\n1.0 0.0 0.0\n1.0 0.0 1.0\n",
"2 2\n1.0 0.0 1.0\n-1.0 0.0 1.0\n",
"2 2\n1.0 0.0 0.0\n0.0 1.0 1.0\n"
] | [
"2.000000000",
"2.414213562",
"2.534324263",
"3.254470198"
] | none | [
{
"input": "2 2\n1.0 0.0 0.0\n-1.0 0.0 0.0",
"output": "2.0000000000000000"
},
{
"input": "2 2\n1.0 0.0 0.0\n1.0 0.0 1.0",
"output": "2.414213562373095"
},
{
"input": "2 2\n1.0 0.0 1.0\n-1.0 0.0 1.0",
"output": "2.534324262661599"
},
{
"input": "2 2\n1.0 0.0 0.0\n0.0 1.0 1.0"... | 92 | 0 | 0 | 4,257 | |
598 | Queries on a String | [
"implementation",
"strings"
] | null | null | You are given a string *s* and should process *m* queries. Each query is described by two 1-based indices *l**i*, *r**i* and integer *k**i*. It means that you should cyclically shift the substring *s*[*l**i*... *r**i*] *k**i* times. The queries should be processed one after another in the order they are given.
One operation of a cyclic shift (rotation) is equivalent to moving the last character to the position of the first character and shifting all other characters one position to the right.
For example, if the string *s* is abacaba and the query is *l*1<==<=3,<=*r*1<==<=6,<=*k*1<==<=1 then the answer is abbacaa. If after that we would process the query *l*2<==<=1,<=*r*2<==<=4,<=*k*2<==<=2 then we would get the string baabcaa. | The first line of the input contains the string *s* (1<=≤<=|*s*|<=≤<=10<=000) in its initial state, where |*s*| stands for the length of *s*. It contains only lowercase English letters.
Second line contains a single integer *m* (1<=≤<=*m*<=≤<=300) — the number of queries.
The *i*-th of the next *m* lines contains three integers *l**i*, *r**i* and *k**i* (1<=≤<=*l**i*<=≤<=*r**i*<=≤<=|*s*|,<=1<=≤<=*k**i*<=≤<=1<=000<=000) — the description of the *i*-th query. | Print the resulting string *s* after processing all *m* queries. | [
"abacaba\n2\n3 6 1\n1 4 2\n"
] | [
"baabcaa\n"
] | The sample is described in problem statement. | [
{
"input": "abacaba\n2\n3 6 1\n1 4 2",
"output": "baabcaa"
},
{
"input": "u\n1\n1 1 1",
"output": "u"
},
{
"input": "p\n5\n1 1 5\n1 1 9\n1 1 10\n1 1 10\n1 1 4",
"output": "p"
},
{
"input": "ssssssssss\n5\n5 7 9\n3 9 3\n2 7 1\n7 7 10\n1 9 6",
"output": "ssssssssss"
},
... | 2,000 | 1,433,600 | 0 | 4,260 | |
915 | Imbalance Value of a Tree | [
"data structures",
"dsu",
"graphs",
"trees"
] | null | null | You are given a tree *T* consisting of *n* vertices. A number is written on each vertex; the number written on vertex *i* is *a**i*. Let's denote the function *I*(*x*,<=*y*) as the difference between maximum and minimum value of *a**i* on a simple path connecting vertices *x* and *y*.
Your task is to calculate . | The first line contains one integer number *n* (1<=≤<=*n*<=≤<=106) — the number of vertices in the tree.
The second line contains *n* integer numbers *a*1, *a*2, ..., *a**n* (1<=≤<=*a**i*<=≤<=106) — the numbers written on the vertices.
Then *n*<=-<=1 lines follow. Each line contains two integers *x* and *y* denoting an edge connecting vertex *x* and vertex *y* (1<=≤<=*x*,<=*y*<=≤<=*n*, *x*<=≠<=*y*). It is guaranteed that these edges denote a tree. | Print one number equal to . | [
"4\n2 2 3 1\n1 2\n1 3\n1 4\n"
] | [
"6\n"
] | none | [
{
"input": "4\n2 2 3 1\n1 2\n1 3\n1 4",
"output": "6"
}
] | 93 | 2,867,200 | 0 | 4,276 | |
675 | Restoring Painting | [
"brute force",
"constructive algorithms",
"math"
] | null | null | Vasya works as a watchman in the gallery. Unfortunately, one of the most expensive paintings was stolen while he was on duty. He doesn't want to be fired, so he has to quickly restore the painting. He remembers some facts about it.
- The painting is a square 3<=×<=3, each cell contains a single integer from 1 to *n*, and different cells may contain either different or equal integers. - The sum of integers in each of four squares 2<=×<=2 is equal to the sum of integers in the top left square 2<=×<=2. - Four elements *a*, *b*, *c* and *d* are known and are located as shown on the picture below.
Help Vasya find out the number of distinct squares the satisfy all the conditions above. Note, that this number may be equal to 0, meaning Vasya remembers something wrong.
Two squares are considered to be different, if there exists a cell that contains two different integers in different squares. | The first line of the input contains five integers *n*, *a*, *b*, *c* and *d* (1<=≤<=*n*<=≤<=100<=000, 1<=≤<=*a*,<=*b*,<=*c*,<=*d*<=≤<=*n*) — maximum possible value of an integer in the cell and four integers that Vasya remembers. | Print one integer — the number of distinct valid squares. | [
"2 1 1 1 2\n",
"3 3 1 2 3\n"
] | [
"2\n",
"6\n"
] | Below are all the possible paintings for the first sample. <img class="tex-graphics" src="https://espresso.codeforces.com/c4c53d4e7b6814d8aad7b72604b6089d61dadb48.png" style="max-width: 100.0%;max-height: 100.0%;"/> <img class="tex-graphics" src="https://espresso.codeforces.com/46a6ad6a5d3db202f3779b045b9dc77fc2348cf1.png" style="max-width: 100.0%;max-height: 100.0%;"/>
In the second sample, only paintings displayed below satisfy all the rules. <img class="tex-graphics" src="https://espresso.codeforces.com/776f231305f8ce7c33e79e887722ce46aa8b6e61.png" style="max-width: 100.0%;max-height: 100.0%;"/> <img class="tex-graphics" src="https://espresso.codeforces.com/2fce9e9a31e70f1e46ea26f11d7305b3414e9b6b.png" style="max-width: 100.0%;max-height: 100.0%;"/> <img class="tex-graphics" src="https://espresso.codeforces.com/be084a4d1f7e475be1183f7dff10e9c89eb175ef.png" style="max-width: 100.0%;max-height: 100.0%;"/> <img class="tex-graphics" src="https://espresso.codeforces.com/96afdb4a35ac14f595d29bea2282f621098902f4.png" style="max-width: 100.0%;max-height: 100.0%;"/> <img class="tex-graphics" src="https://espresso.codeforces.com/79ca8d720334a74910514f017ecf1d0166009a03.png" style="max-width: 100.0%;max-height: 100.0%;"/> <img class="tex-graphics" src="https://espresso.codeforces.com/ad3c37e950bf5702d54f05756db35c831da59ad9.png" style="max-width: 100.0%;max-height: 100.0%;"/> | [
{
"input": "2 1 1 1 2",
"output": "2"
},
{
"input": "3 3 1 2 3",
"output": "6"
},
{
"input": "1 1 1 1 1",
"output": "1"
},
{
"input": "1000 522 575 426 445",
"output": "774000"
},
{
"input": "99000 52853 14347 64237 88869",
"output": "1296306000"
},
{
... | 124 | 307,200 | 3 | 4,286 | |
963 | Frequency of String | [
"hashing",
"string suffix structures",
"strings"
] | null | null | You are given a string $s$. You should answer $n$ queries. The $i$-th query consists of integer $k_i$ and string $m_i$. The answer for this query is the minimum length of such a string $t$ that $t$ is a substring of $s$ and $m_i$ has at least $k_i$ occurrences as a substring in $t$.
A substring of a string is a continuous segment of characters of the string.
It is guaranteed that for any two queries the strings $m_i$ from these queries are different. | The first line contains string $s$ $(1 \leq \left | s \right | \leq 10^{5})$.
The second line contains an integer $n$ ($1 \leq n \leq 10^5$).
Each of next $n$ lines contains an integer $k_i$ $(1 \leq k_i \leq |s|)$ and a non-empty string $m_i$ — parameters of the query with number $i$, in this order.
All strings in input consists of lowercase English letters. Sum of length of all strings in input doesn't exceed $10^5$. All $m_i$ are distinct. | For each query output the answer for it in a separate line.
If a string $m_{i}$ occurs in $s$ less that $k_{i}$ times, output -1. | [
"aaaaa\n5\n3 a\n3 aa\n2 aaa\n3 aaaa\n1 aaaaa\n",
"abbb\n7\n4 b\n1 ab\n3 bb\n1 abb\n2 bbb\n1 a\n2 abbb\n"
] | [
"3\n4\n4\n-1\n5\n",
"-1\n2\n-1\n3\n-1\n1\n-1\n"
] | none | [] | 0 | 0 | -1 | 4,301 | |
165 | Burning Midnight Oil | [
"binary search",
"implementation"
] | null | null | One day a highly important task was commissioned to Vasya — writing a program in a night. The program consists of *n* lines of code. Vasya is already exhausted, so he works like that: first he writes *v* lines of code, drinks a cup of tea, then he writes as much as lines, drinks another cup of tea, then he writes lines and so on: , , , ...
The expression is regarded as the integral part from dividing number *a* by number *b*.
The moment the current value equals 0, Vasya immediately falls asleep and he wakes up only in the morning, when the program should already be finished.
Vasya is wondering, what minimum allowable value *v* can take to let him write not less than *n* lines of code before he falls asleep. | The input consists of two integers *n* and *k*, separated by spaces — the size of the program in lines and the productivity reduction coefficient, 1<=≤<=*n*<=≤<=109, 2<=≤<=*k*<=≤<=10. | Print the only integer — the minimum value of *v* that lets Vasya write the program in one night. | [
"7 2\n",
"59 9\n"
] | [
"4\n",
"54\n"
] | In the first sample the answer is *v* = 4. Vasya writes the code in the following portions: first 4 lines, then 2, then 1, and then Vasya falls asleep. Thus, he manages to write 4 + 2 + 1 = 7 lines in a night and complete the task.
In the second sample the answer is *v* = 54. Vasya writes the code in the following portions: 54, 6. The total sum is 54 + 6 = 60, that's even more than *n* = 59. | [
{
"input": "7 2",
"output": "4"
},
{
"input": "59 9",
"output": "54"
},
{
"input": "1 9",
"output": "1"
},
{
"input": "11 2",
"output": "7"
},
{
"input": "747 2",
"output": "376"
},
{
"input": "6578 2",
"output": "3293"
},
{
"input": "37212... | 154 | 2,867,200 | -1 | 4,307 | |
331 | Oh Sweet Beaverette | [
"data structures",
"sortings"
] | null | null | — Oh my sweet Beaverette, would you fancy a walk along a wonderful woodland belt with me?
— Of course, my Smart Beaver! Let us enjoy the splendid view together. How about Friday night?
At this point the Smart Beaver got rushing. Everything should be perfect by Friday, so he needed to prepare the belt to the upcoming walk. He needed to cut down several trees.
Let's consider the woodland belt as a sequence of trees. Each tree *i* is described by the esthetic appeal *a**i* — some trees are very esthetically pleasing, others are 'so-so', and some trees are positively ugly!
The Smart Beaver calculated that he needed the following effects to win the Beaverette's heart:
- The first objective is to please the Beaverette: the sum of esthetic appeal of the remaining trees must be maximum possible; - the second objective is to surprise the Beaverette: the esthetic appeal of the first and the last trees in the resulting belt must be the same; - and of course, the walk should be successful: there must be at least two trees in the woodland belt left.
Now help the Smart Beaver! Which trees does he need to cut down to win the Beaverette's heart? | The first line contains a single integer *n* — the initial number of trees in the woodland belt, 2<=≤<=*n*. The second line contains space-separated integers *a**i* — the esthetic appeals of each tree. All esthetic appeals do not exceed 109 in their absolute value.
- to get 30 points, you need to solve the problem with constraints: *n*<=≤<=100 (subproblem A1); - to get 100 points, you need to solve the problem with constraints: *n*<=≤<=3·105 (subproblems A1+A2). | In the first line print two integers — the total esthetic appeal of the woodland belt after the Smart Beaver's intervention and the number of the cut down trees *k*.
In the next line print *k* integers — the numbers of the trees the Beaver needs to cut down. Assume that the trees are numbered from 1 to *n* from left to right.
If there are multiple solutions, print any of them. It is guaranteed that at least two trees have equal esthetic appeal. | [
"5\n1 2 3 1 2\n",
"5\n1 -2 3 1 -2\n"
] | [
"8 1\n1 ",
"5 2\n2 5 "
] | none | [
{
"input": "5\n1 2 3 1 2",
"output": "8 1\n1 "
},
{
"input": "5\n1 -2 3 1 -2",
"output": "5 2\n2 5 "
},
{
"input": "2\n0 0",
"output": "0 0"
},
{
"input": "3\n0 -1 0",
"output": "0 1\n2 "
},
{
"input": "3\n1 1 1",
"output": "3 0"
},
{
"input": "4\n-1 1... | 92 | 0 | 0 | 4,320 | |
133 | Unary | [
"implementation"
] | null | null | Unary is a minimalistic Brainfuck dialect in which programs are written using only one token.
Brainfuck programs use 8 commands: "+", "-", "[", "]", "<", ">", "." and "," (their meaning is not important for the purposes of this problem). Unary programs are created from Brainfuck programs using the following algorithm. First, replace each command with a corresponding binary code, using the following conversion table:
- ">" <=→<= 1000, - "<" <=→<= 1001, - "+" <=→<= 1010, - "-" <=→<= 1011, - "." <=→<= 1100, - "," <=→<= 1101, - "[" <=→<= 1110, - "]" <=→<= 1111.
Next, concatenate the resulting binary codes into one binary number in the same order as in the program. Finally, write this number using unary numeral system — this is the Unary program equivalent to the original Brainfuck one.
You are given a Brainfuck program. Your task is to calculate the size of the equivalent Unary program, and print it modulo 1000003 (106<=+<=3). | The input will consist of a single line *p* which gives a Brainfuck program. String *p* will contain between 1 and 100 characters, inclusive. Each character of *p* will be "+", "-", "[", "]", "<", ">", "." or ",". | Output the size of the equivalent Unary program modulo 1000003 (106<=+<=3). | [
",.\n",
"++++[>,.<-]\n"
] | [
"220\n",
"61425\n"
] | To write a number *n* in unary numeral system, one simply has to write 1 *n* times. For example, 5 written in unary system will be 11111.
In the first example replacing Brainfuck commands with binary code will give us 1101 1100. After we concatenate the codes, we'll get 11011100 in binary system, or 220 in decimal. That's exactly the number of tokens in the equivalent Unary program. | [
{
"input": ",.",
"output": "220"
},
{
"input": "++++[>,.<-]",
"output": "61425"
},
{
"input": "[-],<],<<,<[,>,+>[[<>.,[>-[-[<><>><<<<]>,.-].>-[[>+,>,[,-,.-,-[[]>..<>,<[+,-<]-++.<+.]<,[[.<<-><<<],",
"output": "43789"
},
{
"input": "+",
"output": "10"
},
{
"input": ... | 124 | 0 | 3 | 4,325 | |
320 | Ping-Pong (Easy Version) | [
"dfs and similar",
"graphs"
] | null | null | In this problem at each moment you have a set of intervals. You can move from interval (*a*,<=*b*) from our set to interval (*c*,<=*d*) from our set if and only if *c*<=<<=*a*<=<<=*d* or *c*<=<<=*b*<=<<=*d*. Also there is a path from interval *I*1 from our set to interval *I*2 from our set if there is a sequence of successive moves starting from *I*1 so that we can reach *I*2.
Your program should handle the queries of the following two types:
1. "1 x y" (*x*<=<<=*y*) — add the new interval (*x*,<=*y*) to the set of intervals. The length of the new interval is guaranteed to be strictly greater than all the previous intervals.1. "2 a b" (*a*<=≠<=*b*) — answer the question: is there a path from *a*-th (one-based) added interval to *b*-th (one-based) added interval?
Answer all the queries. Note, that initially you have an empty set of intervals. | The first line of the input contains integer *n* denoting the number of queries, (1<=≤<=*n*<=≤<=100). Each of the following lines contains a query as described above. All numbers in the input are integers and don't exceed 109 by their absolute value.
It's guaranteed that all queries are correct. | For each query of the second type print "YES" or "NO" on a separate line depending on the answer. | [
"5\n1 1 5\n1 5 11\n2 1 2\n1 2 9\n2 1 2\n"
] | [
"NO\nYES\n"
] | none | [
{
"input": "5\n1 1 5\n1 5 11\n2 1 2\n1 2 9\n2 1 2",
"output": "NO\nYES"
},
{
"input": "10\n1 -311 -186\n1 -1070 -341\n1 -1506 -634\n1 688 1698\n2 2 4\n1 70 1908\n2 1 2\n2 2 4\n1 -1053 1327\n2 5 4",
"output": "NO\nNO\nNO\nYES"
},
{
"input": "10\n1 -1365 -865\n1 1244 1834\n2 1 2\n1 -1508 -... | 124 | 0 | 0 | 4,334 | |
787 | The Monster | [
"brute force",
"math",
"number theory"
] | null | null | A monster is chasing after Rick and Morty on another planet. They're so frightened that sometimes they scream. More accurately, Rick screams at times *b*,<=*b*<=+<=*a*,<=*b*<=+<=2*a*,<=*b*<=+<=3*a*,<=... and Morty screams at times *d*,<=*d*<=+<=*c*,<=*d*<=+<=2*c*,<=*d*<=+<=3*c*,<=....
The Monster will catch them if at any point they scream at the same time, so it wants to know when it will catch them (the first time they scream at the same time) or that they will never scream at the same time. | The first line of input contains two integers *a* and *b* (1<=≤<=*a*,<=*b*<=≤<=100).
The second line contains two integers *c* and *d* (1<=≤<=*c*,<=*d*<=≤<=100). | Print the first time Rick and Morty will scream at the same time, or <=-<=1 if they will never scream at the same time. | [
"20 2\n9 19\n",
"2 1\n16 12\n"
] | [
"82\n",
"-1\n"
] | In the first sample testcase, Rick's 5th scream and Morty's 8th time are at time 82.
In the second sample testcase, all Rick's screams will be at odd times and Morty's will be at even times, so they will never scream at the same time. | [
{
"input": "20 2\n9 19",
"output": "82"
},
{
"input": "2 1\n16 12",
"output": "-1"
},
{
"input": "39 52\n88 78",
"output": "1222"
},
{
"input": "59 96\n34 48",
"output": "1748"
},
{
"input": "87 37\n91 29",
"output": "211"
},
{
"input": "11 81\n49 7",
... | 514 | 4,608,000 | 3 | 4,338 | |
0 | none | [
"none"
] | null | null | As we all know Barney's job is "PLEASE" and he has not much to do at work. That's why he started playing "cups and key". In this game there are three identical cups arranged in a line from left to right. Initially key to Barney's heart is under the middle cup.
Then at one turn Barney swaps the cup in the middle with any of other two cups randomly (he choses each with equal probability), so the chosen cup becomes the middle one. Game lasts *n* turns and Barney independently choses a cup to swap with the middle one within each turn, and the key always remains in the cup it was at the start.
After *n*-th turn Barney asks a girl to guess which cup contains the key. The girl points to the middle one but Barney was distracted while making turns and doesn't know if the key is under the middle cup. That's why he asked you to tell him the probability that girl guessed right.
Number *n* of game turns can be extremely large, that's why Barney did not give it to you. Instead he gave you an array *a*1,<=*a*2,<=...,<=*a**k* such that
in other words, *n* is multiplication of all elements of the given array.
Because of precision difficulties, Barney asked you to tell him the answer as an irreducible fraction. In other words you need to find it as a fraction *p*<=/<=*q* such that , where is the greatest common divisor. Since *p* and *q* can be extremely large, you only need to find the remainders of dividing each of them by 109<=+<=7.
Please note that we want of *p* and *q* to be 1, not of their remainders after dividing by 109<=+<=7. | The first line of input contains a single integer *k* (1<=≤<=*k*<=≤<=105) — the number of elements in array Barney gave you.
The second line contains *k* integers *a*1,<=*a*2,<=...,<=*a**k* (1<=≤<=*a**i*<=≤<=1018) — the elements of the array. | In the only line of output print a single string *x*<=/<=*y* where *x* is the remainder of dividing *p* by 109<=+<=7 and *y* is the remainder of dividing *q* by 109<=+<=7. | [
"1\n2\n",
"3\n1 1 1\n"
] | [
"1/2\n",
"0/1\n"
] | none | [
{
"input": "1\n2",
"output": "1/2"
},
{
"input": "3\n1 1 1",
"output": "0/1"
},
{
"input": "1\n983155795040951739",
"output": "145599903/436799710"
},
{
"input": "2\n467131402341701583 956277077729692725",
"output": "63467752/190403257"
},
{
"input": "10\n21767322... | 62 | 1,228,800 | 0 | 4,342 | |
879 | Borya's Diagnosis | [
"implementation"
] | null | null | It seems that Borya is seriously sick. He is going visit *n* doctors to find out the exact diagnosis. Each of the doctors needs the information about all previous visits, so Borya has to visit them in the prescribed order (i.e. Borya should first visit doctor 1, then doctor 2, then doctor 3 and so on). Borya will get the information about his health from the last doctor.
Doctors have a strange working schedule. The doctor *i* goes to work on the *s**i*-th day and works every *d**i* day. So, he works on days *s**i*,<=*s**i*<=+<=*d**i*,<=*s**i*<=+<=2*d**i*,<=....
The doctor's appointment takes quite a long time, so Borya can not see more than one doctor per day. What is the minimum time he needs to visit all doctors? | First line contains an integer *n* — number of doctors (1<=≤<=*n*<=≤<=1000).
Next *n* lines contain two numbers *s**i* and *d**i* (1<=≤<=*s**i*,<=*d**i*<=≤<=1000). | Output a single integer — the minimum day at which Borya can visit the last doctor. | [
"3\n2 2\n1 2\n2 2\n",
"2\n10 1\n6 5\n"
] | [
"4\n",
"11\n"
] | In the first sample case, Borya can visit all doctors on days 2, 3 and 4.
In the second sample case, Borya can visit all doctors on days 10 and 11. | [
{
"input": "3\n2 2\n1 2\n2 2",
"output": "4"
},
{
"input": "2\n10 1\n6 5",
"output": "11"
},
{
"input": "3\n6 10\n3 3\n8 2",
"output": "10"
},
{
"input": "4\n4 8\n10 10\n4 2\n8 2",
"output": "14"
},
{
"input": "5\n7 1\n5 1\n6 1\n1 6\n6 8",
"output": "14"
},
... | 62 | 0 | 0 | 4,362 | |
975 | Mancala | [
"brute force",
"implementation"
] | null | null | Mancala is a game famous in the Middle East. It is played on a board that consists of 14 holes.
Initially, each hole has $a_i$ stones. When a player makes a move, he chooses a hole which contains a positive number of stones. He takes all the stones inside it and then redistributes these stones one by one in the next holes in a counter-clockwise direction.
Note that the counter-clockwise order means if the player takes the stones from hole $i$, he will put one stone in the $(i+1)$-th hole, then in the $(i+2)$-th, etc. If he puts a stone in the $14$-th hole, the next one will be put in the first hole.
After the move, the player collects all the stones from holes that contain even number of stones. The number of stones collected by player is the score, according to Resli.
Resli is a famous Mancala player. He wants to know the maximum score he can obtain after one move. | The only line contains 14 integers $a_1, a_2, \ldots, a_{14}$ ($0 \leq a_i \leq 10^9$) — the number of stones in each hole.
It is guaranteed that for any $i$ ($1\leq i \leq 14$) $a_i$ is either zero or odd, and there is at least one stone in the board. | Output one integer, the maximum possible score after one move. | [
"0 1 1 0 0 0 0 0 0 7 0 0 0 0\n",
"5 1 1 1 1 0 0 0 0 0 0 0 0 0\n"
] | [
"4\n",
"8\n"
] | In the first test case the board after the move from the hole with $7$ stones will look like 1 2 2 0 0 0 0 0 0 0 1 1 1 1. Then the player collects the even numbers and ends up with a score equal to $4$. | [
{
"input": "0 1 1 0 0 0 0 0 0 7 0 0 0 0",
"output": "4"
},
{
"input": "5 1 1 1 1 0 0 0 0 0 0 0 0 0",
"output": "8"
},
{
"input": "10001 10001 10001 10001 10001 10001 10001 10001 10001 10001 10001 10001 10001 1",
"output": "54294"
},
{
"input": "0 0 0 0 0 0 0 0 0 0 0 0 0 15",
... | 46 | 409,600 | 3 | 4,364 | |
992 | Nastya and an Array | [
"implementation",
"sortings"
] | null | null | Nastya owns too many arrays now, so she wants to delete the least important of them. However, she discovered that this array is magic! Nastya now knows that the array has the following properties:
- In one second we can add an arbitrary (possibly negative) integer to all elements of the array that are not equal to zero. - When all elements of the array become equal to zero, the array explodes.
Nastya is always busy, so she wants to explode the array as fast as possible. Compute the minimum time in which the array can be exploded. | The first line contains a single integer *n* (1<=≤<=*n*<=≤<=105) — the size of the array.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (<=-<=105<=≤<=*a**i*<=≤<=105) — the elements of the array. | Print a single integer — the minimum number of seconds needed to make all elements of the array equal to zero. | [
"5\n1 1 1 1 1\n",
"3\n2 0 -1\n",
"4\n5 -6 -5 1\n"
] | [
"1\n",
"2\n",
"4\n"
] | In the first example you can add - 1 to all non-zero elements in one second and make them equal to zero.
In the second example you can add - 2 on the first second, then the array becomes equal to [0, 0, - 3]. On the second second you can add 3 to the third (the only non-zero) element. | [
{
"input": "5\n1 1 1 1 1",
"output": "1"
},
{
"input": "3\n2 0 -1",
"output": "2"
},
{
"input": "4\n5 -6 -5 1",
"output": "4"
},
{
"input": "1\n0",
"output": "0"
},
{
"input": "2\n21794 -79194",
"output": "2"
},
{
"input": "3\n-63526 95085 -5239",
... | 1,000 | 13,619,200 | 0 | 4,380 | |
88 | Chord | [
"brute force",
"implementation"
] | A. Chord | 2 | 256 | Vasya studies music.
He has learned lots of interesting stuff. For example, he knows that there are 12 notes: C, C#, D, D#, E, F, F#, G, G#, A, B, H. He also knows that the notes are repeated cyclically: after H goes C again, and before C stands H. We will consider the C note in the row's beginning and the C note after the H similar and we will identify them with each other. The distance between the notes along the musical scale is measured in tones: between two consecutive notes there's exactly one semitone, that is, 0.5 tone. The distance is taken from the lowest tone to the uppest one, that is, the distance between C and E is 4 semitones and between E and C is 8 semitones
Vasya also knows what a chord is. A chord is an unordered set of no less than three notes. However, for now Vasya only works with triads, that is with the chords that consist of exactly three notes. He can already distinguish between two types of triads — major and minor.
Let's define a major triad. Let the triad consist of notes *X*, *Y* and *Z*. If we can order the notes so as the distance along the musical scale between *X* and *Y* equals 4 semitones and the distance between *Y* and *Z* is 3 semitones, then the triad is major. The distance between *X* and *Z*, accordingly, equals 7 semitones.
A minor triad is different in that the distance between *X* and *Y* should be 3 semitones and between *Y* and *Z* — 4 semitones.
For example, the triad "C E G" is major: between C and E are 4 semitones, and between E and G are 3 semitones. And the triplet "C# B F" is minor, because if we order the notes as "B C# F", than between B and C# will be 3 semitones, and between C# and F — 4 semitones.
Help Vasya classify the triad the teacher has given to him. | The only line contains 3 space-separated notes in the above-given notation. | Print "major" if the chord is major, "minor" if it is minor, and "strange" if the teacher gave Vasya some weird chord which is neither major nor minor. Vasya promises you that the answer will always be unambiguous. That is, there are no chords that are both major and minor simultaneously. | [
"C E G\n",
"C# B F\n",
"A B H\n"
] | [
"major\n",
"minor\n",
"strange\n"
] | none | [
{
"input": "C E G",
"output": "major"
},
{
"input": "C# B F",
"output": "minor"
},
{
"input": "A B H",
"output": "strange"
},
{
"input": "G H E",
"output": "minor"
},
{
"input": "D# B G",
"output": "major"
},
{
"input": "D# B F#",
"output": "minor"... | 310 | 0 | 3.9225 | 4,389 |
253 | Physics Practical | [
"binary search",
"dp",
"sortings",
"two pointers"
] | null | null | One day Vasya was on a physics practical, performing the task on measuring the capacitance. He followed the teacher's advice and did as much as *n* measurements, and recorded the results in the notebook. After that he was about to show the results to the teacher, but he remembered that at the last lesson, the teacher had made his friend Petya redo the experiment because the largest and the smallest results differed by more than two times. Vasya is lazy, and he does not want to redo the experiment. He wants to do the task and go home play computer games. So he decided to cheat: before Vasya shows the measurements to the teacher, he will erase some of them, so as to make the largest and the smallest results of the remaining measurements differ in no more than two times. In other words, if the remaining measurements have the smallest result *x*, and the largest result *y*, then the inequality *y*<=≤<=2·*x* must fulfill. Of course, to avoid the teacher's suspicion, Vasya wants to remove as few measurement results as possible from his notes.
Help Vasya, find what minimum number of measurement results he will have to erase from his notes so that the largest and the smallest of the remaining results of the measurements differed in no more than two times. | The first line contains integer *n* (2<=≤<=*n*<=≤<=105) — the number of measurements Vasya made. The second line contains *n* integers *c*1,<=*c*2,<=...,<=*c**n* (1<=≤<=*c**i*<=≤<=5000) — the results of the measurements. The numbers on the second line are separated by single spaces. | Print a single integer — the minimum number of results Vasya will have to remove. | [
"6\n4 5 3 8 3 7\n",
"4\n4 3 2 4\n"
] | [
"2\n",
"0\n"
] | In the first sample you can remove the fourth and the sixth measurement results (values 8 and 7). Then the maximum of the remaining values will be 5, and the minimum one will be 3. Or else, you can remove the third and fifth results (both equal 3). After that the largest remaining result will be 8, and the smallest one will be 4. | [
{
"input": "6\n4 5 3 8 3 7",
"output": "2"
},
{
"input": "4\n4 3 2 4",
"output": "0"
},
{
"input": "6\n5 6 4 9 4 8",
"output": "1"
},
{
"input": "4\n5 4 1 5",
"output": "1"
},
{
"input": "2\n3 2",
"output": "0"
},
{
"input": "10\n39 9 18 13 6 16 47 15 ... | 92 | 0 | 0 | 4,414 | |
863 | 1-2-3 | [
"graphs",
"implementation"
] | null | null | Ilya is working for the company that constructs robots. Ilya writes programs for entertainment robots, and his current project is "Bob", a new-generation game robot. Ilya's boss wants to know his progress so far. Especially he is interested if Bob is better at playing different games than the previous model, "Alice".
So now Ilya wants to compare his robots' performance in a simple game called "1-2-3". This game is similar to the "Rock-Paper-Scissors" game: both robots secretly choose a number from the set {1,<=2,<=3} and say it at the same moment. If both robots choose the same number, then it's a draw and noone gets any points. But if chosen numbers are different, then one of the robots gets a point: 3 beats 2, 2 beats 1 and 1 beats 3.
Both robots' programs make them choose their numbers in such a way that their choice in (*i*<=+<=1)-th game depends only on the numbers chosen by them in *i*-th game.
Ilya knows that the robots will play *k* games, Alice will choose number *a* in the first game, and Bob will choose *b* in the first game. He also knows both robots' programs and can tell what each robot will choose depending on their choices in previous game. Ilya doesn't want to wait until robots play all *k* games, so he asks you to predict the number of points they will have after the final game. | The first line contains three numbers *k*, *a*, *b* (1<=≤<=*k*<=≤<=1018, 1<=≤<=*a*,<=*b*<=≤<=3).
Then 3 lines follow, *i*-th of them containing 3 numbers *A**i*,<=1, *A**i*,<=2, *A**i*,<=3, where *A**i*,<=*j* represents Alice's choice in the game if Alice chose *i* in previous game and Bob chose *j* (1<=≤<=*A**i*,<=*j*<=≤<=3).
Then 3 lines follow, *i*-th of them containing 3 numbers *B**i*,<=1, *B**i*,<=2, *B**i*,<=3, where *B**i*,<=*j* represents Bob's choice in the game if Alice chose *i* in previous game and Bob chose *j* (1<=≤<=*B**i*,<=*j*<=≤<=3). | Print two numbers. First of them has to be equal to the number of points Alice will have, and second of them must be Bob's score after *k* games. | [
"10 2 1\n1 1 1\n1 1 1\n1 1 1\n2 2 2\n2 2 2\n2 2 2\n",
"8 1 1\n2 2 1\n3 3 1\n3 1 3\n1 1 1\n2 1 1\n1 2 3\n",
"5 1 1\n1 2 2\n2 2 2\n2 2 2\n1 2 2\n2 2 2\n2 2 2\n"
] | [
"1 9\n",
"5 2\n",
"0 0\n"
] | In the second example game goes like this:
<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/1e21b6e200707470571d69c9946ace6b56f5279b.png" style="max-width: 100.0%;max-height: 100.0%;"/>
The fourth and the seventh game are won by Bob, the first game is draw and the rest are won by Alice. | [
{
"input": "10 2 1\n1 1 1\n1 1 1\n1 1 1\n2 2 2\n2 2 2\n2 2 2",
"output": "1 9"
},
{
"input": "8 1 1\n2 2 1\n3 3 1\n3 1 3\n1 1 1\n2 1 1\n1 2 3",
"output": "5 2"
},
{
"input": "5 1 1\n1 2 2\n2 2 2\n2 2 2\n1 2 2\n2 2 2\n2 2 2",
"output": "0 0"
},
{
"input": "1 1 1\n3 3 1\n1 1 1\... | 61 | 204,800 | -1 | 4,415 | |
808 | Selling Souvenirs | [
"binary search",
"dp",
"greedy",
"ternary search"
] | null | null | After several latest reforms many tourists are planning to visit Berland, and Berland people understood that it's an opportunity to earn money and changed their jobs to attract tourists. Petya, for example, left the IT corporation he had been working for and started to sell souvenirs at the market.
This morning, as usual, Petya will come to the market. Petya has *n* different souvenirs to sell; *i*th souvenir is characterised by its weight *w**i* and cost *c**i*. Petya knows that he might not be able to carry all the souvenirs to the market. So Petya wants to choose a subset of souvenirs such that its total weight is not greater than *m*, and total cost is maximum possible.
Help Petya to determine maximum possible total cost. | The first line contains two integers *n* and *m* (1<=≤<=*n*<=≤<=100000, 1<=≤<=*m*<=≤<=300000) — the number of Petya's souvenirs and total weight that he can carry to the market.
Then *n* lines follow. *i*th line contains two integers *w**i* and *c**i* (1<=≤<=*w**i*<=≤<=3, 1<=≤<=*c**i*<=≤<=109) — the weight and the cost of *i*th souvenir. | Print one number — maximum possible total cost of souvenirs that Petya can carry to the market. | [
"1 1\n2 1\n",
"2 2\n1 3\n2 2\n",
"4 3\n3 10\n2 7\n2 8\n1 1\n"
] | [
"0\n",
"3\n",
"10\n"
] | none | [
{
"input": "1 1\n2 1",
"output": "0"
},
{
"input": "2 2\n1 3\n2 2",
"output": "3"
},
{
"input": "4 3\n3 10\n2 7\n2 8\n1 1",
"output": "10"
},
{
"input": "5 5\n3 5\n2 6\n3 2\n1 1\n1 6",
"output": "13"
},
{
"input": "6 6\n1 6\n1 4\n1 8\n3 2\n3 2\n2 8",
"output":... | 2,000 | 62,361,600 | 0 | 4,416 | |
284 | Cows and Primitive Roots | [
"implementation",
"math",
"number theory"
] | null | null | The cows have just learned what a primitive root is! Given a prime *p*, a primitive root is an integer *x* (1<=≤<=*x*<=<<=*p*) such that none of integers *x*<=-<=1,<=*x*2<=-<=1,<=...,<=*x**p*<=-<=2<=-<=1 are divisible by *p*, but *x**p*<=-<=1<=-<=1 is.
Unfortunately, computing primitive roots can be time consuming, so the cows need your help. Given a prime *p*, help the cows find the number of primitive roots . | The input contains a single line containing an integer *p* (2<=≤<=*p*<=<<=2000). It is guaranteed that *p* is a prime. | Output on a single line the number of primitive roots . | [
"3\n",
"5\n"
] | [
"1\n",
"2\n"
] | The only primitive root <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3722298ba062e95b18705d1253eb4e5d31e3b2d1.png" style="max-width: 100.0%;max-height: 100.0%;"/> is 2.
The primitive roots <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/1d85c6a17ef1c42b53cf94d00bc49a7ac458fd58.png" style="max-width: 100.0%;max-height: 100.0%;"/> are 2 and 3. | [
{
"input": "3",
"output": "1"
},
{
"input": "5",
"output": "2"
},
{
"input": "7",
"output": "2"
},
{
"input": "11",
"output": "4"
},
{
"input": "17",
"output": "8"
},
{
"input": "19",
"output": "6"
},
{
"input": "1583",
"output": "672"
... | 92 | 0 | 0 | 4,423 | |
171 | Broken checker | [
"*special",
"brute force"
] | null | null | "This problem is rubbish! There is not statement, and there are only 5 test cases. The problemsetter took liberties with this problem!" — people complained in the comments to one round on Codeforces. And even more... No, wait, the checker for the problem was alright, that's a mercy. | The only line of the input contains an integer between 1 and 5, inclusive. All tests for this problem are different. The contents of the test case doesn't need to be equal to its index. | The only line of the output contains an integer between 1 and 3, inclusive. | [] | [] | This problem has no samples, since there so few test cases. | [
{
"input": "3",
"output": "1"
},
{
"input": "1",
"output": "2"
},
{
"input": "4",
"output": "2"
},
{
"input": "2",
"output": "3"
},
{
"input": "5",
"output": "1"
}
] | 186 | 0 | 0 | 4,426 | |
11 | Jumping Jack | [
"math"
] | B. Jumping Jack | 1 | 64 | Jack is working on his jumping skills recently. Currently he's located at point zero of the number line. He would like to get to the point *x*. In order to train, he has decided that he'll first jump by only one unit, and each subsequent jump will be exactly one longer than the previous one. He can go either left or right with each jump. He wonders how many jumps he needs to reach *x*. | The input data consists of only one integer *x* (<=-<=109<=≤<=*x*<=≤<=109). | Output the minimal number of jumps that Jack requires to reach *x*. | [
"2\n",
"6\n",
"0\n"
] | [
"3\n",
"3\n",
"0\n"
] | none | [
{
"input": "2",
"output": "3"
},
{
"input": "6",
"output": "3"
},
{
"input": "0",
"output": "0"
},
{
"input": "-1000000000",
"output": "44723"
},
{
"input": "999961560",
"output": "44720"
},
{
"input": "999961561",
"output": "44721"
},
{
"i... | 92 | 0 | 0 | 4,428 |
524 | Возможно, вы знаете этих людей? | [
"implementation"
] | null | null | Основой любой социальной сети является отношение дружбы между двумя пользователями в том или ином смысле. В одной известной социальной сети дружба симметрична, то есть если *a* является другом *b*, то *b* также является другом *a*.
В этой же сети есть функция, которая демонстрирует множество людей, имеющих высокую вероятность быть знакомыми для пользователя. Эта функция работает следующим образом. Зафиксируем пользователя *x*. Пусть некоторый другой человек *y*, не являющийся другом *x* на текущий момент, является другом не менее, чем для *k*% друзей *x*. Тогда он является предполагаемым другом для *x*.
У каждого человека в социальной сети есть свой уникальный идентификатор — это целое число от 1 до 109. Вам дан список пар пользователей, являющихся друзьями. Определите для каждого упомянутого пользователя множество его предполагаемых друзей. | В первой строке следуют два целых числа *m* и *k* (1<=≤<=*m*<=≤<=100, 0<=≤<=*k*<=≤<=100) — количество пар друзей и необходимый процент общих друзей для того, чтобы считаться предполагаемым другом.
В последующих *m* строках записано по два числа *a**i*,<=*b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=109, *a**i*<=≠<=*b**i*), обозначающих идентификаторы пользователей, являющихся друзьями.
Гарантируется, что каждая пара людей фигурирует в списке не более одного раза. | Для всех упомянутых людей в порядке возрастания id выведите информацию о предполагаемых друзьях. Информация должна иметь вид "*id*:<= *k* *id*1 *id*2 ... *id**k*", где *id* — это id самого человека, *k* — количество его предполагаемых друзей, а *id*1, *id*2, ..., *id**k* — идентификаторы его предполагаемых друзей в возрастающем порядке. | [
"5 51\n10 23\n23 42\n39 42\n10 39\n39 58\n",
"5 100\n1 2\n1 3\n1 4\n2 3\n2 4\n"
] | [
"10: 1 42\n23: 1 39\n39: 1 23\n42: 1 10\n58: 2 10 42\n",
"1: 0\n2: 0\n3: 1 4\n4: 1 3\n"
] | none | [
{
"input": "5 51\n10 23\n23 42\n39 42\n10 39\n39 58",
"output": "10: 1 42\n23: 1 39\n39: 1 23\n42: 1 10\n58: 2 10 42"
},
{
"input": "5 100\n1 2\n1 3\n1 4\n2 3\n2 4",
"output": "1: 0\n2: 0\n3: 1 4\n4: 1 3"
},
{
"input": "4 1\n1 2\n1 3\n2 3\n4 5",
"output": "1: 0\n2: 0\n3: 0\n4: 0\n5: ... | 93 | 0 | 0 | 4,434 | |
106 | Card Game | [
"implementation"
] | A. Card Game | 2 | 256 | There is a card game called "Durak", which means "Fool" in Russian. The game is quite popular in the countries that used to form USSR. The problem does not state all the game's rules explicitly — you can find them later yourselves if you want.
To play durak you need a pack of 36 cards. Each card has a suit ("S", "H", "D" and "C") and a rank (in the increasing order "6", "7", "8", "9", "T", "J", "Q", "K" and "A"). At the beginning of the game one suit is arbitrarily chosen as trump.
The players move like that: one player puts one or several of his cards on the table and the other one should beat each of them with his cards.
A card beats another one if both cards have similar suits and the first card has a higher rank then the second one. Besides, a trump card can beat any non-trump card whatever the cards’ ranks are. In all other cases you can not beat the second card with the first one.
You are given the trump suit and two different cards. Determine whether the first one beats the second one or not. | The first line contains the tramp suit. It is "S", "H", "D" or "C".
The second line contains the description of the two different cards. Each card is described by one word consisting of two symbols. The first symbol stands for the rank ("6", "7", "8", "9", "T", "J", "Q", "K" and "A"), and the second one stands for the suit ("S", "H", "D" and "C"). | Print "YES" (without the quotes) if the first cards beats the second one. Otherwise, print "NO" (also without the quotes). | [
"H\nQH 9S\n",
"S\n8D 6D\n",
"C\n7H AS\n"
] | [
"YES\n",
"YES",
"NO"
] | none | [
{
"input": "H\nQH 9S",
"output": "YES"
},
{
"input": "S\n8D 6D",
"output": "YES"
},
{
"input": "C\n7H AS",
"output": "NO"
},
{
"input": "C\nKC 9C",
"output": "YES"
},
{
"input": "D\n7D KD",
"output": "NO"
},
{
"input": "H\n7H KD",
"output": "YES"
... | 92 | 307,200 | 0 | 4,441 |
401 | Team | [
"constructive algorithms",
"greedy",
"implementation"
] | null | null | Now it's time of Olympiads. Vanya and Egor decided to make his own team to take part in a programming Olympiad. They've been best friends ever since primary school and hopefully, that can somehow help them in teamwork.
For each team Olympiad, Vanya takes his play cards with numbers. He takes only the cards containing numbers 1 and 0. The boys are very superstitious. They think that they can do well at the Olympiad if they begin with laying all the cards in a row so that:
- there wouldn't be a pair of any side-adjacent cards with zeroes in a row; - there wouldn't be a group of three consecutive cards containing numbers one.
Today Vanya brought *n* cards with zeroes and *m* cards with numbers one. The number of cards was so much that the friends do not know how to put all those cards in the described way. Help them find the required arrangement of the cards or else tell the guys that it is impossible to arrange cards in such a way. | The first line contains two integers: *n* (1<=≤<=*n*<=≤<=106) — the number of cards containing number 0; *m* (1<=≤<=*m*<=≤<=106) — the number of cards containing number 1. | In a single line print the required sequence of zeroes and ones without any spaces. If such sequence is impossible to obtain, print -1. | [
"1 2\n",
"4 8\n",
"4 10\n",
"1 5\n"
] | [
"101\n",
"110110110101\n",
"11011011011011\n",
"-1\n"
] | none | [
{
"input": "1 2",
"output": "101"
},
{
"input": "4 8",
"output": "110110110101"
},
{
"input": "4 10",
"output": "11011011011011"
},
{
"input": "1 5",
"output": "-1"
},
{
"input": "3 4",
"output": "1010101"
},
{
"input": "3 10",
"output": "-1"
},
... | 1,000 | 8,294,400 | 0 | 4,444 | |
346 | Lucky Common Subsequence | [
"dp",
"strings"
] | null | null | In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. For example, the sequence BDF is a subsequence of ABCDEF. A substring of a string is a continuous subsequence of the string. For example, BCD is a substring of ABCDEF.
You are given two strings *s*1, *s*2 and another string called *virus*. Your task is to find the longest common subsequence of *s*1 and *s*2, such that it doesn't contain *virus* as a substring. | The input contains three strings in three separate lines: *s*1, *s*2 and *virus* (1<=≤<=|*s*1|,<=|*s*2|,<=|*virus*|<=≤<=100). Each string consists only of uppercase English letters. | Output the longest common subsequence of *s*1 and *s*2 without *virus* as a substring. If there are multiple answers, any of them will be accepted.
If there is no valid common subsequence, output 0. | [
"AJKEQSLOBSROFGZ\nOVGURWZLWVLUXTH\nOZ\n",
"AA\nA\nA\n"
] | [
"ORZ\n",
"0\n"
] | none | [
{
"input": "AJKEQSLOBSROFGZ\nOVGURWZLWVLUXTH\nOZ",
"output": "ORZ"
},
{
"input": "AA\nA\nA",
"output": "0"
},
{
"input": "PWBJTZPQHA\nZJMKLWSROQ\nUQ",
"output": "WQ"
},
{
"input": "QNHRPFYMAAPJDUHBAEXNEEZSTMYHVGQPYKNMVKMBVSVLIYGUVMJHEFLJEPIWFHSLISTGOKRXNMSCXYKMAXBPKCOCNTIRPCU... | 404 | 2,048,000 | -1 | 4,446 | |
789 | Masha and geometric depression | [
"brute force",
"implementation",
"math"
] | null | null | Masha really loves algebra. On the last lesson, her strict teacher Dvastan gave she new exercise.
You are given geometric progression *b* defined by two integers *b*1 and *q*. Remind that a geometric progression is a sequence of integers *b*1,<=*b*2,<=*b*3,<=..., where for each *i*<=><=1 the respective term satisfies the condition *b**i*<==<=*b**i*<=-<=1·*q*, where *q* is called the common ratio of the progression. Progressions in Uzhlyandia are unusual: both *b*1 and *q* can equal 0. Also, Dvastan gave Masha *m* "bad" integers *a*1,<=*a*2,<=...,<=*a**m*, and an integer *l*.
Masha writes all progression terms one by one onto the board (including repetitive) while condition |*b**i*|<=≤<=*l* is satisfied (|*x*| means absolute value of *x*). There is an exception: if a term equals one of the "bad" integers, Masha skips it (doesn't write onto the board) and moves forward to the next term.
But the lesson is going to end soon, so Masha has to calculate how many integers will be written on the board. In order not to get into depression, Masha asked you for help: help her calculate how many numbers she will write, or print "inf" in case she needs to write infinitely many integers. | The first line of input contains four integers *b*1, *q*, *l*, *m* (-109<=≤<=*b*1,<=*q*<=≤<=109, 1<=≤<=*l*<=≤<=109, 1<=≤<=*m*<=≤<=105) — the initial term and the common ratio of progression, absolute value of maximal number that can be written on the board and the number of "bad" integers, respectively.
The second line contains *m* distinct integers *a*1,<=*a*2,<=...,<=*a**m* (-109<=≤<=*a**i*<=≤<=109) — numbers that will never be written on the board. | Print the only integer, meaning the number of progression terms that will be written on the board if it is finite, or "inf" (without quotes) otherwise. | [
"3 2 30 4\n6 14 25 48\n",
"123 1 2143435 4\n123 11 -5453 141245\n",
"123 1 2143435 4\n54343 -13 6 124\n"
] | [
"3",
"0",
"inf"
] | In the first sample case, Masha will write integers 3, 12, 24. Progression term 6 will be skipped because it is a "bad" integer. Terms bigger than 24 won't be written because they exceed *l* by absolute value.
In the second case, Masha won't write any number because all terms are equal 123 and this is a "bad" integer.
In the third case, Masha will write infinitely integers 123. | [
{
"input": "3 2 30 4\n6 14 25 48",
"output": "3"
},
{
"input": "123 1 2143435 4\n123 11 -5453 141245",
"output": "0"
},
{
"input": "123 1 2143435 4\n54343 -13 6 124",
"output": "inf"
},
{
"input": "3 2 25 2\n379195692 -69874783",
"output": "4"
},
{
"input": "3 2 3... | 93 | 15,667,200 | 3 | 4,458 | |
992 | Nastya and a Game | [
"brute force",
"implementation",
"math"
] | null | null | Nastya received one more array on her birthday, this array can be used to play a traditional Byteland game on it. However, to play the game the players should first select such a subsegment of the array that , where *p* is the product of all integers on the given array, *s* is their sum, and *k* is a given constant for all subsegments.
Nastya wonders how many subsegments of the array fit the described conditions. A subsegment of an array is several consecutive integers of the array. | The first line contains two integers *n* and *k* (1<=≤<=*n*<=≤<=2·105, 1<=≤<=*k*<=≤<=105), where *n* is the length of the array and *k* is the constant described above.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=108) — the elements of the array. | In the only line print the number of subsegments such that the ratio between the product and the sum on them is equal to *k*. | [
"1 1\n1\n",
"4 2\n6 3 8 1\n"
] | [
"1\n",
"2\n"
] | In the first example the only subsegment is [1]. The sum equals 1, the product equals 1, so it suits us because <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/627b2899a459d42fe3b2ca04fc812d4132b5f2ca.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
There are two suitable subsegments in the second example — [6, 3] and [3, 8, 1]. Subsegment [6, 3] has sum 9 and product 18, so it suits us because <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/107ecd38fde9817d6565e2059ccd064562470543.png" style="max-width: 100.0%;max-height: 100.0%;"/>. Subsegment [3, 8, 1] has sum 12 and product 24, so it suits us because <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/8abc1793efa3061313ddd52d670a94b430133564.png" style="max-width: 100.0%;max-height: 100.0%;"/>. | [
{
"input": "1 1\n1",
"output": "1"
},
{
"input": "4 2\n6 3 8 1",
"output": "2"
},
{
"input": "94 58\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 29 58 1 1 1 29 58 58 1 1 29 1 1 1 1 2 1 58 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 29 1 1 1 1 1 58 1 29 1 1 1 1 1 1 1 1 1 1 1 1 58 1 1 1 ... | 109 | 2,150,400 | -1 | 4,461 | |
20 | Equation | [
"math"
] | B. Equation | 1 | 256 | You are given an equation:
Your task is to find the number of distinct roots of the equation and print all of them in ascending order. | The first line contains three integer numbers *A*,<=*B* and *C* (<=-<=105<=≤<=*A*,<=*B*,<=*C*<=≤<=105). Any coefficient may be equal to 0. | In case of infinite root count print the only integer -1. In case of no roots print the only integer 0. In other cases print the number of root on the first line and the roots on the following lines in the ascending order. Print roots with at least 5 digits after the decimal point. | [
"1 -5 6\n"
] | [
"2\n2.0000000000\n3.0000000000"
] | none | [
{
"input": "1 -5 6",
"output": "2\n2.0000000000\n3.0000000000"
},
{
"input": "1 1 1",
"output": "0"
},
{
"input": "1 2 1",
"output": "1\n-1.0000000000"
},
{
"input": "0 0 0",
"output": "-1"
},
{
"input": "0 -2 1",
"output": "1\n0.5000000000"
},
{
"inpu... | 46 | 0 | -1 | 4,475 |
949 | Zebras | [
"greedy"
] | null | null | Oleg writes down the history of the days he lived. For each day he decides if it was good or bad. Oleg calls a non-empty sequence of days a zebra, if it starts with a bad day, ends with a bad day, and good and bad days are alternating in it. Let us denote bad days as 0 and good days as 1. Then, for example, sequences of days 0, 010, 01010 are zebras, while sequences 1, 0110, 0101 are not.
Oleg tells you the story of days he lived in chronological order in form of string consisting of 0 and 1. Now you are interested if it is possible to divide Oleg's life history into several subsequences, each of which is a zebra, and the way it can be done. Each day must belong to exactly one of the subsequences. For each of the subsequences, days forming it must be ordered chronologically. Note that subsequence does not have to be a group of consecutive days. | In the only line of input data there is a non-empty string *s* consisting of characters 0 and 1, which describes the history of Oleg's life. Its length (denoted as |*s*|) does not exceed 200<=000 characters. | If there is a way to divide history into zebra subsequences, in the first line of output you should print an integer *k* (1<=≤<=*k*<=≤<=|*s*|), the resulting number of subsequences. In the *i*-th of following *k* lines first print the integer *l**i* (1<=≤<=*l**i*<=≤<=|*s*|), which is the length of the *i*-th subsequence, and then *l**i* indices of days forming the subsequence. Indices must follow in ascending order. Days are numbered starting from 1. Each index from 1 to *n* must belong to exactly one subsequence. If there is no way to divide day history into zebra subsequences, print -1.
Subsequences may be printed in any order. If there are several solutions, you may print any of them. You do not have to minimize nor maximize the value of *k*. | [
"0010100\n",
"111\n"
] | [
"3\n3 1 3 4\n3 2 5 6\n1 7\n",
"-1\n"
] | none | [
{
"input": "0010100",
"output": "3\n1 1\n5 2 3 4 5 6\n1 7"
},
{
"input": "111",
"output": "-1"
},
{
"input": "0",
"output": "1\n1 1"
},
{
"input": "1",
"output": "-1"
},
{
"input": "0101010101",
"output": "-1"
},
{
"input": "010100001",
"output": "... | 61 | 20,172,800 | 0 | 4,476 | |
914 | Bash and a Tough Math Puzzle | [
"data structures",
"number theory"
] | null | null | Bash likes playing with arrays. He has an array *a*1,<=*a*2,<=... *a**n* of *n* integers. He likes to guess the greatest common divisor (gcd) of different segments of the array. Of course, sometimes the guess is not correct. However, Bash will be satisfied if his guess is almost correct.
Suppose he guesses that the gcd of the elements in the range [*l*,<=*r*] of *a* is *x*. He considers the guess to be almost correct if he can change at most one element in the segment such that the gcd of the segment is *x* after making the change. Note that when he guesses, he doesn't actually change the array — he just wonders if the gcd of the segment can be made *x*. Apart from this, he also sometimes makes changes to the array itself.
Since he can't figure it out himself, Bash wants you to tell him which of his guesses are almost correct. Formally, you have to process *q* queries of one of the following forms:
- 1<=*l*<=*r*<=*x* — Bash guesses that the gcd of the range [*l*,<=*r*] is *x*. Report if this guess is almost correct. - 2<=*i*<=*y* — Bash sets *a**i* to *y*.
Note: The array is 1-indexed. | The first line contains an integer *n* (1<=≤<=*n*<=≤<=5·105) — the size of the array.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=109) — the elements of the array.
The third line contains an integer *q* (1<=≤<=*q*<=≤<=4·105) — the number of queries.
The next *q* lines describe the queries and may have one of the following forms:
- 1<=*l*<=*r*<=*x* (1<=≤<=*l*<=≤<=*r*<=≤<=*n*,<=1<=≤<=*x*<=≤<=109). - 2<=*i*<=*y* (1<=≤<=*i*<=≤<=*n*,<=1<=≤<=*y*<=≤<=109).
Guaranteed, that there is at least one query of first type. | For each query of first type, output "YES" (without quotes) if Bash's guess is almost correct and "NO" (without quotes) otherwise. | [
"3\n2 6 3\n4\n1 1 2 2\n1 1 3 3\n2 1 9\n1 1 3 2\n",
"5\n1 2 3 4 5\n6\n1 1 4 2\n2 3 6\n1 1 4 2\n1 1 5 2\n2 5 10\n1 1 5 2\n"
] | [
"YES\nYES\nNO\n",
"NO\nYES\nNO\nYES\n"
] | In the first sample, the array initially is {2, 6, 3}.
For query 1, the first two numbers already have their gcd as 2.
For query 2, we can achieve a gcd of 3 by changing the first element of the array to 3. Note that the changes made during queries of type 1 are temporary and do not get reflected in the array.
After query 3, the array is now {9, 6, 3}.
For query 4, no matter which element you change, you cannot get the gcd of the range to be 2. | [
{
"input": "3\n2 6 3\n4\n1 1 2 2\n1 1 3 3\n2 1 9\n1 1 3 2",
"output": "YES\nYES\nNO"
},
{
"input": "5\n1 2 3 4 5\n6\n1 1 4 2\n2 3 6\n1 1 4 2\n1 1 5 2\n2 5 10\n1 1 5 2",
"output": "NO\nYES\nNO\nYES"
},
{
"input": "1\n1000000000\n1\n1 1 1 1000000000",
"output": "YES"
},
{
"inpu... | 61 | 1,843,200 | 0 | 4,485 | |
350 | Resort | [
"graphs"
] | null | null | Valera's finally decided to go on holiday! He packed up and headed for a ski resort.
Valera's fancied a ski trip but he soon realized that he could get lost in this new place. Somebody gave him a useful hint: the resort has *n* objects (we will consider the objects indexed in some way by integers from 1 to *n*), each object is either a hotel or a mountain.
Valera has also found out that the ski resort had multiple ski tracks. Specifically, for each object *v*, the resort has at most one object *u*, such that there is a ski track built from object *u* to object *v*. We also know that no hotel has got a ski track leading from the hotel to some object.
Valera is afraid of getting lost on the resort. So he wants you to come up with a path he would walk along. The path must consist of objects *v*1,<=*v*2,<=...,<=*v**k* (*k*<=≥<=1) and meet the following conditions:
1. Objects with numbers *v*1,<=*v*2,<=...,<=*v**k*<=-<=1 are mountains and the object with number *v**k* is the hotel. 1. For any integer *i* (1<=≤<=*i*<=<<=*k*), there is exactly one ski track leading from object *v**i*. This track goes to object *v**i*<=+<=1. 1. The path contains as many objects as possible (*k* is maximal).
Help Valera. Find such path that meets all the criteria of our hero! | The first line contains integer *n* (1<=≤<=*n*<=≤<=105) — the number of objects.
The second line contains *n* space-separated integers *type*1,<=*type*2,<=...,<=*type**n* — the types of the objects. If *type**i* equals zero, then the *i*-th object is the mountain. If *type**i* equals one, then the *i*-th object is the hotel. It is guaranteed that at least one object is a hotel.
The third line of the input contains *n* space-separated integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=*n*) — the description of the ski tracks. If number *a**i* equals zero, then there is no such object *v*, that has a ski track built from *v* to *i*. If number *a**i* doesn't equal zero, that means that there is a track built from object *a**i* to object *i*. | In the first line print *k* — the maximum possible path length for Valera. In the second line print *k* integers *v*1,<=*v*2,<=...,<=*v**k* — the path. If there are multiple solutions, you can print any of them. | [
"5\n0 0 0 0 1\n0 1 2 3 4\n",
"5\n0 0 1 0 1\n0 1 2 2 4\n",
"4\n1 0 0 0\n2 3 4 2\n"
] | [
"5\n1 2 3 4 5\n",
"2\n4 5\n",
"1\n1\n"
] | none | [
{
"input": "5\n0 0 0 0 1\n0 1 2 3 4",
"output": "5\n1 2 3 4 5"
},
{
"input": "5\n0 0 1 0 1\n0 1 2 2 4",
"output": "2\n4 5"
},
{
"input": "4\n1 0 0 0\n2 3 4 2",
"output": "1\n1"
},
{
"input": "10\n0 0 0 0 0 0 0 0 0 1\n4 0 8 4 7 8 5 5 7 2",
"output": "2\n2 10"
},
{
... | 340 | 19,660,800 | 3 | 4,489 | |
471 | MUH and Important Things | [
"implementation",
"sortings"
] | null | null | It's time polar bears Menshykov and Uslada from the zoo of St. Petersburg and elephant Horace from the zoo of Kiev got down to business. In total, there are *n* tasks for the day and each animal should do each of these tasks. For each task, they have evaluated its difficulty. Also animals decided to do the tasks in order of their difficulty. Unfortunately, some tasks can have the same difficulty, so the order in which one can perform the tasks may vary.
Menshykov, Uslada and Horace ask you to deal with this nuisance and come up with individual plans for each of them. The plan is a sequence describing the order in which an animal should do all the *n* tasks. Besides, each of them wants to have its own unique plan. Therefore three plans must form three different sequences. You are to find the required plans, or otherwise deliver the sad news to them by stating that it is impossible to come up with three distinct plans for the given tasks. | The first line contains integer *n* (1<=≤<=*n*<=≤<=2000) — the number of tasks. The second line contains *n* integers *h*1,<=*h*2,<=...,<=*h**n* (1<=≤<=*h**i*<=≤<=2000), where *h**i* is the difficulty of the *i*-th task. The larger number *h**i* is, the more difficult the *i*-th task is. | In the first line print "YES" (without the quotes), if it is possible to come up with three distinct plans of doing the tasks. Otherwise print in the first line "NO" (without the quotes). If three desired plans do exist, print in the second line *n* distinct integers that represent the numbers of the tasks in the order they are done according to the first plan. In the third and fourth line print two remaining plans in the same form.
If there are multiple possible answers, you can print any of them. | [
"4\n1 3 3 1\n",
"5\n2 4 1 4 8\n"
] | [
"YES\n1 4 2 3 \n4 1 2 3 \n4 1 3 2 \n",
"NO"
] | In the first sample the difficulty of the tasks sets one limit: tasks 1 and 4 must be done before tasks 2 and 3. That gives the total of four possible sequences of doing tasks : [1, 4, 2, 3], [4, 1, 2, 3], [1, 4, 3, 2], [4, 1, 3, 2]. You can print any three of them in the answer.
In the second sample there are only two sequences of tasks that meet the conditions — [3, 1, 2, 4, 5] and [3, 1, 4, 2, 5]. Consequently, it is impossible to make three distinct sequences of tasks. | [
{
"input": "4\n1 3 3 1",
"output": "YES\n1 4 2 3 \n4 1 2 3 \n4 1 3 2 "
},
{
"input": "5\n2 4 1 4 8",
"output": "NO"
},
{
"input": "8\n1 5 4 12 7 2 10 11",
"output": "NO"
},
{
"input": "6\n5 1 2 5 2 4",
"output": "YES\n2 3 5 6 1 4 \n2 5 3 6 1 4 \n2 5 3 6 4 1 "
},
{
... | 124 | 0 | 3 | 4,498 | |
557 | Pasha and Tea | [
"constructive algorithms",
"implementation",
"math",
"sortings"
] | null | null | Pasha decided to invite his friends to a tea party. For that occasion, he has a large teapot with the capacity of *w* milliliters and 2*n* tea cups, each cup is for one of Pasha's friends. The *i*-th cup can hold at most *a**i* milliliters of water.
It turned out that among Pasha's friends there are exactly *n* boys and exactly *n* girls and all of them are going to come to the tea party. To please everyone, Pasha decided to pour the water for the tea as follows:
- Pasha can boil the teapot exactly once by pouring there at most *w* milliliters of water; - Pasha pours the same amount of water to each girl; - Pasha pours the same amount of water to each boy; - if each girl gets *x* milliliters of water, then each boy gets 2*x* milliliters of water.
In the other words, each boy should get two times more water than each girl does.
Pasha is very kind and polite, so he wants to maximize the total amount of the water that he pours to his friends. Your task is to help him and determine the optimum distribution of cups between Pasha's friends. | The first line of the input contains two integers, *n* and *w* (1<=≤<=*n*<=≤<=105, 1<=≤<=*w*<=≤<=109) — the number of Pasha's friends that are boys (equal to the number of Pasha's friends that are girls) and the capacity of Pasha's teapot in milliliters.
The second line of the input contains the sequence of integers *a**i* (1<=≤<=*a**i*<=≤<=109, 1<=≤<=*i*<=≤<=2*n*) — the capacities of Pasha's tea cups in milliliters. | Print a single real number — the maximum total amount of water in milliliters that Pasha can pour to his friends without violating the given conditions. Your answer will be considered correct if its absolute or relative error doesn't exceed 10<=-<=6. | [
"2 4\n1 1 1 1\n",
"3 18\n4 4 4 2 2 2\n",
"1 5\n2 3\n"
] | [
"3",
"18",
"4.5"
] | Pasha also has candies that he is going to give to girls but that is another task... | [
{
"input": "2 4\n1 1 1 1",
"output": "3.0000000000"
},
{
"input": "3 18\n4 4 4 2 2 2",
"output": "18.0000000000"
},
{
"input": "1 5\n2 3",
"output": "4.5000000000"
},
{
"input": "1 1\n1000000000 1000000000",
"output": "1.0000000000"
},
{
"input": "4 1000000000\n1 ... | 358 | 17,100,800 | 3 | 4,512 | |
147 | Punctuation | [
"implementation",
"strings"
] | null | null | You are given a text that consists of lowercase Latin letters, spaces and punctuation marks (dot, comma, exclamation mark and question mark). A word is defined as a sequence of consecutive Latin letters.
Your task is to add spaces to the text by the following rules:
- if there is no punctuation mark between two words, then they should be separated by exactly one space - there should be no spaces before each punctuation mark - there should be exactly one space after each punctuation mark
It is guaranteed that there is at least one word between any two punctuation marks. The text begins and ends with a Latin letter. | The input data contains of a single non-empty line — the text whose length is no more than 10000 characters. | Print the text, edited according to the rules. In this problem you should follow the output format very strictly. For example, extra space at the end of the output line is considered as wrong answer. Note that a newline character at the end of the line doesn't matter. | [
"galileo galilei was an italian physicist ,mathematician,astronomer\n",
"galileo was born in pisa\n"
] | [
"galileo galilei was an italian physicist, mathematician, astronomer\n",
"galileo was born in pisa\n"
] | none | [
{
"input": "galileo galilei was an italian physicist ,mathematician,astronomer",
"output": "galileo galilei was an italian physicist, mathematician, astronomer"
},
{
"input": "galileo was born in pisa",
"output": "galileo was born in pisa"
},
{
"input": "jkhksdfhsdfsf",
"outpu... | 124 | 5,120,000 | 3 | 4,527 | |
612 | The Union of k-Segments | [
"greedy",
"sortings"
] | null | null | You are given *n* segments on the coordinate axis Ox and the number *k*. The point is satisfied if it belongs to at least *k* segments. Find the smallest (by the number of segments) set of segments on the coordinate axis Ox which contains all satisfied points and no others. | The first line contains two integers *n* and *k* (1<=≤<=*k*<=≤<=*n*<=≤<=106) — the number of segments and the value of *k*.
The next *n* lines contain two integers *l**i*,<=*r**i* (<=-<=109<=≤<=*l**i*<=≤<=*r**i*<=≤<=109) each — the endpoints of the *i*-th segment. The segments can degenerate and intersect each other. The segments are given in arbitrary order. | First line contains integer *m* — the smallest number of segments.
Next *m* lines contain two integers *a**j*,<=*b**j* (*a**j*<=≤<=*b**j*) — the ends of *j*-th segment in the answer. The segments should be listed in the order from left to right. | [
"3 2\n0 5\n-3 2\n3 8\n",
"3 2\n0 5\n-3 3\n3 8\n"
] | [
"2\n0 2\n3 5\n",
"1\n0 5\n"
] | none | [
{
"input": "3 2\n0 5\n-3 2\n3 8",
"output": "2\n0 2\n3 5"
},
{
"input": "3 2\n0 5\n-3 3\n3 8",
"output": "1\n0 5"
},
{
"input": "1 1\n-1 1",
"output": "1\n-1 1"
},
{
"input": "10 2\n27 96\n-22 45\n-68 26\n46 69\n-91 86\n12 73\n-89 76\n-11 33\n17 47\n-57 78",
"output": "1\... | 4,000 | 218,112,000 | 0 | 4,534 | |
140 | New Year Snowmen | [
"binary search",
"data structures",
"greedy"
] | null | null | As meticulous Gerald sets the table and caring Alexander sends the postcards, Sergey makes snowmen. Each showman should consist of three snowballs: a big one, a medium one and a small one. Sergey's twins help him: they've already made *n* snowballs with radii equal to *r*1, *r*2, ..., *r**n*. To make a snowman, one needs any three snowballs whose radii are pairwise different. For example, the balls with radii 1, 2 and 3 can be used to make a snowman but 2, 2, 3 or 2, 2, 2 cannot. Help Sergey and his twins to determine what maximum number of snowmen they can make from those snowballs. | The first line contains integer *n* (1<=≤<=*n*<=≤<=105) — the number of snowballs. The next line contains *n* integers — the balls' radii *r*1, *r*2, ..., *r**n* (1<=≤<=*r**i*<=≤<=109). The balls' radii can coincide. | Print on the first line a single number *k* — the maximum number of the snowmen. Next *k* lines should contain the snowmen's descriptions. The description of each snowman should consist of three space-separated numbers — the big ball's radius, the medium ball's radius and the small ball's radius. It is allowed to print the snowmen in any order. If there are several solutions, print any of them. | [
"7\n1 2 3 4 5 6 7\n",
"3\n2 2 3\n"
] | [
"2\n3 2 1\n6 5 4\n",
"0\n"
] | none | [
{
"input": "7\n1 2 3 4 5 6 7",
"output": "2\n7 5 3\n6 4 2"
},
{
"input": "3\n2 2 3",
"output": "0"
},
{
"input": "1\n255317",
"output": "0"
},
{
"input": "6\n1 1 2 2 3 3",
"output": "2\n3 2 1\n3 2 1"
},
{
"input": "6\n1 2 2 2 3 3",
"output": "1\n3 2 1"
},
... | 122 | 0 | 0 | 4,547 | |
989 | A Mist of Florescence | [
"constructive algorithms",
"graphs"
] | null | null | "I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of $n$ rows and $m$ columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are $a$, $b$, $c$ and $d$ respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with $n$ and $m$ arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary $n$ and $m$ under the constraints below, they are not given in the input. | The first and only line of input contains four space-separated integers $a$, $b$, $c$ and $d$ ($1 \leq a, b, c, d \leq 100$) — the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively. | In the first line, output two space-separated integers $n$ and $m$ ($1 \leq n, m \leq 50$) — the number of rows and the number of columns in the grid respectively.
Then output $n$ lines each consisting of $m$ consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower). | [
"5 3 2 1\n",
"50 50 1 1\n",
"1 6 4 5\n"
] | [
"4 7\nDDDDDDD\nDABACAD\nDBABACD\nDDDDDDD",
"4 50\nCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC\nABABABABABABABABABABABABABABABABABABABABABABABABAB\nBABABABABABABABABABABABABABABABABABABABABABABABABA\nDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD",
"7 7\nDDDDDDD\nDDDBDBD\nDDCDCDD\nDBDADBD\nDDCDCDD\nDB... | In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one. | [
{
"input": "5 3 2 1",
"output": "5 13\nAABABBBBCDDAD\nABAABBBBCDADD\nAAAABBBBCDDAD\nAAAABCBBCDADD\nAAAABBBBCDDDD"
},
{
"input": "50 50 1 1",
"output": "10 50\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\nABABABABABABABABABABABABABABABABABABABABABABABABAA\nBABABABABABABABABABABABABABABABAB... | 77 | 0 | -1 | 4,550 | |
864 | Make a Permutation! | [
"greedy",
"implementation",
"math"
] | null | null | Ivan has an array consisting of *n* elements. Each of the elements is an integer from 1 to *n*.
Recently Ivan learned about permutations and their lexicographical order. Now he wants to change (replace) minimum number of elements in his array in such a way that his array becomes a permutation (i.e. each of the integers from 1 to *n* was encountered in his array exactly once). If there are multiple ways to do it he wants to find the lexicographically minimal permutation among them.
Thus minimizing the number of changes has the first priority, lexicographical minimizing has the second priority.
In order to determine which of the two permutations is lexicographically smaller, we compare their first elements. If they are equal — compare the second, and so on. If we have two permutations *x* and *y*, then *x* is lexicographically smaller if *x**i*<=<<=*y**i*, where *i* is the first index in which the permutations *x* and *y* differ.
Determine the array Ivan will obtain after performing all the changes. | The first line contains an single integer *n* (2<=≤<=*n*<=≤<=200<=000) — the number of elements in Ivan's array.
The second line contains a sequence of integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=*n*) — the description of Ivan's array. | In the first line print *q* — the minimum number of elements that need to be changed in Ivan's array in order to make his array a permutation. In the second line, print the lexicographically minimal permutation which can be obtained from array with *q* changes. | [
"4\n3 2 2 3\n",
"6\n4 5 6 3 2 1\n",
"10\n6 8 4 6 7 1 6 3 4 5\n"
] | [
"2\n1 2 4 3 \n",
"0\n4 5 6 3 2 1 \n",
"3\n2 8 4 6 7 1 9 3 10 5 \n"
] | In the first example Ivan needs to replace number three in position 1 with number one, and number two in position 3 with number four. Then he will get a permutation [1, 2, 4, 3] with only two changed numbers — this permutation is lexicographically minimal among all suitable.
In the second example Ivan does not need to change anything because his array already is a permutation. | [
{
"input": "4\n3 2 2 3",
"output": "2\n1 2 4 3 "
},
{
"input": "6\n4 5 6 3 2 1",
"output": "0\n4 5 6 3 2 1 "
},
{
"input": "10\n6 8 4 6 7 1 6 3 4 5",
"output": "3\n2 8 4 6 7 1 9 3 10 5 "
},
{
"input": "6\n5 5 5 6 4 6",
"output": "3\n1 2 5 3 4 6 "
},
{
"input": "50... | 124 | 0 | 0 | 4,562 | |
835 | Palindromic characteristics | [
"brute force",
"dp",
"hashing",
"strings"
] | null | null | Palindromic characteristics of string *s* with length |*s*| is a sequence of |*s*| integers, where *k*-th number is the total number of non-empty substrings of *s* which are *k*-palindromes.
A string is 1-palindrome if and only if it reads the same backward as forward.
A string is *k*-palindrome (*k*<=><=1) if and only if:
1. Its left half equals to its right half. 1. Its left and right halfs are non-empty (*k*<=-<=1)-palindromes.
The left half of string *t* is its prefix of length ⌊|*t*|<=/<=2⌋, and right half — the suffix of the same length. ⌊|*t*|<=/<=2⌋ denotes the length of string *t* divided by 2, rounded down.
Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times. | The first line contains the string *s* (1<=≤<=|*s*|<=≤<=5000) consisting of lowercase English letters. | Print |*s*| integers — palindromic characteristics of string *s*. | [
"abba\n",
"abacaba\n"
] | [
"6 1 0 0 \n",
"12 4 1 0 0 0 0 \n"
] | In the first example 1-palindromes are substring «a», «b», «b», «a», «bb», «abba», the substring «bb» is 2-palindrome. There are no 3- and 4-palindromes here. | [
{
"input": "abba",
"output": "6 1 0 0 "
},
{
"input": "abacaba",
"output": "12 4 1 0 0 0 0 "
},
{
"input": "qqqpvmgd",
"output": "11 3 0 0 0 0 0 0 "
},
{
"input": "wyemcafatp",
"output": "11 1 0 0 0 0 0 0 0 0 "
}
] | 3,000 | 1,024,000 | 0 | 4,572 | |
588 | Duff in Love | [
"math"
] | null | null | Duff is in love with lovely numbers! A positive integer *x* is called lovely if and only if there is no such positive integer *a*<=><=1 such that *a*2 is a divisor of *x*.
Malek has a number store! In his store, he has only divisors of positive integer *n* (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.
Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store. | The first and only line of input contains one integer, *n* (1<=≤<=*n*<=≤<=1012). | Print the answer in one line. | [
"10\n",
"12\n"
] | [
"10\n",
"6\n"
] | In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.
In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 2<sup class="upper-index">2</sup>, so 12 is not lovely, while 6 is indeed lovely. | [
{
"input": "10",
"output": "10"
},
{
"input": "12",
"output": "6"
},
{
"input": "1",
"output": "1"
},
{
"input": "2",
"output": "2"
},
{
"input": "4",
"output": "2"
},
{
"input": "8",
"output": "2"
},
{
"input": "3",
"output": "3"
},
... | 202 | 22,528,000 | 3 | 4,578 | |
75 | Big Maximum Sum | [
"data structures",
"dp",
"greedy",
"implementation",
"math",
"trees"
] | D. Big Maximum Sum | 2 | 256 | Ahmed and Mostafa used to compete together in many programming contests for several years. Their coach Fegla asked them to solve one challenging problem, of course Ahmed was able to solve it but Mostafa couldn't.
This problem is similar to a standard problem but it has a different format and constraints.
In the standard problem you are given an array of integers, and you have to find one or more consecutive elements in this array where their sum is the maximum possible sum.
But in this problem you are given *n* small arrays, and you will create one big array from the concatenation of one or more instances of the small arrays (each small array could occur more than once). The big array will be given as an array of indexes (1-based) of the small arrays, and the concatenation should be done in the same order as in this array. Then you should apply the standard problem mentioned above on the resulting big array.
For example let's suppose that the small arrays are {1, 6, -2}, {3, 3} and {-5, 1}. And the indexes in the big array are {2, 3, 1, 3}. So the actual values in the big array after formatting it as concatenation of the small arrays will be {3, 3, -5, 1, 1, 6, -2, -5, 1}. In this example the maximum sum is 9.
Can you help Mostafa solve this problem? | The first line contains two integers *n* and *m*, *n* is the number of the small arrays (1<=≤<=*n*<=≤<=50), and *m* is the number of indexes in the big array (1<=≤<=*m*<=≤<=250000). Then follow *n* lines, the *i*-th line starts with one integer *l* which is the size of the *i*-th array (1<=≤<=*l*<=≤<=5000), followed by *l* integers each one will be greater than or equal -1000 and less than or equal 1000. The last line contains *m* integers which are the indexes in the big array, and you should concatenate the small arrays in the same order, and each index will be greater than or equal to 1 and less than or equal to *n*.
The small arrays are numbered from 1 to *n* in the same order as given in the input. Some of the given small arrays may not be used in big array.
Note, that the array is very big. So if you try to build it straightforwardly, you will probably get time or/and memory limit exceeded. | Print one line containing the maximum sum in the big array after formatting it as described above. You must choose at least one element for the sum, i. e. it cannot be empty.
Please, do not use %lld specificator to write 64-bit integers in C++. It is preferred to use cout (also you may use %I64d). | [
"3 4\n3 1 6 -2\n2 3 3\n2 -5 1\n2 3 1 3\n",
"6 1\n4 0 8 -3 -10\n8 3 -2 -5 10 8 -9 -5 -4\n1 0\n1 -3\n3 -8 5 6\n2 9 6\n1\n"
] | [
"9\n",
"8\n"
] | none | [
{
"input": "3 4\n3 1 6 -2\n2 3 3\n2 -5 1\n2 3 1 3",
"output": "9"
},
{
"input": "6 1\n4 0 8 -3 -10\n8 3 -2 -5 10 8 -9 -5 -4\n1 0\n1 -3\n3 -8 5 6\n2 9 6\n1",
"output": "8"
},
{
"input": "4 3\n6 6 8 -5 4 10 -2\n1 -2\n1 -10\n5 -10 10 8 -7 -10\n2 4 1",
"output": "24"
},
{
"input"... | 2,000 | 10,854,400 | 0 | 4,596 |
35 | Fire Again | [
"brute force",
"dfs and similar",
"shortest paths"
] | C. Fire Again | 2 | 64 | After a terrifying forest fire in Berland a forest rebirth program was carried out. Due to it *N* rows with *M* trees each were planted and the rows were so neat that one could map it on a system of coordinates so that the *j*-th tree in the *i*-th row would have the coordinates of (*i*,<=*j*). However a terrible thing happened and the young forest caught fire. Now we must find the coordinates of the tree that will catch fire last to plan evacuation.
The burning began in *K* points simultaneously, which means that initially *K* trees started to burn. Every minute the fire gets from the burning trees to the ones that aren’t burning and that the distance from them to the nearest burning tree equals to 1.
Find the tree that will be the last to start burning. If there are several such trees, output any. | The first input line contains two integers *N*,<=*M* (1<=≤<=*N*,<=*M*<=≤<=2000) — the size of the forest. The trees were planted in all points of the (*x*,<=*y*) (1<=≤<=*x*<=≤<=*N*,<=1<=≤<=*y*<=≤<=*M*) type, *x* and *y* are integers.
The second line contains an integer *K* (1<=≤<=*K*<=≤<=10) — amount of trees, burning in the beginning.
The third line contains *K* pairs of integers: *x*1,<=*y*1,<=*x*2,<=*y*2,<=...,<=*x**k*,<=*y**k* (1<=≤<=*x**i*<=≤<=*N*,<=1<=≤<=*y**i*<=≤<=*M*) — coordinates of the points from which the fire started. It is guaranteed that no two points coincide. | Output a line with two space-separated integers *x* and *y* — coordinates of the tree that will be the last one to start burning. If there are several such trees, output any. | [
"3 3\n1\n2 2\n",
"3 3\n1\n1 1\n",
"3 3\n2\n1 1 3 3\n"
] | [
"1 1\n",
"3 3\n",
"2 2"
] | none | [
{
"input": "3 3\n1\n2 2",
"output": "1 1"
},
{
"input": "3 3\n1\n1 1",
"output": "3 3"
},
{
"input": "3 3\n2\n1 1 3 3",
"output": "1 3"
},
{
"input": "1 1\n1\n1 1",
"output": "1 1"
},
{
"input": "2 2\n1\n2 2",
"output": "1 1"
},
{
"input": "2 2\n2\n1 1... | 998 | 4,505,600 | 3.716931 | 4,600 |
328 | Sheldon and Ice Pieces | [
"greedy"
] | null | null | Do you remember how Kai constructed the word "eternity" using pieces of ice as components?
Little Sheldon plays with pieces of ice, each piece has exactly one digit between 0 and 9. He wants to construct his favourite number *t*. He realized that digits 6 and 9 are very similar, so he can rotate piece of ice with 6 to use as 9 (and vice versa). Similary, 2 and 5 work the same. There is no other pair of digits with similar effect. He called this effect "Digital Mimicry".
Sheldon favourite number is *t*. He wants to have as many instances of *t* as possible. How many instances he can construct using the given sequence of ice pieces. He can use any piece at most once. | The first line contains integer *t* (1<=≤<=*t*<=≤<=10000). The second line contains the sequence of digits on the pieces. The length of line is equal to the number of pieces and between 1 and 200, inclusive. It contains digits between 0 and 9. | Print the required number of instances. | [
"42\n23454\n",
"169\n12118999\n"
] | [
"2\n",
"1\n"
] | This problem contains very weak pretests. | [
{
"input": "42\n23454",
"output": "2"
},
{
"input": "169\n12118999",
"output": "1"
},
{
"input": "1\n1",
"output": "1"
},
{
"input": "7\n777",
"output": "3"
},
{
"input": "18\n8118",
"output": "2"
},
{
"input": "33\n33333333",
"output": "4"
},
... | 342 | 409,600 | 0 | 4,602 | |
84 | Toy Army | [
"math",
"number theory"
] | A. Toy Army | 2 | 256 | The hero of our story, Valera, and his best friend Arcady are still in school, and therefore they spend all the free time playing turn-based strategy "GAGA: Go And Go Again". The gameplay is as follows.
There are two armies on the playing field each of which consists of *n* men (*n* is always even). The current player specifies for each of her soldiers an enemy's soldier he will shoot (a target) and then all the player's soldiers shot simultaneously. This is a game world, and so each soldier shoots perfectly, that is he absolutely always hits the specified target. If an enemy soldier is hit, he will surely die. It may happen that several soldiers had been indicated the same target. Killed soldiers do not participate in the game anymore.
The game "GAGA" consists of three steps: first Valera makes a move, then Arcady, then Valera again and the game ends.
You are asked to calculate the maximum total number of soldiers that may be killed during the game. | The input data consist of a single integer *n* (2<=≤<=*n*<=≤<=108, *n* is even). Please note that before the game starts there are 2*n* soldiers on the fields. | Print a single number — a maximum total number of soldiers that could be killed in the course of the game in three turns. | [
"2\n",
"4\n"
] | [
"3\n",
"6\n"
] | The first sample test:
1) Valera's soldiers 1 and 2 shoot at Arcady's soldier 1.
2) Arcady's soldier 2 shoots at Valera's soldier 1.
3) Valera's soldier 1 shoots at Arcady's soldier 2.
There are 3 soldiers killed in total: Valera's soldier 1 and Arcady's soldiers 1 and 2. | [
{
"input": "2",
"output": "3"
},
{
"input": "4",
"output": "6"
},
{
"input": "6",
"output": "9"
},
{
"input": "8",
"output": "12"
},
{
"input": "10",
"output": "15"
},
{
"input": "140",
"output": "210"
},
{
"input": "500",
"output": "75... | 0 | 0 | -1 | 4,605 |
168 | Wizards and Minimal Spell | [
"implementation",
"strings"
] | null | null | Let's dive into one of the most interesting areas of magic — writing spells. Learning this exciting but challenging science is very troublesome, so now you will not learn the magic words, but only get to know the basic rules of writing spells.
Each spell consists of several lines. The line, whose first non-space character is character "#" is an amplifying line and it is responsible for spell power. The remaining lines are common, and determine the effect of the spell.
You came across the text of some spell. Spell was too long, so you cannot understand its meaning. So you want to make it as short as possible without changing the meaning.
The only way to shorten a spell that you know is the removal of some spaces and line breaks. We know that when it comes to texts of spells, the spaces carry meaning only in the amplifying lines, so we should remove all spaces in other lines. Newlines also do not matter, unless any of the two separated lines is amplifying. Thus, if two consecutive lines are not amplifying, they need to be joined into one (i.e. we should concatenate the second line to the first one). Removing spaces in amplifying lines and concatenating the amplifying lines to anything is forbidden.
Note that empty lines must be processed just like all the others: they must be joined to the adjacent non-amplifying lines, or preserved in the output, if they are surrounded with amplifying lines on both sides (i.e. the line above it, if there is one, is amplifying, and the line below it, if there is one, is amplifying too).
For now those are the only instructions for removing unnecessary characters that you have to follow (oh yes, a newline is a character, too).
The input contains the text of the spell, which should be reduced. Remove the extra characters and print the result to the output. | The input contains multiple lines. All characters in the lines have codes from 32 to 127 (inclusive). Please note that the lines may begin with or end with one or more spaces. The size of the input does not exceed 1048576 (<==<=220) bytes. Newlines are included in this size.
In the Windows operating system used on the testing computer, a newline is a sequence of characters with codes #13#10. It is guaranteed that after each line of input there is a newline. In particular, the input ends with a newline. Note that the newline is the end of the line, and not the beginning of the next one.
It is guaranteed that the input contains at least one character other than a newline.
It is recommended to organize the input-output line by line, in this case the newlines will be processed correctly by the language means. | Print the text of the spell where all extra characters are deleted. Please note that each output line should be followed by a newline.
Please be careful: your answers will be validated by comparing them to the jury's answer byte-by-byte. So, all spaces and newlines matter. | [
"# include <cstdio>\n\nusing namespace std;\n\nint main ( ){\nputs(\"Hello # World\"); #\n#\n}\n",
"#\n\n#\n"
] | [
"# include <cstdio>\nusingnamespacestd;intmain(){puts(\"Hello#World\");#\n#\n}\n",
"#\n\n#\n"
] | In the first sample the amplifying lines are lines 1 and 7. So, lines 2 to 6 are concatenated to each other, all spaces are deleted from them.
In the second sample the amplifying lines are lines 1 and 3. So, no lines are concatenated to each other. | [
{
"input": " # include <cstdio>\n\nusing namespace std;\n\nint main ( ){\nputs(\"Hello # World\"); #\n#\n}",
"output": " # include <cstdio>\nusingnamespacestd;intmain(){puts(\"Hello#World\");#\n#\n}"
},
{
"input": "#\n\n#",
"output": "#\n\n#"
},
{
"input": "#\n \n#",
"... | 186 | 0 | 0 | 4,611 | |
911 | Nearest Minimums | [
"implementation"
] | null | null | You are given an array of *n* integer numbers *a*0,<=*a*1,<=...,<=*a**n*<=-<=1. Find the distance between two closest (nearest) minimums in it. It is guaranteed that in the array a minimum occurs at least two times. | The first line contains positive integer *n* (2<=≤<=*n*<=≤<=105) — size of the given array. The second line contains *n* integers *a*0,<=*a*1,<=...,<=*a**n*<=-<=1 (1<=≤<=*a**i*<=≤<=109) — elements of the array. It is guaranteed that in the array a minimum occurs at least two times. | Print the only number — distance between two nearest minimums in the array. | [
"2\n3 3\n",
"3\n5 6 5\n",
"9\n2 1 3 5 4 1 2 3 1\n"
] | [
"1\n",
"2\n",
"3\n"
] | none | [
{
"input": "2\n3 3",
"output": "1"
},
{
"input": "3\n5 6 5",
"output": "2"
},
{
"input": "9\n2 1 3 5 4 1 2 3 1",
"output": "3"
},
{
"input": "6\n4 6 7 8 6 4",
"output": "5"
},
{
"input": "2\n1000000000 1000000000",
"output": "1"
},
{
"input": "42\n1 1 ... | 2,000 | 1,126,400 | 0 | 4,612 | |
598 | Tricky Sum | [
"math"
] | null | null | In this problem you are to calculate the sum of all integers from 1 to *n*, but you should take all powers of two with minus in the sum.
For example, for *n*<==<=4 the sum is equal to <=-<=1<=-<=2<=+<=3<=-<=4<==<=<=-<=4, because 1, 2 and 4 are 20, 21 and 22 respectively.
Calculate the answer for *t* values of *n*. | The first line of the input contains a single integer *t* (1<=≤<=*t*<=≤<=100) — the number of values of *n* to be processed.
Each of next *t* lines contains a single integer *n* (1<=≤<=*n*<=≤<=109). | Print the requested sum for each of *t* integers *n* given in the input. | [
"2\n4\n1000000000\n"
] | [
"-4\n499999998352516354\n"
] | The answer for the first sample is explained in the statement. | [
{
"input": "2\n4\n1000000000",
"output": "-4\n499999998352516354"
},
{
"input": "10\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10",
"output": "-1\n-3\n0\n-4\n1\n7\n14\n6\n15\n25"
},
{
"input": "10\n10\n9\n47\n33\n99\n83\n62\n1\n100\n53",
"output": "25\n15\n1002\n435\n4696\n3232\n1827\n-1\n4796\n130... | 46 | 0 | 3 | 4,619 | |
40 | Interesting Sequence | [
"math"
] | D. Interesting Sequence | 3 | 256 | Berland scientists noticed long ago that the world around them depends on Berland population. Due to persistent research in this area the scientists managed to find out that the Berland chronology starts from the moment when the first two people came to that land (it is considered to have happened in the first year). After one Berland year after the start of the chronology the population had already equaled 13 people (the second year). However, tracing the population number during the following years was an ultimately difficult task, still it was found out that if *d**i* — the number of people in Berland in the year of *i*, then either *d**i*<==<=12*d**i*<=-<=2, or *d**i*<==<=13*d**i*<=-<=1<=-<=12*d**i*<=-<=2. Of course no one knows how many people are living in Berland at the moment, but now we can tell if there could possibly be a year in which the country population equaled *A*. That's what we ask you to determine. Also, if possible, you have to find out in which years it could be (from the beginning of Berland chronology). Let's suppose that it could be in the years of *a*1,<=*a*2,<=...,<=*a**k*. Then you have to define how many residents could be in the country during those years apart from the *A* variant. Look at the examples for further explanation. | The first line contains integer *A* (1<=≤<=*A*<=<<=10300). It is guaranteed that the number doesn't contain leading zeros. | On the first output line print YES, if there could be a year in which the total population of the country equaled *A*, otherwise print NO.
If the answer is YES, then you also have to print number *k* — the number of years in which the population could equal *A*. On the next line you have to output precisely *k* space-separated numbers — *a*1,<=*a*2,<=...,<=*a**k*. Those numbers have to be output in the increasing order.
On the next line you should output number *p* — how many variants of the number of people could be in the years of *a*1,<=*a*2,<=...,<=*a**k*, apart from the *A* variant. On each of the next *p* lines you have to print one number — the sought number of residents. Those number also have to go in the increasing order.
If any number (or both of them) *k* or *p* exceeds 1000, then you have to print 1000 instead of it and only the first 1000 possible answers in the increasing order.
The numbers should have no leading zeros. | [
"2\n",
"3\n",
"13\n",
"1729\n"
] | [
"YES\n1\n1\n0\n",
"NO\n",
"YES\n1\n2\n0\n",
"YES\n1\n4\n1\n156\n"
] | none | [
{
"input": "2",
"output": "YES\n1\n1\n0"
},
{
"input": "3",
"output": "NO"
},
{
"input": "13",
"output": "YES\n1\n2\n0"
},
{
"input": "1729",
"output": "YES\n1\n4\n1\n156"
},
{
"input": "1",
"output": "NO"
},
{
"input": "156",
"output": "YES\n1\n4\... | 404 | 1,126,400 | 0 | 4,622 |
171 | MYSTERIOUS LANGUAGE | [
"*special"
] | null | null | You are given a mysterious language (codenamed "Secret") available in "Custom Test" tab. Find out what this language is and write a program which outputs its name. Note that the program must be written in this language. | This program has only one test, and it's empty (it doesn't give your program anything to read). | Output the name of the mysterious language. | [] | [] | none | [
{
"input": "1",
"output": "INTERCAL"
}
] | 0 | 0 | -1 | 4,636 | |
952 | Cheese Board | [] | null | null | Not to be confused with [chessboard](https://en.wikipedia.org/wiki/Chessboard). | The first line of input contains a single integer *N* (1<=≤<=*N*<=≤<=100) — the number of cheeses you have.
The next *N* lines describe the cheeses you have. Each line contains two space-separated strings: the name of the cheese and its type. The name is a string of lowercase English letters between 1 and 10 characters long. The type is either "soft" or "hard. All cheese names are distinct. | Output a single number. | [
"9\nbrie soft\ncamembert soft\nfeta soft\ngoat soft\nmuenster soft\nasiago hard\ncheddar hard\ngouda hard\nswiss hard\n",
"6\nparmesan hard\nemmental hard\nedam hard\ncolby hard\ngruyere hard\nasiago hard\n"
] | [
"3\n",
"4\n"
] | none | [
{
"input": "9\nbrie soft\ncamembert soft\nfeta soft\ngoat soft\nmuenster soft\nasiago hard\ncheddar hard\ngouda hard\nswiss hard",
"output": "3"
},
{
"input": "6\nparmesan hard\nemmental hard\nedam hard\ncolby hard\ngruyere hard\nasiago hard",
"output": "4"
},
{
"input": "9\ngorgonzola s... | 46 | 0 | 3 | 4,641 | |
0 | none | [
"none"
] | null | null | This is an interactive problem. In the output section below you will see the information about flushing the output.
Bear Limak thinks of some hidden number — an integer from interval [2,<=100]. Your task is to say if the hidden number is prime or composite.
Integer *x*<=><=1 is called prime if it has exactly two distinct divisors, 1 and *x*. If integer *x*<=><=1 is not prime, it's called composite.
You can ask up to 20 queries about divisors of the hidden number. In each query you should print an integer from interval [2,<=100]. The system will answer "yes" if your integer is a divisor of the hidden number. Otherwise, the answer will be "no".
For example, if the hidden number is 14 then the system will answer "yes" only if you print 2, 7 or 14.
When you are done asking queries, print "prime" or "composite" and terminate your program.
You will get the Wrong Answer verdict if you ask more than 20 queries, or if you print an integer not from the range [2,<=100]. Also, you will get the Wrong Answer verdict if the printed answer isn't correct.
You will get the Idleness Limit Exceeded verdict if you don't print anything (but you should) or if you forget about flushing the output (more info below). | After each query you should read one string from the input. It will be "yes" if the printed integer is a divisor of the hidden number, and "no" otherwise. | Up to 20 times you can ask a query — print an integer from interval [2,<=100] in one line. You have to both print the end-of-line character and flush the output. After flushing you should read a response from the input.
In any moment you can print the answer "prime" or "composite" (without the quotes). After that, flush the output and terminate your program.
To flush you can use (just after printing an integer and end-of-line):
- fflush(stdout) in C++; - System.out.flush() in Java; - stdout.flush() in Python; - flush(output) in Pascal; - See the documentation for other languages.
Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2,<=100]. Of course, his/her solution won't be able to read the hidden number from the input. | [
"yes\nno\nyes\n",
"no\nyes\nno\nno\nno\n"
] | [
"2\n80\n5\ncomposite\n",
"58\n59\n78\n78\n2\nprime\n"
] | The hidden number in the first query is 30. In a table below you can see a better form of the provided example of the communication process.
<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/ea790051c34ea7d2761cd9b096412ca7c647a173.png" style="max-width: 100.0%;max-height: 100.0%;"/>
The hidden number is divisible by both 2 and 5. Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30.
<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/35c6952617fa94ec3e0ea8e63aa1c3c49b3ba420.png" style="max-width: 100.0%;max-height: 100.0%;"/>
59 is a divisor of the hidden number. In the interval [2, 100] there is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries). | [
{
"input": "30",
"output": "composite 4"
},
{
"input": "59",
"output": "prime 15"
},
{
"input": "2",
"output": "prime 16"
},
{
"input": "7",
"output": "prime 16"
},
{
"input": "9",
"output": "composite 3"
},
{
"input": "13",
"output": "prime 15"
... | 77 | 0 | 3 | 4,643 | |
385 | Bear and Prime Numbers | [
"binary search",
"brute force",
"data structures",
"dp",
"implementation",
"math",
"number theory"
] | null | null | Recently, the bear started studying data structures and faced the following problem.
You are given a sequence of integers *x*1,<=*x*2,<=...,<=*x**n* of length *n* and *m* queries, each of them is characterized by two integers *l**i*,<=*r**i*. Let's introduce *f*(*p*) to represent the number of such indexes *k*, that *x**k* is divisible by *p*. The answer to the query *l**i*,<=*r**i* is the sum: , where *S*(*l**i*,<=*r**i*) is a set of prime numbers from segment [*l**i*,<=*r**i*] (both borders are included in the segment).
Help the bear cope with the problem. | The first line contains integer *n* (1<=≤<=*n*<=≤<=106). The second line contains *n* integers *x*1,<=*x*2,<=...,<=*x**n* (2<=≤<=*x**i*<=≤<=107). The numbers are not necessarily distinct.
The third line contains integer *m* (1<=≤<=*m*<=≤<=50000). Each of the following *m* lines contains a pair of space-separated integers, *l**i* and *r**i* (2<=≤<=*l**i*<=≤<=*r**i*<=≤<=2·109) — the numbers that characterize the current query. | Print *m* integers — the answers to the queries on the order the queries appear in the input. | [
"6\n5 5 7 10 14 15\n3\n2 11\n3 12\n4 4\n",
"7\n2 3 5 7 11 4 8\n2\n8 10\n2 123\n"
] | [
"9\n7\n0\n",
"0\n7\n"
] | Consider the first sample. Overall, the first sample has 3 queries.
1. The first query *l* = 2, *r* = 11 comes. You need to count *f*(2) + *f*(3) + *f*(5) + *f*(7) + *f*(11) = 2 + 1 + 4 + 2 + 0 = 9. 1. The second query comes *l* = 3, *r* = 12. You need to count *f*(3) + *f*(5) + *f*(7) + *f*(11) = 1 + 4 + 2 + 0 = 7. 1. The third query comes *l* = 4, *r* = 4. As this interval has no prime numbers, then the sum equals 0. | [
{
"input": "6\n5 5 7 10 14 15\n3\n2 11\n3 12\n4 4",
"output": "9\n7\n0"
},
{
"input": "7\n2 3 5 7 11 4 8\n2\n8 10\n2 123",
"output": "0\n7"
},
{
"input": "9\n50 50 50 50 50 50 50 50 50\n7\n20 20\n8 13\n13 13\n6 14\n3 5\n15 17\n341 1792",
"output": "0\n0\n0\n0\n9\n0\n0"
},
{
"... | 2,000 | 83,558,400 | 0 | 4,645 | |
787 | Not Afraid | [
"greedy",
"implementation",
"math"
] | null | null | Since the giant heads have appeared in the sky all humanity is in danger, so all Ricks and Mortys from all parallel universes are gathering in groups to find a solution to get rid of them.
There are *n* parallel universes participating in this event (*n* Ricks and *n* Mortys). I. e. each of *n* universes has one Rick and one Morty. They're gathering in *m* groups. Each person can be in many groups and a group can contain an arbitrary number of members.
Ricks and Mortys have registered online in these groups. So, a person can have joined a group more than once (developer of this website hadn't considered this possibility).
Summer from universe #1 knows that in each parallel universe (including hers) exactly one of Rick and Morty from that universe is a traitor and is loyal, but no one knows which one. She knows that we are doomed if there's a group such that every member in that group is a traitor (they will plan and destroy the world).
Summer knows that if there's a possibility that world ends (there's a group where all members are traitors) she should immediately cancel this event. So she wants to know if she should cancel the event. You have to tell her yes if and only if there's at least one scenario (among all 2*n* possible scenarios, 2 possible scenarios for who a traitor in each universe) such that in that scenario the world will end. | The first line of input contains two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=104) — number of universes and number of groups respectively.
The next *m* lines contain the information about the groups. *i*-th of them first contains an integer *k* (number of times someone joined *i*-th group, *k*<=><=0) followed by *k* integers *v**i*,<=1,<=*v**i*,<=2,<=...,<=*v**i*,<=*k*. If *v**i*,<=*j* is negative, it means that Rick from universe number <=-<=*v**i*,<=*j* has joined this group and otherwise it means that Morty from universe number *v**i*,<=*j* has joined it.
Sum of *k* for all groups does not exceed 104. | In a single line print the answer to Summer's question. Print "YES" if she should cancel the event and "NO" otherwise. | [
"4 2\n1 -3\n4 -2 3 2 -3\n",
"5 2\n5 3 -2 1 -1 5\n3 -5 2 5\n",
"7 2\n3 -1 6 7\n7 -5 4 2 4 7 -3 4\n"
] | [
"YES\n",
"NO\n",
"YES\n"
] | In the first sample testcase, 1st group only contains the Rick from universe number 3, so in case he's a traitor, then all members of this group are traitors and so Summer should cancel the event. | [
{
"input": "4 2\n1 -3\n4 -2 3 2 -3",
"output": "YES"
},
{
"input": "5 2\n5 3 -2 1 -1 5\n3 -5 2 5",
"output": "NO"
},
{
"input": "7 2\n3 -1 6 7\n7 -5 4 2 4 7 -3 4",
"output": "YES"
},
{
"input": "2 1\n2 -2 2",
"output": "NO"
},
{
"input": "7 7\n1 -2\n1 6\n2 7 -6\n2... | 46 | 1,433,600 | 3 | 4,650 | |
835 | Star sky | [
"dp",
"implementation"
] | null | null | The Cartesian coordinate system is set in the sky. There you can see *n* stars, the *i*-th has coordinates (*x**i*, *y**i*), a maximum brightness *c*, equal for all stars, and an initial brightness *s**i* (0<=≤<=*s**i*<=≤<=*c*).
Over time the stars twinkle. At moment 0 the *i*-th star has brightness *s**i*. Let at moment *t* some star has brightness *x*. Then at moment (*t*<=+<=1) this star will have brightness *x*<=+<=1, if *x*<=+<=1<=≤<=*c*, and 0, otherwise.
You want to look at the sky *q* times. In the *i*-th time you will look at the moment *t**i* and you will see a rectangle with sides parallel to the coordinate axes, the lower left corner has coordinates (*x*1*i*, *y*1*i*) and the upper right — (*x*2*i*, *y*2*i*). For each view, you want to know the total brightness of the stars lying in the viewed rectangle.
A star lies in a rectangle if it lies on its border or lies strictly inside it. | The first line contains three integers *n*, *q*, *c* (1<=≤<=*n*,<=*q*<=≤<=105, 1<=≤<=*c*<=≤<=10) — the number of the stars, the number of the views and the maximum brightness of the stars.
The next *n* lines contain the stars description. The *i*-th from these lines contains three integers *x**i*, *y**i*, *s**i* (1<=≤<=*x**i*,<=*y**i*<=≤<=100, 0<=≤<=*s**i*<=≤<=*c*<=≤<=10) — the coordinates of *i*-th star and its initial brightness.
The next *q* lines contain the views description. The *i*-th from these lines contains five integers *t**i*, *x*1*i*, *y*1*i*, *x*2*i*, *y*2*i* (0<=≤<=*t**i*<=≤<=109, 1<=≤<=*x*1*i*<=<<=*x*2*i*<=≤<=100, 1<=≤<=*y*1*i*<=<<=*y*2*i*<=≤<=100) — the moment of the *i*-th view and the coordinates of the viewed rectangle. | For each view print the total brightness of the viewed stars. | [
"2 3 3\n1 1 1\n3 2 0\n2 1 1 2 2\n0 2 1 4 5\n5 1 1 5 5\n",
"3 4 5\n1 1 2\n2 3 0\n3 3 1\n0 1 1 100 100\n1 2 2 4 4\n2 2 1 4 7\n1 50 50 51 51\n"
] | [
"3\n0\n3\n",
"3\n3\n5\n0\n"
] | Let's consider the first example.
At the first view, you can see only the first star. At moment 2 its brightness is 3, so the answer is 3.
At the second view, you can see only the second star. At moment 0 its brightness is 0, so the answer is 0.
At the third view, you can see both stars. At moment 5 brightness of the first is 2, and brightness of the second is 1, so the answer is 3. | [
{
"input": "2 3 3\n1 1 1\n3 2 0\n2 1 1 2 2\n0 2 1 4 5\n5 1 1 5 5",
"output": "3\n0\n3"
},
{
"input": "3 4 5\n1 1 2\n2 3 0\n3 3 1\n0 1 1 100 100\n1 2 2 4 4\n2 2 1 4 7\n1 50 50 51 51",
"output": "3\n3\n5\n0"
}
] | 623 | 10,854,400 | 3 | 4,655 | |
656 | Scrambled | [
"*special",
"implementation"
] | null | null | Btoh yuo adn yuor roomatme lhoate wianshg disehs, btu stlil sdmoeboy msut peorrfm tihs cohre dialy. Oen dya yuo decdie to idourtcne smoe syestm. Yuor rmmotaoe sstgegus teh fooniwllg dael. Yuo argee on tow arayrs of ientgres M adn R, nmebur upmicnog dyas (induiclng teh cunrret oen) wtih sicsescuve irnegets (teh ceurrnt dya is zreo), adn yuo wsah teh diehss on dya D if adn olny if terhe etsixs an iednx i scuh taht *D* *mod* *M*[*i*]<==<=*R*[*i*], otwsehrie yuor rmootmae deos it. Yuo lkie teh cncepot, btu yuor rmotaome's cuinnng simle meaks yuo ssecupt sthnoemig, so yuo itennd to vefriy teh fnerisas of teh aemnrgeet.
Yuo aer geivn ayarrs M adn R. Cuaclatle teh pceanregte of dyas on wchih yuo edn up dnoig teh wisahng. Amsuse taht yuo hvae iiiftlneny mnay dyas aehad of yuo. | The first line of input contains a single integer N (1<=≤<=*N*<=≤<=16).
The second and third lines of input contain N integers each, all between 0 and 16, inclusive, and represent arrays M and R, respectively. All *M*[*i*] are positive, for each *i* *R*[*i*]<=<<=*M*[*i*]. | Output a single real number. The answer is considered to be correct if its absolute or relative error does not exceed 10<=-<=4. | [
"1\n2\n0\n",
"2\n2 3\n1 0\n"
] | [
"0.500000\n",
"0.666667\n"
] | none | [
{
"input": "1\n2\n0",
"output": "0.500000"
},
{
"input": "2\n2 3\n1 0",
"output": "0.666667"
},
{
"input": "3\n2 4 4\n0 1 3",
"output": "1.000000"
},
{
"input": "1\n16\n15",
"output": "0.062500"
},
{
"input": "16\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16\n0 1 2 3 4 ... | 296 | 6,041,600 | 3 | 4,660 | |
570 | Replacement | [
"constructive algorithms",
"data structures",
"implementation"
] | null | null | Daniel has a string *s*, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string *s*, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string *s* contains no two consecutive periods, then nothing happens.
Let's define *f*(*s*) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process *m* queries, the *i*-th results in that the character at position *x**i* (1<=≤<=*x**i*<=≤<=*n*) of string *s* is assigned value *c**i*. After each operation you have to calculate and output the value of *f*(*s*).
Help Daniel to process all queries. | The first line contains two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=300<=000) the length of the string and the number of queries.
The second line contains string *s*, consisting of *n* lowercase English letters and period signs.
The following *m* lines contain the descriptions of queries. The *i*-th line contains integer *x**i* and *c**i* (1<=≤<=*x**i*<=≤<=*n*, *c**i* — a lowercas English letter or a period sign), describing the query of assigning symbol *c**i* to position *x**i*. | Print *m* numbers, one per line, the *i*-th of these numbers must be equal to the value of *f*(*s*) after performing the *i*-th assignment. | [
"10 3\n.b..bz....\n1 h\n3 c\n9 f\n",
"4 4\n.cc.\n2 .\n3 .\n2 a\n1 a\n"
] | [
"4\n3\n1\n",
"1\n3\n1\n1\n"
] | Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
- after the first query *f*(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")- after the second query *f*(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")- after the third query *f*(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
- after the first query: *f*(..c.) = 1 ("[..]c." → ".c.")- after the second query: *f*(....) = 3 ("[..].." → "[..]." → "[..]" → ".")- after the third query: *f*(.a..) = 1 (".a[..]" → ".a.")- after the fourth query: *f*(aa..) = 1 ("aa[..]" → "aa.") | [
{
"input": "10 3\n.b..bz....\n1 h\n3 c\n9 f",
"output": "4\n3\n1"
},
{
"input": "4 4\n.cc.\n2 .\n3 .\n2 a\n1 a",
"output": "1\n3\n1\n1"
},
{
"input": "3 3\n...\n1 .\n2 a\n3 b",
"output": "2\n0\n0"
},
{
"input": "5 1\n.....\n5 z",
"output": "3"
},
{
"input": "1 5\n... | 46 | 0 | 0 | 4,663 | |
19 | Checkout Assistant | [
"dp"
] | B. Checkout Assistant | 1 | 256 | Bob came to a cash & carry store, put *n* items into his trolley, and went to the checkout counter to pay. Each item is described by its price *c**i* and time *t**i* in seconds that a checkout assistant spends on this item. While the checkout assistant is occupied with some item, Bob can steal some other items from his trolley. To steal one item Bob needs exactly 1 second. What is the minimum amount of money that Bob will have to pay to the checkout assistant? Remember, please, that it is Bob, who determines the order of items for the checkout assistant. | The first input line contains number *n* (1<=≤<=*n*<=≤<=2000). In each of the following *n* lines each item is described by a pair of numbers *t**i*, *c**i* (0<=≤<=*t**i*<=≤<=2000,<=1<=≤<=*c**i*<=≤<=109). If *t**i* is 0, Bob won't be able to steal anything, while the checkout assistant is occupied with item *i*. | Output one number — answer to the problem: what is the minimum amount of money that Bob will have to pay. | [
"4\n2 10\n0 20\n1 5\n1 3\n",
"3\n0 1\n0 10\n0 100\n"
] | [
"8\n",
"111\n"
] | none | [
{
"input": "4\n2 10\n0 20\n1 5\n1 3",
"output": "8"
},
{
"input": "3\n0 1\n0 10\n0 100",
"output": "111"
},
{
"input": "2\n0 635254032\n0 75159864",
"output": "710413896"
},
{
"input": "2\n0 861438648\n1 469893784",
"output": "469893784"
},
{
"input": "2\n2 876232... | 109 | 307,200 | 0 | 4,669 |
888 | K-Dominant Character | [
"binary search",
"implementation",
"two pointers"
] | null | null | You are given a string *s* consisting of lowercase Latin letters. Character *c* is called *k*-dominant iff each substring of *s* with length at least *k* contains this character *c*.
You have to find minimum *k* such that there exists at least one *k*-dominant character. | The first line contains string *s* consisting of lowercase Latin letters (1<=≤<=|*s*|<=≤<=100000). | Print one number — the minimum value of *k* such that there exists at least one *k*-dominant character. | [
"abacaba\n",
"zzzzz\n",
"abcde\n"
] | [
"2\n",
"1\n",
"3\n"
] | none | [
{
"input": "abacaba",
"output": "2"
},
{
"input": "zzzzz",
"output": "1"
},
{
"input": "abcde",
"output": "3"
},
{
"input": "bcaccacaaabaacaabaaabcbbcbcaacacbcbaaaacccacbbcbaabcbacaacbabacacacaccbbccbcbacbbbbccccabcabaaab",
"output": "8"
},
{
"input": "daabcdabbab... | 2,000 | 10,956,800 | 0 | 4,678 | |
216 | Forming Teams | [
"dfs and similar",
"implementation"
] | null | null | One day *n* students come to the stadium. They want to play football, and for that they need to split into teams, the teams must have an equal number of people.
We know that this group of people has archenemies. Each student has at most two archenemies. Besides, if student *A* is an archenemy to student *B*, then student *B* is an archenemy to student *A*.
The students want to split so as no two archenemies were in one team. If splitting in the required manner is impossible, some students will have to sit on the bench.
Determine the minimum number of students you will have to send to the bench in order to form the two teams in the described manner and begin the game at last. | The first line contains two integers *n* and *m* (2<=≤<=*n*<=≤<=100, 1<=≤<=*m*<=≤<=100) — the number of students and the number of pairs of archenemies correspondingly.
Next *m* lines describe enmity between students. Each enmity is described as two numbers *a**i* and *b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*, *a**i*<=≠<=*b**i*) — the indexes of the students who are enemies to each other. Each enmity occurs in the list exactly once. It is guaranteed that each student has no more than two archenemies.
You can consider the students indexed in some manner with distinct integers from 1 to *n*. | Print a single integer — the minimum number of students you will have to send to the bench in order to start the game. | [
"5 4\n1 2\n2 4\n5 3\n1 4\n",
"6 2\n1 4\n3 4\n",
"6 6\n1 2\n2 3\n3 1\n4 5\n5 6\n6 4\n"
] | [
"1",
"0",
"2"
] | none | [
{
"input": "5 4\n1 2\n2 4\n5 3\n1 4",
"output": "1"
},
{
"input": "6 2\n1 4\n3 4",
"output": "0"
},
{
"input": "6 6\n1 2\n2 3\n3 1\n4 5\n5 6\n6 4",
"output": "2"
},
{
"input": "5 1\n1 2",
"output": "1"
},
{
"input": "8 8\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n7 8\n8 1",
... | 592 | 31,539,200 | 0 | 4,682 | |
676 | Nicholas and Permutation | [
"constructive algorithms",
"implementation"
] | null | null | Nicholas has an array *a* that contains *n* distinct integers from 1 to *n*. In other words, Nicholas has a permutation of size *n*.
Nicholas want the minimum element (integer 1) and the maximum element (integer *n*) to be as far as possible from each other. He wants to perform exactly one swap in order to maximize the distance between the minimum and the maximum elements. The distance between two elements is considered to be equal to the absolute difference between their positions. | The first line of the input contains a single integer *n* (2<=≤<=*n*<=≤<=100) — the size of the permutation.
The second line of the input contains *n* distinct integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=*n*), where *a**i* is equal to the element at the *i*-th position. | Print a single integer — the maximum possible distance between the minimum and the maximum elements Nicholas can achieve by performing exactly one swap. | [
"5\n4 5 1 3 2\n",
"7\n1 6 5 3 4 7 2\n",
"6\n6 5 4 3 2 1\n"
] | [
"3\n",
"6\n",
"5\n"
] | In the first sample, one may obtain the optimal answer by swapping elements 1 and 2.
In the second sample, the minimum and the maximum elements will be located in the opposite ends of the array if we swap 7 and 2.
In the third sample, the distance between the minimum and the maximum elements is already maximum possible, so we just perform some unnecessary swap, for example, one can swap 5 and 2. | [
{
"input": "5\n4 5 1 3 2",
"output": "3"
},
{
"input": "7\n1 6 5 3 4 7 2",
"output": "6"
},
{
"input": "6\n6 5 4 3 2 1",
"output": "5"
},
{
"input": "2\n1 2",
"output": "1"
},
{
"input": "2\n2 1",
"output": "1"
},
{
"input": "3\n2 3 1",
"output": "... | 62 | 0 | 0 | 4,691 | |
289 | Polo the Penguin and Segments | [
"brute force",
"implementation"
] | null | null | Little penguin Polo adores integer segments, that is, pairs of integers [*l*; *r*] (*l*<=≤<=*r*).
He has a set that consists of *n* integer segments: [*l*1; *r*1],<=[*l*2; *r*2],<=...,<=[*l**n*; *r**n*]. We know that no two segments of this set intersect. In one move Polo can either widen any segment of the set 1 unit to the left or 1 unit to the right, that is transform [*l*; *r*] to either segment [*l*<=-<=1; *r*], or to segment [*l*; *r*<=+<=1].
The value of a set of segments that consists of *n* segments [*l*1; *r*1],<=[*l*2; *r*2],<=...,<=[*l**n*; *r**n*] is the number of integers *x*, such that there is integer *j*, for which the following inequality holds, *l**j*<=≤<=*x*<=≤<=*r**j*.
Find the minimum number of moves needed to make the value of the set of Polo's segments divisible by *k*. | The first line contains two integers *n* and *k* (1<=≤<=*n*,<=*k*<=≤<=105). Each of the following *n* lines contain a segment as a pair of integers *l**i* and *r**i* (<=-<=105<=≤<=*l**i*<=≤<=*r**i*<=≤<=105), separated by a space.
It is guaranteed that no two segments intersect. In other words, for any two integers *i*,<=*j* (1<=≤<=*i*<=<<=*j*<=≤<=*n*) the following inequality holds, *min*(*r**i*,<=*r**j*)<=<<=*max*(*l**i*,<=*l**j*). | In a single line print a single integer — the answer to the problem. | [
"2 3\n1 2\n3 4\n",
"3 7\n1 2\n3 3\n4 7\n"
] | [
"2\n",
"0\n"
] | none | [
{
"input": "2 3\n1 2\n3 4",
"output": "2"
},
{
"input": "3 7\n1 2\n3 3\n4 7",
"output": "0"
},
{
"input": "3 7\n1 10\n11 47\n74 128",
"output": "3"
},
{
"input": "5 4\n1 1\n2 2\n3 3\n4 4\n5 5",
"output": "3"
},
{
"input": "7 4\n2 2\n-1 -1\n0 1\n7 8\n-3 -2\n9 9\n4 ... | 654 | 0 | 3 | 4,694 | |
319 | Psychos in a Line | [
"data structures",
"implementation"
] | null | null | There are *n* psychos standing in a line. Each psycho is assigned a unique integer from 1 to *n*. At each step every psycho who has an id greater than the psycho to his right (if exists) kills his right neighbor in the line. Note that a psycho might kill and get killed at the same step.
You're given the initial arrangement of the psychos in the line. Calculate how many steps are needed to the moment of time such, that nobody kills his neighbor after that moment. Look notes to understand the statement more precise. | The first line of input contains integer *n* denoting the number of psychos, (1<=≤<=*n*<=≤<=105). In the second line there will be a list of *n* space separated distinct integers each in range 1 to *n*, inclusive — ids of the psychos in the line from left to right. | Print the number of steps, so that the line remains the same afterward. | [
"10\n10 9 7 8 6 5 3 4 2 1\n",
"6\n1 2 3 4 5 6\n"
] | [
"2\n",
"0\n"
] | In the first sample line of the psychos transforms as follows: [10 9 7 8 6 5 3 4 2 1] → [10 8 4] → [10]. So, there are two steps. | [
{
"input": "10\n10 9 7 8 6 5 3 4 2 1",
"output": "2"
},
{
"input": "6\n1 2 3 4 5 6",
"output": "0"
},
{
"input": "6\n6 5 4 3 2 1",
"output": "1"
},
{
"input": "10\n10 7 4 2 5 8 9 6 3 1",
"output": "4"
},
{
"input": "15\n15 9 5 10 7 11 14 6 2 3 12 1 8 13 4",
"o... | 0 | 0 | -1 | 4,695 | |
36 | Fractal | [
"implementation"
] | B. Fractal | 2 | 64 | Ever since Kalevitch, a famous Berland abstractionist, heard of fractals, he made them the main topic of his canvases. Every morning the artist takes a piece of graph paper and starts with making a model of his future canvas. He takes a square as big as *n*<=×<=*n* squares and paints some of them black. Then he takes a clean square piece of paper and paints the fractal using the following algorithm:
Step 1. The paper is divided into *n*2 identical squares and some of them are painted black according to the model.
Step 2. Every square that remains white is divided into *n*2 smaller squares and some of them are painted black according to the model.
Every following step repeats step 2.
Unfortunately, this tiresome work demands too much time from the painting genius. Kalevitch has been dreaming of making the process automatic to move to making 3D or even 4D fractals. | The first line contains integers *n* and *k* (2<=≤<=*n*<=≤<=3, 1<=≤<=*k*<=≤<=5), where *k* is the amount of steps of the algorithm. Each of the following *n* lines contains *n* symbols that determine the model. Symbol «.» stands for a white square, whereas «*» stands for a black one. It is guaranteed that the model has at least one white square. | Output a matrix *n**k*<=×<=*n**k* which is what a picture should look like after *k* steps of the algorithm. | [
"2 3\n.*\n..\n",
"3 2\n.*.\n***\n.*.\n"
] | [
".*******\n..******\n.*.*****\n....****\n.***.***\n..**..**\n.*.*.*.*\n........\n",
".*.***.*.\n*********\n.*.***.*.\n*********\n*********\n*********\n.*.***.*.\n*********\n.*.***.*.\n"
] | none | [
{
"input": "2 3\n.*\n..",
"output": ".*******\n..******\n.*.*****\n....****\n.***.***\n..**..**\n.*.*.*.*\n........"
},
{
"input": "3 2\n.*.\n***\n.*.",
"output": ".*.***.*.\n*********\n.*.***.*.\n*********\n*********\n*********\n.*.***.*.\n*********\n.*.***.*."
},
{
"input": "2 1\n..\n.... | 218 | 921,600 | 3.938634 | 4,702 |
402 | Trees in a Row | [
"brute force",
"implementation"
] | null | null | The Queen of England has *n* trees growing in a row in her garden. At that, the *i*-th (1<=≤<=*i*<=≤<=*n*) tree from the left has height *a**i* meters. Today the Queen decided to update the scenery of her garden. She wants the trees' heights to meet the condition: for all *i* (1<=≤<=*i*<=<<=*n*), *a**i*<=+<=1<=-<=*a**i*<==<=*k*, where *k* is the number the Queen chose.
Unfortunately, the royal gardener is not a machine and he cannot fulfill the desire of the Queen instantly! In one minute, the gardener can either decrease the height of a tree to any positive integer height or increase the height of a tree to any positive integer height. How should the royal gardener act to fulfill a whim of Her Majesty in the minimum number of minutes? | The first line contains two space-separated integers: *n*, *k* (1<=≤<=*n*,<=*k*<=≤<=1000). The second line contains *n* space-separated integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=1000) — the heights of the trees in the row. | In the first line print a single integer *p* — the minimum number of minutes the gardener needs. In the next *p* lines print the description of his actions.
If the gardener needs to increase the height of the *j*-th (1<=≤<=*j*<=≤<=*n*) tree from the left by *x* (*x*<=≥<=1) meters, then print in the corresponding line "+ j x". If the gardener needs to decrease the height of the *j*-th (1<=≤<=*j*<=≤<=*n*) tree from the left by *x* (*x*<=≥<=1) meters, print on the corresponding line "- j x".
If there are multiple ways to make a row of trees beautiful in the minimum number of actions, you are allowed to print any of them. | [
"4 1\n1 2 1 5\n",
"4 1\n1 2 3 4\n"
] | [
"2\n+ 3 2\n- 4 1\n",
"0\n"
] | none | [
{
"input": "4 1\n1 2 1 5",
"output": "2\n+ 3 2\n- 4 1"
},
{
"input": "4 1\n1 2 3 4",
"output": "0"
},
{
"input": "50 1\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50",
"output": "0"
},
... | 46 | 0 | -1 | 4,703 | |
567 | Geometric Progression | [
"binary search",
"data structures",
"dp"
] | null | null | Polycarp loves geometric progressions very much. Since he was only three years old, he loves only the progressions of length three. He also has a favorite integer *k* and a sequence *a*, consisting of *n* integers.
He wants to know how many subsequences of length three can be selected from *a*, so that they form a geometric progression with common ratio *k*.
A subsequence of length three is a combination of three such indexes *i*1,<=*i*2,<=*i*3, that 1<=≤<=*i*1<=<<=*i*2<=<<=*i*3<=≤<=*n*. That is, a subsequence of length three are such groups of three elements that are not necessarily consecutive in the sequence, but their indexes are strictly increasing.
A geometric progression with common ratio *k* is a sequence of numbers of the form *b*·*k*0,<=*b*·*k*1,<=...,<=*b*·*k**r*<=-<=1.
Polycarp is only three years old, so he can not calculate this number himself. Help him to do it. | The first line of the input contains two integers, *n* and *k* (1<=≤<=*n*,<=*k*<=≤<=2·105), showing how many numbers Polycarp's sequence has and his favorite number.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (<=-<=109<=≤<=*a**i*<=≤<=109) — elements of the sequence. | Output a single number — the number of ways to choose a subsequence of length three, such that it forms a geometric progression with a common ratio *k*. | [
"5 2\n1 1 2 2 4\n",
"3 1\n1 1 1\n",
"10 3\n1 2 6 2 3 6 9 18 3 9\n"
] | [
"4",
"1",
"6"
] | In the first sample test the answer is four, as any of the two 1s can be chosen as the first element, the second element can be any of the 2s, and the third element of the subsequence must be equal to 4. | [
{
"input": "5 2\n1 1 2 2 4",
"output": "4"
},
{
"input": "3 1\n1 1 1",
"output": "1"
},
{
"input": "10 3\n1 2 6 2 3 6 9 18 3 9",
"output": "6"
},
{
"input": "20 2\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20",
"output": "5"
},
{
"input": "5 3\n5 15 15 15 45... | 233 | 38,195,200 | 3 | 4,721 | |
18 | Platforms | [
"brute force",
"math"
] | B. Platforms | 2 | 64 | In one one-dimensional world there are *n* platforms. Platform with index *k* (platforms are numbered from 1) is a segment with coordinates [(*k*<=-<=1)*m*,<=(*k*<=-<=1)*m*<=+<=*l*], and *l*<=<<=*m*. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly *d* units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down. | The first input line contains 4 integer numbers *n*, *d*, *m*, *l* (1<=≤<=*n*,<=*d*,<=*m*,<=*l*<=≤<=106,<=*l*<=<<=*m*) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers *m* and *l* needed to find coordinates of the *k*-th platform: [(*k*<=-<=1)*m*,<=(*k*<=-<=1)*m*<=+<=*l*]. | Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down. | [
"2 2 5 3\n",
"5 4 11 8\n"
] | [
"4\n",
"20\n"
] | none | [
{
"input": "2 2 5 3",
"output": "4"
},
{
"input": "5 4 11 8",
"output": "20"
},
{
"input": "228385 744978 699604 157872",
"output": "2979912"
},
{
"input": "773663 427904 329049 243542",
"output": "1283712"
},
{
"input": "835293 627183 442142 361649",
"output"... | 966 | 50,892,800 | -1 | 4,726 |
0 | none | [
"none"
] | null | null | Two players play the following game. Initially, the players have a knife and a rectangular sheet of paper, divided into equal square grid cells of unit size. The players make moves in turn, the player who can't make a move loses. In one move, a player can take the knife and cut the paper along any segment of the grid line (not necessarily from border to border). The part of the paper, that touches the knife at least once, is considered cut. There is one limit not to turn the game into an infinite cycle: each move has to cut the paper, that is the knife has to touch the part of the paper that is not cut before.
Obviously, the game ends when the entire sheet is cut into 1<=×<=1 blocks. During the game, the pieces of the sheet are not allowed to move. It is also prohibited to cut along the border. The coordinates of the ends of each cut must be integers.
You are given an *n*<=×<=*m* piece of paper, somebody has already made *k* cuts there. Your task is to determine who will win if the players start to play on this sheet. You can consider that both players play optimally well. If the first player wins, you also need to find the winning first move. | The first line contains three integers *n*, *m*, *k* (1<=≤<=*n*,<=*m*<=≤<=109,<=0<=≤<=*k*<=≤<=105) — the sizes of the piece of paper and the number of cuts. Then follow *k* lines, each containing 4 integers *xb**i*,<=*yb**i*,<=*xe**i*,<=*ye**i* (0<=≤<=*xb**i*,<=*xe**i*<=≤<=*n*,<=0<=≤<=*yb**i*,<=*ye**i*<=≤<=*m*) — the coordinates of the ends of the existing cuts.
It is guaranteed that each cut has a non-zero length, is either vertical or horizontal and doesn't go along the sheet border.
The cuts may intersect, overlap and even be the same. That is, it is not guaranteed that the cuts were obtained during any correct game. | If the second player wins, print "SECOND". Otherwise, in the first line print "FIRST", and in the second line print any winning move of the first player (the coordinates of the cut ends, follow input format to print them). | [
"2 1 0\n",
"2 2 4\n0 1 2 1\n0 1 2 1\n1 2 1 0\n1 1 1 2\n"
] | [
"FIRST\n1 0 1 1\n",
"SECOND\n"
] | none | [] | 92 | 0 | 0 | 4,737 | |
821 | Okabe and Banana Trees | [
"brute force",
"math"
] | null | null | Okabe needs bananas for one of his experiments for some strange reason. So he decides to go to the forest and cut banana trees.
Consider the point (*x*,<=*y*) in the 2D plane such that *x* and *y* are integers and 0<=≤<=*x*,<=*y*. There is a tree in such a point, and it has *x*<=+<=*y* bananas. There are no trees nor bananas in other points. Now, Okabe draws a line with equation . Okabe can select a single rectangle with axis aligned sides with all points on or under the line and cut all the trees in all points that are inside or on the border of this rectangle and take their bananas. Okabe's rectangle can be degenerate; that is, it can be a line segment or even a point.
Help Okabe and find the maximum number of bananas he can get if he chooses the rectangle wisely.
Okabe is sure that the answer does not exceed 1018. You can trust him. | The first line of input contains two space-separated integers *m* and *b* (1<=≤<=*m*<=≤<=1000, 1<=≤<=*b*<=≤<=10000). | Print the maximum number of bananas Okabe can get from the trees he cuts. | [
"1 5\n",
"2 3\n"
] | [
"30\n",
"25\n"
] | The graph above corresponds to sample test 1. The optimal rectangle is shown in red and has 30 bananas. | [
{
"input": "1 5",
"output": "30"
},
{
"input": "2 3",
"output": "25"
},
{
"input": "4 6",
"output": "459"
},
{
"input": "6 3",
"output": "171"
},
{
"input": "1 1",
"output": "1"
},
{
"input": "10 1",
"output": "55"
},
{
"input": "20 10",
... | 78 | 5,529,600 | 3 | 4,739 | |
624 | Save Luke | [
"math"
] | null | null | Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and *L*, and they move towards each other with speed *v*1 and *v*2, respectively. Luke has width *d* and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive. | The first line of the input contains four integers *d*, *L*, *v*1, *v*2 (1<=≤<=*d*,<=*L*,<=*v*1,<=*v*2<=≤<=10<=000,<=*d*<=<<=*L*) — Luke's width, the initial position of the second press and the speed of the first and second presses, respectively. | Print a single real value — the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10<=-<=6.
Namely: let's assume that your answer is *a*, and the answer of the jury is *b*. The checker program will consider your answer correct, if . | [
"2 6 2 2\n",
"1 9 1 2\n"
] | [
"1.00000000000000000000\n",
"2.66666666666666650000\n"
] | In the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.
In the second sample he needs to occupy the position <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/71395c777960eaded59a9fdc428a9625f152605b.png" style="max-width: 100.0%;max-height: 100.0%;"/>. In this case both presses move to his edges at the same time. | [
{
"input": "2 6 2 2",
"output": "1.00000000000000000000"
},
{
"input": "1 9 1 2",
"output": "2.66666666666666650000"
},
{
"input": "1 10000 1 1",
"output": "4999.50000000000000000000"
},
{
"input": "9999 10000 10000 10000",
"output": "0.00005000000000000000"
},
{
... | 46 | 0 | 3 | 4,746 | |
413 | Spyke Chatting | [
"implementation"
] | null | null | The R2 company has *n* employees working for it. The work involves constant exchange of ideas, sharing the stories of success and upcoming challenging. For that, R2 uses a famous instant messaging program Spyke.
R2 has *m* Spyke chats just to discuss all sorts of issues. In each chat, some group of employees exchanges messages daily. An employee can simultaneously talk in multiple chats. If some employee is in the *k*-th chat, he can write messages to this chat and receive notifications about messages from this chat. If an employee writes a message in the chat, all other participants of the chat receive a message notification.
The R2 company is conducting an audit. Now the specialists study effective communication between the employees. For this purpose, they have a chat log and the description of chat structure. You, as one of audit specialists, are commissioned to write a program that will use this data to determine the total number of message notifications received by each employee. | The first line contains three space-separated integers *n*, *m* and *k* (2<=≤<=*n*<=≤<=2·104; 1<=≤<=*m*<=≤<=10; 1<=≤<=*k*<=≤<=2·105) — the number of the employees, the number of chats and the number of events in the log, correspondingly.
Next *n* lines contain matrix *a* of size *n*<=×<=*m*, consisting of numbers zero and one. The element of this matrix, recorded in the *j*-th column of the *i*-th line, (let's denote it as *a**ij*) equals 1, if the *i*-th employee is the participant of the *j*-th chat, otherwise the element equals 0. Assume that the employees are numbered from 1 to *n* and the chats are numbered from 1 to *m*.
Next *k* lines contain the description of the log events. The *i*-th line contains two space-separated integers *x**i* and *y**i* (1<=≤<=*x**i*<=≤<=*n*; 1<=≤<=*y**i*<=≤<=*m*) which mean that the employee number *x**i* sent one message to chat number *y**i*. It is guaranteed that employee number *x**i* is a participant of chat *y**i*. It is guaranteed that each chat contains at least two employees. | Print in the single line *n* space-separated integers, where the *i*-th integer shows the number of message notifications the *i*-th employee receives. | [
"3 4 5\n1 1 1 1\n1 0 1 1\n1 1 0 0\n1 1\n3 1\n1 3\n2 4\n3 2\n",
"4 3 4\n0 1 1\n1 0 1\n1 1 1\n0 0 0\n1 2\n2 1\n3 1\n1 3\n"
] | [
"3 3 1 ",
"0 2 3 0 "
] | none | [
{
"input": "3 4 5\n1 1 1 1\n1 0 1 1\n1 1 0 0\n1 1\n3 1\n1 3\n2 4\n3 2",
"output": "3 3 1 "
},
{
"input": "4 3 4\n0 1 1\n1 0 1\n1 1 1\n0 0 0\n1 2\n2 1\n3 1\n1 3",
"output": "0 2 3 0 "
},
{
"input": "2 1 1\n1\n1\n1 1",
"output": "0 1 "
},
{
"input": "3 3 1\n1 1 1\n1 1 1\n1 1 1\... | 1,000 | 10,956,800 | 0 | 4,747 | |
609 | Load Balancing | [
"implementation",
"math"
] | null | null | In the school computer room there are *n* servers which are responsible for processing several computing tasks. You know the number of scheduled tasks for each server: there are *m**i* tasks assigned to the *i*-th server.
In order to balance the load for each server, you want to reassign some tasks to make the difference between the most loaded server and the least loaded server as small as possible. In other words you want to minimize expression *m**a*<=-<=*m**b*, where *a* is the most loaded server and *b* is the least loaded one.
In one second you can reassign a single task. Thus in one second you can choose any pair of servers and move a single task from one server to another.
Write a program to find the minimum number of seconds needed to balance the load of servers. | The first line contains positive number *n* (1<=≤<=*n*<=≤<=105) — the number of the servers.
The second line contains the sequence of non-negative integers *m*1,<=*m*2,<=...,<=*m**n* (0<=≤<=*m**i*<=≤<=2·104), where *m**i* is the number of tasks assigned to the *i*-th server. | Print the minimum number of seconds required to balance the load. | [
"2\n1 6\n",
"7\n10 11 10 11 10 11 11\n",
"5\n1 2 3 4 5\n"
] | [
"2\n",
"0\n",
"3\n"
] | In the first example two seconds are needed. In each second, a single task from server #2 should be moved to server #1. After two seconds there should be 3 tasks on server #1 and 4 tasks on server #2.
In the second example the load is already balanced.
A possible sequence of task movements for the third example is:
1. move a task from server #4 to server #1 (the sequence *m* becomes: 2 2 3 3 5); 1. then move task from server #5 to server #1 (the sequence *m* becomes: 3 2 3 3 4); 1. then move task from server #5 to server #2 (the sequence *m* becomes: 3 3 3 3 3).
The above sequence is one of several possible ways to balance the load of servers in three seconds. | [
{
"input": "2\n1 6",
"output": "2"
},
{
"input": "7\n10 11 10 11 10 11 11",
"output": "0"
},
{
"input": "5\n1 2 3 4 5",
"output": "3"
},
{
"input": "10\n0 0 0 0 0 0 0 0 0 0",
"output": "0"
},
{
"input": "1\n0",
"output": "0"
},
{
"input": "1\n20000",
... | 46 | 0 | 0 | 4,749 | |
1,009 | Annoying Present | [
"greedy",
"math"
] | null | null | Alice got an array of length $n$ as a birthday present once again! This is the third year in a row!
And what is more disappointing, it is overwhelmengly boring, filled entirely with zeros. Bob decided to apply some changes to the array to cheer up Alice.
Bob has chosen $m$ changes of the following form. For some integer numbers $x$ and $d$, he chooses an arbitrary position $i$ ($1 \le i \le n$) and for every $j \in [1, n]$ adds $x + d \cdot dist(i, j)$ to the value of the $j$-th cell. $dist(i, j)$ is the distance between positions $i$ and $j$ (i.e. $dist(i, j) = |i - j|$, where $|x|$ is an absolute value of $x$).
For example, if Alice currently has an array $[2, 1, 2, 2]$ and Bob chooses position $3$ for $x = -1$ and $d = 2$ then the array will become $[2 - 1 + 2 \cdot 2,~1 - 1 + 2 \cdot 1,~2 - 1 + 2 \cdot 0,~2 - 1 + 2 \cdot 1]$ = $[5, 2, 1, 3]$. Note that Bob can't choose position $i$ outside of the array (that is, smaller than $1$ or greater than $n$).
Alice will be the happiest when the elements of the array are as big as possible. Bob claimed that the arithmetic mean value of the elements will work fine as a metric.
What is the maximum arithmetic mean value Bob can achieve? | The first line contains two integers $n$ and $m$ ($1 \le n, m \le 10^5$) — the number of elements of the array and the number of changes.
Each of the next $m$ lines contains two integers $x_i$ and $d_i$ ($-10^3 \le x_i, d_i \le 10^3$) — the parameters for the $i$-th change. | Print the maximal average arithmetic mean of the elements Bob can achieve.
Your answer is considered correct if its absolute or relative error doesn't exceed $10^{-6}$. | [
"2 3\n-1 3\n0 0\n-1 -4\n",
"3 2\n0 2\n5 0\n"
] | [
"-2.500000000000000\n",
"7.000000000000000\n"
] | none | [
{
"input": "2 3\n-1 3\n0 0\n-1 -4",
"output": "-2.500000000000000"
},
{
"input": "3 2\n0 2\n5 0",
"output": "7.000000000000000"
},
{
"input": "8 8\n-21 -60\n-96 -10\n-4 -19\n-27 -4\n57 -15\n-95 62\n-42 1\n-17 64",
"output": "-16.500000000000000"
},
{
"input": "1 1\n0 0",
... | 405 | 307,200 | 0 | 4,764 | |
0 | none | [
"none"
] | null | null | Little Artem is fond of dancing. Most of all dances Artem likes rueda — Cuban dance that is danced by pairs of boys and girls forming a circle and dancing together.
More detailed, there are *n* pairs of boys and girls standing in a circle. Initially, boy number 1 dances with a girl number 1, boy number 2 dances with a girl number 2 and so on. Girls are numbered in the clockwise order. During the dance different moves are announced and all pairs perform this moves. While performing moves boys move along the circle, while girls always stay at their initial position. For the purpose of this problem we consider two different types of moves:
1. Value *x* and some direction are announced, and all boys move *x* positions in the corresponding direction. 1. Boys dancing with even-indexed girls swap positions with boys who are dancing with odd-indexed girls. That is the one who was dancing with the girl 1 swaps with the one who was dancing with the girl number 2, while the one who was dancing with girl number 3 swaps with the one who was dancing with the girl number 4 and so one. It's guaranteed that *n* is even.
Your task is to determine the final position of each boy. | The first line of the input contains two integers *n* and *q* (2<=≤<=*n*<=≤<=1<=000<=000, 1<=≤<=*q*<=≤<=2<=000<=000) — the number of couples in the rueda and the number of commands to perform, respectively. It's guaranteed that *n* is even.
Next *q* lines contain the descriptions of the commands. Each command has type as the integer 1 or 2 first. Command of the first type is given as *x* (<=-<=*n*<=≤<=*x*<=≤<=*n*), where 0<=≤<=*x*<=≤<=*n* means all boys moves *x* girls in clockwise direction, while <=-<=*x* means all boys move *x* positions in counter-clockwise direction. There is no other input for commands of the second type. | Output *n* integers, the *i*-th of them should be equal to the index of boy the *i*-th girl is dancing with after performing all *q* moves. | [
"6 3\n1 2\n2\n1 2\n",
"2 3\n1 1\n2\n1 -2\n",
"4 2\n2\n1 3\n"
] | [
"4 3 6 5 2 1\n",
"1 2\n",
"1 4 3 2\n"
] | none | [
{
"input": "6 3\n1 2\n2\n1 2",
"output": "4 3 6 5 2 1"
},
{
"input": "2 3\n1 1\n2\n1 -2",
"output": "1 2"
},
{
"input": "4 2\n2\n1 3",
"output": "1 4 3 2"
},
{
"input": "6 8\n1 2\n2\n2\n2\n2\n1 1\n1 -5\n2",
"output": "4 3 6 5 2 1"
},
{
"input": "6 8\n1 -1\n2\n2\n1... | 61 | 4,608,000 | 0 | 4,767 | |
47 | Triangular numbers | [
"brute force",
"math"
] | A. Triangular numbers | 2 | 256 | A triangular number is the number of dots in an equilateral triangle uniformly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangular number. The *n*-th triangular number is the number of dots in a triangle with *n* dots on a side. . You can learn more about these numbers from Wikipedia (http://en.wikipedia.org/wiki/Triangular_number).
Your task is to find out if a given integer is a triangular number. | The first line contains the single number *n* (1<=≤<=*n*<=≤<=500) — the given integer. | If the given integer is a triangular number output YES, otherwise output NO. | [
"1\n",
"2\n",
"3\n"
] | [
"YES\n",
"NO\n",
"YES\n"
] | none | [
{
"input": "1",
"output": "YES"
},
{
"input": "2",
"output": "NO"
},
{
"input": "3",
"output": "YES"
},
{
"input": "4",
"output": "NO"
},
{
"input": "5",
"output": "NO"
},
{
"input": "6",
"output": "YES"
},
{
"input": "7",
"output": "NO... | 92 | 0 | 3.977 | 4,772 |
113 | Grammar Lessons | [
"implementation",
"strings"
] | A. Grammar Lessons | 5 | 256 | Petya got interested in grammar on his third year in school. He invented his own language called Petya's. Petya wanted to create a maximally simple language that would be enough to chat with friends, that's why all the language's grammar can be described with the following set of rules:
- There are three parts of speech: the adjective, the noun, the verb. Each word in his language is an adjective, noun or verb. - There are two genders: masculine and feminine. Each word in his language has gender either masculine or feminine. - Masculine adjectives end with -lios, and feminine adjectives end with -liala. - Masculine nouns end with -etr, and feminime nouns end with -etra. - Masculine verbs end with -initis, and feminime verbs end with -inites. - Thus, each word in the Petya's language has one of the six endings, given above. There are no other endings in Petya's language. - It is accepted that the whole word consists of an ending. That is, words "lios", "liala", "etr" and so on belong to the Petya's language. - There aren't any punctuation marks, grammatical tenses, singular/plural forms or other language complications. - A sentence is either exactly one valid language word or exactly one statement.
Statement is any sequence of the Petya's language, that satisfy both conditions:
- Words in statement follow in the following order (from the left to the right): zero or more adjectives followed by exactly one noun followed by zero or more verbs. - All words in the statement should have the same gender.
After Petya's friend Vasya wrote instant messenger (an instant messaging program) that supported the Petya's language, Petya wanted to add spelling and grammar checking to the program. As Vasya was in the country and Petya didn't feel like waiting, he asked you to help him with this problem. Your task is to define by a given sequence of words, whether it is true that the given text represents exactly one sentence in Petya's language. | The first line contains one or more words consisting of lowercase Latin letters. The overall number of characters (including letters and spaces) does not exceed 105.
It is guaranteed that any two consecutive words are separated by exactly one space and the input data do not contain any other spaces. It is possible that given words do not belong to the Petya's language. | If some word of the given text does not belong to the Petya's language or if the text contains more that one sentence, print "NO" (without the quotes). Otherwise, print "YES" (without the quotes). | [
"petr\n",
"etis atis animatis etis atis amatis\n",
"nataliala kataliala vetra feinites\n"
] | [
"YES\n",
"NO\n",
"YES\n"
] | none | [
{
"input": "petr",
"output": "YES"
},
{
"input": "etis atis animatis etis atis amatis",
"output": "NO"
},
{
"input": "nataliala kataliala vetra feinites",
"output": "YES"
},
{
"input": "qweasbvflios",
"output": "YES"
},
{
"input": "lios lios petr initis qwe",
... | 62 | 4,505,600 | 0 | 4,778 |
219 | Special Offer! Super Price 999 Bourles! | [
"implementation"
] | null | null | Polycarpus is an amateur businessman. Recently he was surprised to find out that the market for paper scissors is completely free! Without further ado, Polycarpus decided to start producing and selling such scissors.
Polycaprus calculated that the optimal celling price for such scissors would be *p* bourles. However, he read somewhere that customers are attracted by prices that say something like "Special Offer! Super price 999 bourles!". So Polycarpus decided to lower the price a little if it leads to the desired effect.
Polycarpus agrees to lower the price by no more than *d* bourles so that the number of nines at the end of the resulting price is maximum. If there are several ways to do it, he chooses the maximum possible price.
Note, Polycarpus counts only the trailing nines in a price. | The first line contains two integers *p* and *d* (1<=≤<=*p*<=≤<=1018; 0<=≤<=*d*<=<<=*p*) — the initial price of scissors and the maximum possible price reduction.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier. | Print the required price — the maximum price that ends with the largest number of nines and that is less than *p* by no more than *d*.
The required number shouldn't have leading zeroes. | [
"1029 102\n",
"27191 17\n"
] | [
"999\n",
"27189\n"
] | none | [
{
"input": "1029 102",
"output": "999"
},
{
"input": "27191 17",
"output": "27189"
},
{
"input": "1 0",
"output": "1"
},
{
"input": "9 0",
"output": "9"
},
{
"input": "20 1",
"output": "19"
},
{
"input": "100 23",
"output": "99"
},
{
"input... | 310 | 0 | 0 | 4,785 | |
988 | Points and Powers of Two | [
"brute force",
"math"
] | null | null | There are $n$ distinct points on a coordinate line, the coordinate of $i$-th point equals to $x_i$. Choose a subset of the given set of points such that the distance between each pair of points in a subset is an integral power of two. It is necessary to consider each pair of points, not only adjacent. Note that any subset containing one element satisfies the condition above. Among all these subsets, choose a subset with maximum possible size.
In other words, you have to choose the maximum possible number of points $x_{i_1}, x_{i_2}, \dots, x_{i_m}$ such that for each pair $x_{i_j}$, $x_{i_k}$ it is true that $|x_{i_j} - x_{i_k}| = 2^d$ where $d$ is some non-negative integer number (not necessarily the same for each pair of points). | The first line contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of points.
The second line contains $n$ pairwise distinct integers $x_1, x_2, \dots, x_n$ ($-10^9 \le x_i \le 10^9$) — the coordinates of points. | In the first line print $m$ — the maximum possible number of points in a subset that satisfies the conditions described above.
In the second line print $m$ integers — the coordinates of points in the subset you have chosen.
If there are multiple answers, print any of them. | [
"6\n3 5 4 7 10 12\n",
"5\n-1 2 5 8 11\n"
] | [
"3\n7 3 5",
"1\n8\n"
] | In the first example the answer is $[7, 3, 5]$. Note, that $|7-3|=4=2^2$, $|7-5|=2=2^1$ and $|3-5|=2=2^1$. You can't find a subset having more points satisfying the required property. | [
{
"input": "6\n3 5 4 7 10 12",
"output": "3\n3 4 5 "
},
{
"input": "5\n-1 2 5 8 11",
"output": "1\n-1 "
},
{
"input": "1\n42",
"output": "1\n42 "
},
{
"input": "3\n0 -536870912 536870912",
"output": "3\n-536870912 0 536870912 "
},
{
"input": "2\n536870912 -5368709... | 670 | 33,894,400 | 0 | 4,787 | |
431 | k-Tree | [
"dp",
"implementation",
"trees"
] | null | null | Quite recently a creative student Lesha had a lecture on trees. After the lecture Lesha was inspired and came up with the tree of his own which he called a *k*-tree.
A *k*-tree is an infinite rooted tree where:
- each vertex has exactly *k* children; - each edge has some weight; - if we look at the edges that goes from some vertex to its children (exactly *k* edges), then their weights will equal 1,<=2,<=3,<=...,<=*k*.
The picture below shows a part of a 3-tree.
Help Dima find an answer to his question. As the number of ways can be rather large, print it modulo 1000000007 (109<=+<=7). | A single line contains three space-separated integers: *n*, *k* and *d* (1<=≤<=*n*,<=*k*<=≤<=100; 1<=≤<=*d*<=≤<=*k*). | Print a single integer — the answer to the problem modulo 1000000007 (109<=+<=7). | [
"3 3 2\n",
"3 3 3\n",
"4 3 2\n",
"4 5 2\n"
] | [
"3\n",
"1\n",
"6\n",
"7\n"
] | none | [
{
"input": "3 3 2",
"output": "3"
},
{
"input": "3 3 3",
"output": "1"
},
{
"input": "4 3 2",
"output": "6"
},
{
"input": "4 5 2",
"output": "7"
},
{
"input": "28 6 3",
"output": "110682188"
},
{
"input": "5 100 1",
"output": "16"
},
{
"inp... | 77 | 2,150,400 | 3 | 4,795 | |
583 | Robot's Task | [
"greedy",
"implementation"
] | null | null | Robot Doc is located in the hall, with *n* computers stand in a line, numbered from left to right from 1 to *n*. Each computer contains exactly one piece of information, each of which Doc wants to get eventually. The computers are equipped with a security system, so to crack the *i*-th of them, the robot needs to collect at least *a**i* any pieces of information from the other computers. Doc can hack the computer only if he is right next to it.
The robot is assembled using modern technologies and can move along the line of computers in either of the two possible directions, but the change of direction requires a large amount of resources from Doc. Tell the minimum number of changes of direction, which the robot will have to make to collect all *n* parts of information if initially it is next to computer with number 1.
It is guaranteed that there exists at least one sequence of the robot's actions, which leads to the collection of all information. Initially Doc doesn't have any pieces of information. | The first line contains number *n* (1<=≤<=*n*<=≤<=1000). The second line contains *n* non-negative integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=<<=*n*), separated by a space. It is guaranteed that there exists a way for robot to collect all pieces of the information. | Print a single number — the minimum number of changes in direction that the robot will have to make in order to collect all *n* parts of information. | [
"3\n0 2 0\n",
"5\n4 2 3 0 1\n",
"7\n0 3 1 0 5 2 6\n"
] | [
"1\n",
"3\n",
"2\n"
] | In the first sample you can assemble all the pieces of information in the optimal manner by assembling first the piece of information in the first computer, then in the third one, then change direction and move to the second one, and then, having 2 pieces of information, collect the last piece.
In the second sample to collect all the pieces of information in the optimal manner, Doc can go to the fourth computer and get the piece of information, then go to the fifth computer with one piece and get another one, then go to the second computer in the same manner, then to the third one and finally, to the first one. Changes of direction will take place before moving from the fifth to the second computer, then from the second to the third computer, then from the third to the first computer.
In the third sample the optimal order of collecting parts from computers can look like that: 1->3->4->6->2->5->7. | [
{
"input": "3\n0 2 0",
"output": "1"
},
{
"input": "5\n4 2 3 0 1",
"output": "3"
},
{
"input": "7\n0 3 1 0 5 2 6",
"output": "2"
},
{
"input": "1\n0",
"output": "0"
},
{
"input": "2\n0 1",
"output": "0"
},
{
"input": "10\n0 0 0 0 0 0 0 0 0 0",
"out... | 233 | 0 | 3 | 4,813 | |
261 | Maxim and Discounts | [
"greedy",
"sortings"
] | null | null | Maxim always goes to the supermarket on Sundays. Today the supermarket has a special offer of discount systems.
There are *m* types of discounts. We assume that the discounts are indexed from 1 to *m*. To use the discount number *i*, the customer takes a special basket, where he puts exactly *q**i* items he buys. Under the terms of the discount system, in addition to the items in the cart the customer can receive at most two items from the supermarket for free. The number of the "free items" (0, 1 or 2) to give is selected by the customer. The only condition imposed on the selected "free items" is as follows: each of them mustn't be more expensive than the cheapest item out of the *q**i* items in the cart.
Maxim now needs to buy *n* items in the shop. Count the minimum sum of money that Maxim needs to buy them, if he use the discount system optimally well.
Please assume that the supermarket has enough carts for any actions. Maxim can use the same discount multiple times. Of course, Maxim can buy items without any discounts. | The first line contains integer *m* (1<=≤<=*m*<=≤<=105) — the number of discount types. The second line contains *m* integers: *q*1,<=*q*2,<=...,<=*q**m* (1<=≤<=*q**i*<=≤<=105).
The third line contains integer *n* (1<=≤<=*n*<=≤<=105) — the number of items Maxim needs. The fourth line contains *n* integers: *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=104) — the items' prices.
The numbers in the lines are separated by single spaces. | In a single line print a single integer — the answer to the problem. | [
"1\n2\n4\n50 50 100 100\n",
"2\n2 3\n5\n50 50 50 50 50\n",
"1\n1\n7\n1 1 1 1 1 1 1\n"
] | [
"200\n",
"150\n",
"3\n"
] | In the first sample Maxim needs to buy two items that cost 100 and get a discount for two free items that cost 50. In that case, Maxim is going to pay 200.
In the second sample the best strategy for Maxim is to buy 3 items and get 2 items for free using the discount. In that case, Maxim is going to pay 150. | [
{
"input": "1\n2\n4\n50 50 100 100",
"output": "200"
},
{
"input": "2\n2 3\n5\n50 50 50 50 50",
"output": "150"
},
{
"input": "1\n1\n7\n1 1 1 1 1 1 1",
"output": "3"
},
{
"input": "60\n7 4 20 15 17 6 2 2 3 18 13 14 16 11 13 12 6 10 14 1 16 6 4 9 10 8 10 15 16 13 13 9 16 11 5 ... | 62 | 0 | 0 | 4,815 | |
884 | Boxes And Balls | [
"data structures",
"greedy"
] | null | null | Ivan has *n* different boxes. The first of them contains some balls of *n* different colors.
Ivan wants to play a strange game. He wants to distribute the balls into boxes in such a way that for every *i* (1<=≤<=*i*<=≤<=*n*) *i*-th box will contain all balls with color *i*.
In order to do this, Ivan will make some turns. Each turn he does the following:
1. Ivan chooses any non-empty box and takes all balls from this box; 1. Then Ivan chooses any *k* empty boxes (the box from the first step becomes empty, and Ivan is allowed to choose it), separates the balls he took on the previous step into *k* non-empty groups and puts each group into one of the boxes. He should put each group into a separate box. He can choose either *k*<==<=2 or *k*<==<=3.
The penalty of the turn is the number of balls Ivan takes from the box during the first step of the turn. And penalty of the game is the total penalty of turns made by Ivan until he distributes all balls to corresponding boxes.
Help Ivan to determine the minimum possible penalty of the game! | The first line contains one integer number *n* (1<=≤<=*n*<=≤<=200000) — the number of boxes and colors.
The second line contains *n* integer numbers *a*1, *a*2, ..., *a**n* (1<=≤<=*a**i*<=≤<=109), where *a**i* is the number of balls with color *i*. | Print one number — the minimum possible penalty of the game. | [
"3\n1 2 3\n",
"4\n2 3 4 5\n"
] | [
"6\n",
"19\n"
] | In the first example you take all the balls from the first box, choose *k* = 3 and sort all colors to corresponding boxes. Penalty is 6.
In the second example you make two turns:
1. Take all the balls from the first box, choose *k* = 3, put balls of color 3 to the third box, of color 4 — to the fourth box and the rest put back into the first box. Penalty is 14; 1. Take all the balls from the first box, choose *k* = 2, put balls of color 1 to the first box, of color 2 — to the second box. Penalty is 5.
Total penalty is 19. | [
{
"input": "3\n1 2 3",
"output": "6"
},
{
"input": "4\n2 3 4 5",
"output": "19"
},
{
"input": "6\n1 4 4 4 4 4",
"output": "38"
},
{
"input": "8\n821407370 380061316 428719552 90851747 825473738 704702117 845629927 245820158",
"output": "8176373828"
},
{
"input": "... | 514 | 15,974,400 | 3 | 4,819 | |
928 | Chat | [
"*special",
"dp"
] | null | null | There are times you recall a good old friend and everything you've come through together. Luckily there are social networks — they store all your message history making it easy to know what you argued over 10 years ago.
More formal, your message history is a sequence of messages ordered by time sent numbered from 1 to *n* where *n* is the total number of messages in the chat.
Each message might contain a link to an earlier message which it is a reply to. When opening a message *x* or getting a link to it, the dialogue is shown in such a way that *k* previous messages, message *x* and *k* next messages are visible (with respect to message *x*). In case there are less than *k* messages somewhere, they are yet all shown.
Digging deep into your message history, you always read all visible messages and then go by the link in the current message *x* (if there is one) and continue reading in the same manner.
Determine the number of messages you'll read if your start from message number *t* for all *t* from 1 to *n*. Calculate these numbers independently. If you start with message *x*, the initial configuration is *x* itself, *k* previous and *k* next messages. Messages read multiple times are considered as one. | The first line contains two integers *n* and *k* (1<=≤<=*n*<=≤<=105, 0<=≤<=*k*<=≤<=*n*) — the total amount of messages and the number of previous and next messages visible.
The second line features a sequence of integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=<<=*i*), where *a**i* denotes the *i*-th message link destination or zero, if there's no link from *i*. All messages are listed in chronological order. It's guaranteed that the link from message *x* goes to message with number strictly less than *x*. | Print *n* integers with *i*-th denoting the number of distinct messages you can read starting from message *i* and traversing the links while possible. | [
"6 0\n0 1 1 2 3 2\n",
"10 1\n0 1 0 3 4 5 2 3 7 0\n",
"2 2\n0 1\n"
] | [
"1 2 2 3 3 3 \n",
"2 3 3 4 5 6 6 6 8 2 \n",
"2 2 \n"
] | Consider *i* = 6 in sample case one. You will read message 6, then 2, then 1 and then there will be no link to go.
In the second sample case *i* = 6 gives you messages 5, 6, 7 since *k* = 1, then 4, 5, 6, then 2, 3, 4 and then the link sequence breaks. The number of distinct messages here is equal to 6. | [
{
"input": "6 0\n0 1 1 2 3 2",
"output": "1 2 2 3 3 3 "
},
{
"input": "10 1\n0 1 0 3 4 5 2 3 7 0",
"output": "2 3 3 4 5 6 6 6 8 2 "
},
{
"input": "2 2\n0 1",
"output": "2 2 "
},
{
"input": "1 1\n0",
"output": "1 "
},
{
"input": "5 2\n0 1 2 3 1",
"output": "3 4... | 295 | 30,924,800 | 0 | 4,826 | |
784 | Kids' Riddle | [
"*special"
] | null | null | Programmers' kids solve this riddle in 5-10 minutes. How fast can you do it? | The input contains a single integer *n* (0<=≤<=*n*<=≤<=2000000000). | Output a single integer. | [
"11\n",
"14\n",
"61441\n",
"571576\n",
"2128506\n"
] | [
"2\n",
"0\n",
"2\n",
"10\n",
"3\n"
] | none | [
{
"input": "11",
"output": "2"
},
{
"input": "14",
"output": "0"
},
{
"input": "61441",
"output": "2"
},
{
"input": "571576",
"output": "10"
},
{
"input": "2128506",
"output": "3"
},
{
"input": "0",
"output": "1"
},
{
"input": "2000000000",... | 78 | 7,065,600 | 3 | 4,843 | |
456 | Fedya and Maths | [
"math",
"number theory"
] | null | null | Fedya studies in a gymnasium. Fedya's maths hometask is to calculate the following expression:
for given value of *n*. Fedya managed to complete the task. Can you? Note that given number *n* can be extremely large (e.g. it can exceed any integer type of your programming language). | The single line contains a single integer *n* (0<=≤<=*n*<=≤<=10105). The number doesn't contain any leading zeroes. | Print the value of the expression without leading zeros. | [
"4\n",
"124356983594583453458888889\n"
] | [
"4\n",
"0\n"
] | Operation *x* *mod* *y* means taking remainder after division *x* by *y*.
Note to the first sample:
<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/825f244180bb10323db01645118c3cfdb312fa89.png" style="max-width: 100.0%;max-height: 100.0%;"/> | [
{
"input": "4",
"output": "4"
},
{
"input": "124356983594583453458888889",
"output": "0"
},
{
"input": "2",
"output": "0"
},
{
"input": "7854",
"output": "0"
},
{
"input": "584660",
"output": "4"
},
{
"input": "464",
"output": "4"
},
{
"inp... | 46 | 0 | 0 | 4,846 | |
615 | Multipliers | [
"math",
"number theory"
] | null | null | Ayrat has number *n*, represented as it's prime factorization *p**i* of size *m*, i.e. *n*<==<=*p*1·*p*2·...·*p**m*. Ayrat got secret information that that the product of all divisors of *n* taken modulo 109<=+<=7 is the password to the secret data base. Now he wants to calculate this value. | The first line of the input contains a single integer *m* (1<=≤<=*m*<=≤<=200<=000) — the number of primes in factorization of *n*.
The second line contains *m* primes numbers *p**i* (2<=≤<=*p**i*<=≤<=200<=000). | Print one integer — the product of all divisors of *n* modulo 109<=+<=7. | [
"2\n2 3\n",
"3\n2 3 2\n"
] | [
"36\n",
"1728\n"
] | In the first sample *n* = 2·3 = 6. The divisors of 6 are 1, 2, 3 and 6, their product is equal to 1·2·3·6 = 36.
In the second sample 2·3·2 = 12. The divisors of 12 are 1, 2, 3, 4, 6 and 12. 1·2·3·4·6·12 = 1728. | [
{
"input": "2\n2 3",
"output": "36"
},
{
"input": "3\n2 3 2",
"output": "1728"
},
{
"input": "1\n2017",
"output": "2017"
},
{
"input": "2\n63997 63997",
"output": "135893224"
},
{
"input": "5\n11 7 11 7 11",
"output": "750455957"
},
{
"input": "5\n2 2 ... | 124 | 0 | 0 | 4,853 | |
670 | Magic Powder - 1 | [
"binary search",
"brute force",
"implementation"
] | null | null | This problem is given in two versions that differ only by constraints. If you can solve this problem in large constraints, then you can just write a single solution to the both versions. If you find the problem too difficult in large constraints, you can write solution to the simplified version only.
Waking up in the morning, Apollinaria decided to bake cookies. To bake one cookie, she needs *n* ingredients, and for each ingredient she knows the value *a**i* — how many grams of this ingredient one needs to bake a cookie. To prepare one cookie Apollinaria needs to use all *n* ingredients.
Apollinaria has *b**i* gram of the *i*-th ingredient. Also she has *k* grams of a magic powder. Each gram of magic powder can be turned to exactly 1 gram of any of the *n* ingredients and can be used for baking cookies.
Your task is to determine the maximum number of cookies, which Apollinaria is able to bake using the ingredients that she has and the magic powder. | The first line of the input contains two positive integers *n* and *k* (1<=≤<=*n*,<=*k*<=≤<=1000) — the number of ingredients and the number of grams of the magic powder.
The second line contains the sequence *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=1000), where the *i*-th number is equal to the number of grams of the *i*-th ingredient, needed to bake one cookie.
The third line contains the sequence *b*1,<=*b*2,<=...,<=*b**n* (1<=≤<=*b**i*<=≤<=1000), where the *i*-th number is equal to the number of grams of the *i*-th ingredient, which Apollinaria has. | Print the maximum number of cookies, which Apollinaria will be able to bake using the ingredients that she has and the magic powder. | [
"3 1\n2 1 4\n11 3 16\n",
"4 3\n4 3 5 6\n11 12 14 20\n"
] | [
"4\n",
"3\n"
] | In the first sample it is profitably for Apollinaria to make the existing 1 gram of her magic powder to ingredient with the index 2, then Apollinaria will be able to bake 4 cookies.
In the second sample Apollinaria should turn 1 gram of magic powder to ingredient with the index 1 and 1 gram of magic powder to ingredient with the index 3. Then Apollinaria will be able to bake 3 cookies. The remaining 1 gram of the magic powder can be left, because it can't be used to increase the answer. | [
{
"input": "3 1\n2 1 4\n11 3 16",
"output": "4"
},
{
"input": "4 3\n4 3 5 6\n11 12 14 20",
"output": "3"
},
{
"input": "10 926\n5 6 8 1 2 5 1 8 4 4\n351 739 998 725 953 970 906 691 707 1000",
"output": "137"
},
{
"input": "20 925\n7 3 1 2 1 3 1 3 1 2 3 1 5 8 1 3 7 3 4 2\n837 ... | 124 | 2,150,400 | -1 | 4,854 | |
771 | Bear and Tree Jumps | [
"dfs and similar",
"dp",
"trees"
] | null | null | A tree is an undirected connected graph without cycles. The distance between two vertices is the number of edges in a simple path between them.
Limak is a little polar bear. He lives in a tree that consists of *n* vertices, numbered 1 through *n*.
Limak recently learned how to jump. He can jump from a vertex to any vertex within distance at most *k*.
For a pair of vertices (*s*,<=*t*) we define *f*(*s*,<=*t*) as the minimum number of jumps Limak needs to get from *s* to *t*. Your task is to find the sum of *f*(*s*,<=*t*) over all pairs of vertices (*s*,<=*t*) such that *s*<=<<=*t*. | The first line of the input contains two integers *n* and *k* (2<=≤<=*n*<=≤<=200<=000, 1<=≤<=*k*<=≤<=5) — the number of vertices in the tree and the maximum allowed jump distance respectively.
The next *n*<=-<=1 lines describe edges in the tree. The *i*-th of those lines contains two integers *a**i* and *b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*) — the indices on vertices connected with *i*-th edge.
It's guaranteed that the given edges form a tree. | Print one integer, denoting the sum of *f*(*s*,<=*t*) over all pairs of vertices (*s*,<=*t*) such that *s*<=<<=*t*. | [
"6 2\n1 2\n1 3\n2 4\n2 5\n4 6\n",
"13 3\n1 2\n3 2\n4 2\n5 2\n3 6\n10 6\n6 7\n6 13\n5 8\n5 9\n9 11\n11 12\n",
"3 5\n2 1\n3 1\n"
] | [
"20\n",
"114\n",
"3\n"
] | In the first sample, the given tree has 6 vertices and it's displayed on the drawing below. Limak can jump to any vertex within distance at most 2. For example, from the vertex 5 he can jump to any of vertices: 1, 2 and 4 (well, he can also jump to the vertex 5 itself).
There are <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/c0295201207e28a36e641d8cf599f45986059e71.png" style="max-width: 100.0%;max-height: 100.0%;"/> pairs of vertices (*s*, *t*) such that *s* < *t*. For 5 of those pairs Limak would need two jumps: (1, 6), (3, 4), (3, 5), (3, 6), (5, 6). For other 10 pairs one jump is enough. So, the answer is 5·2 + 10·1 = 20.
In the third sample, Limak can jump between every two vertices directly. There are 3 pairs of vertices (*s* < *t*), so the answer is 3·1 = 3. | [
{
"input": "6 2\n1 2\n1 3\n2 4\n2 5\n4 6",
"output": "20"
},
{
"input": "13 3\n1 2\n3 2\n4 2\n5 2\n3 6\n10 6\n6 7\n6 13\n5 8\n5 9\n9 11\n11 12",
"output": "114"
},
{
"input": "3 5\n2 1\n3 1",
"output": "3"
},
{
"input": "2 1\n1 2",
"output": "1"
},
{
"input": "2 5... | 46 | 0 | 0 | 4,857 |
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