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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
724 | Batch Sort | [
"brute force",
"greedy",
"implementation",
"math"
] | null | null | You are given a table consisting of *n* rows and *m* columns.
Numbers in each row form a permutation of integers from 1 to *m*.
You are allowed to pick two elements in one row and swap them, but no more than once for each row. Also, no more than once you are allowed to pick two columns and swap them. Thus, you are allowed to perform from 0 to *n*<=+<=1 actions in total. Operations can be performed in any order.
You have to check whether it's possible to obtain the identity permutation 1,<=2,<=...,<=*m* in each row. In other words, check if one can perform some of the operation following the given rules and make each row sorted in increasing order. | The first line of the input contains two integers *n* and *m* (1<=β€<=*n*,<=*m*<=β€<=20)Β β the number of rows and the number of columns in the given table.
Each of next *n* lines contains *m* integersΒ β elements of the table. It's guaranteed that numbers in each line form a permutation of integers from 1 to *m*. | If there is a way to obtain the identity permutation in each row by following the given rules, print "YES" (without quotes) in the only line of the output. Otherwise, print "NO" (without quotes). | [
"2 4\n1 3 2 4\n1 3 4 2\n",
"4 4\n1 2 3 4\n2 3 4 1\n3 4 1 2\n4 1 2 3\n",
"3 6\n2 1 3 4 5 6\n1 2 4 3 5 6\n1 2 3 4 6 5\n"
] | [
"YES\n",
"NO\n",
"YES\n"
] | In the first sample, one can act in the following way:
1. Swap second and third columns. Now the table is <center class="tex-equation">1Β 2Β 3Β 4</center> <center class="tex-equation">1Β 4Β 3Β 2</center> 1. In the second row, swap the second and the fourth elements. Now the table is <center class="tex-equation">1Β 2Β 3Β 4</center> <center class="tex-equation">1Β 2Β 3Β 4</center> | [
{
"input": "2 4\n1 3 2 4\n1 3 4 2",
"output": "YES"
},
{
"input": "4 4\n1 2 3 4\n2 3 4 1\n3 4 1 2\n4 1 2 3",
"output": "NO"
},
{
"input": "3 6\n2 1 3 4 5 6\n1 2 4 3 5 6\n1 2 3 4 6 5",
"output": "YES"
},
{
"input": "3 10\n1 2 3 4 5 6 7 10 9 8\n5 2 3 4 1 6 7 8 9 10\n1 2 3 4 5 6... | 62 | 1,331,200 | 0 | 2,757 | |
991 | Bishwock | [
"dp",
"greedy"
] | null | null | Bishwock is a chess figure that consists of three squares resembling an "L-bar". This figure can be rotated by 90, 180 and 270 degrees so it can have four possible states:
Bishwocks don't attack any squares and can even occupy on the adjacent squares as long as they don't occupy the same square.
Vasya has a board with $2\times n$ squares onto which he wants to put some bishwocks. To his dismay, several squares on this board are already occupied by pawns and Vasya can't put bishwocks there. However, pawns also don't attack bishwocks and they can occupy adjacent squares peacefully.
Knowing the positions of pawns on the board, help Vasya to determine the maximum amount of bishwocks he can put onto the board so that they wouldn't occupy the same squares and wouldn't occupy squares with pawns. | The input contains two nonempty strings that describe Vasya's board. Those strings contain only symbols "0" (zero) that denote the empty squares and symbols "X" (uppercase English letter) that denote the squares occupied by pawns. Strings are nonempty and are of the same length that does not exceed $100$. | Output a single integerΒ β the maximum amount of bishwocks that can be placed onto the given board. | [
"00\n00\n",
"00X00X0XXX0\n0XXX0X00X00\n",
"0X0X0\n0X0X0\n",
"0XXX0\n00000\n"
] | [
"1",
"4",
"0",
"2"
] | none | [
{
"input": "00\n00",
"output": "1"
},
{
"input": "00X00X0XXX0\n0XXX0X00X00",
"output": "4"
},
{
"input": "0X0X0\n0X0X0",
"output": "0"
},
{
"input": "0XXX0\n00000",
"output": "2"
},
{
"input": "0\n0",
"output": "0"
},
{
"input": "0\nX",
"output": "... | 62 | 0 | 0 | 2,761 | |
48 | Ivan the Fool VS Gorynych the Dragon | [
"dp",
"games",
"graphs"
] | E. Ivan the Fool VS Gorynych the Dragon | 2 | 256 | Once upon a time in a kingdom far, far awayβ¦ Okay, letβs start at the point where Ivan the Fool met Gorynych the Dragon. Ivan took out his magic sword and the battle began. First Gorynych had *h* heads and *t* tails. With each strike of the sword Ivan can either cut off several heads (from 1 to *n*, but not more than Gorynych has at the moment), or several tails (from 1 to *m*, but not more than Gorynych has at the moment). At the same time, horrible though it seems, Gorynych the Dragon can also grow new heads and tails. And the number of growing heads and tails is determined uniquely by the number of heads or tails cut by the current strike. When the total number of heads and tails exceeds *R*, Gorynych the Dragon strikes its final blow and destroys Ivan the Fool. Thatβs why Ivan aims to cut off all the dragonβs heads and tails as quickly as possible and win. The events can also develop in a third way: neither of the opponents can win over the other one and they will continue fighting forever.
The tale goes like this; easy to say, hard to do. Your task is to write a program that will determine the battleβs outcome. Consider that Ivan strikes consecutively. After each blow Gorynych grows a number of new heads and tails depending on the number of cut ones. Gorynych the Dragon is defeated if after the blow he loses all his heads and tails and canβt grow new ones. Ivan fights in the optimal way (fools are lucky), i.e.
- if Ivan can win, he wins having struck the least number of blows; - if it is impossible to defeat Gorynych, but is possible to resist him for an infinitely long period of time, then thatβs the strategy Ivan chooses; - if Gorynych wins in any case, Ivan aims to resist him for as long as possible. | The first line contains three integers *h*, *t* and *R* (0<=β€<=*h*,<=*t*,<=*R*<=β€<=200, 0<=<<=*h*<=+<=*t*<=β€<=*R*) which represent the initial numbers of Gorynychβs heads and tails and the largest total number of heads and tails with which Gorynych the Dragon does not yet attack. The next line contains integer *n* (1<=β€<=*n*<=β€<=200). The next *n* contain pairs of non-negative numbers "*h**i* *t**i*" which represent the number of heads and the number of tails correspondingly, that will grow if Gorynych has *i* heads (1<=β€<=*i*<=β€<=*n*) cut. The next line contains an integer *m* (1<=β€<=*m*<=β€<=200) and then β the description of Gorynychβs behavior when his tails are cut off in the format identical to the one described above. All the numbers in the input file do not exceed 200. | Print "Ivan" (without quotes) in the first line if Ivan wins, or "Zmey" (that means a dragon in Russian) if Gorynych the Dragon wins. In the second line print a single integer which represents the number of blows Ivan makes. If the battle will continue forever, print in the first line "Draw". | [
"2 2 4\n2\n1 0\n0 1\n3\n0 1\n0 1\n0 0\n",
"2 2 4\n1\n0 1\n1\n1 0\n",
"2 2 5\n1\n1 1\n1\n3 0\n"
] | [
"Ivan\n2\n",
"Draw\n",
"Zmey\n2\n"
] | none | [] | 92 | 0 | 0 | 2,773 |
901 | Hashing Trees | [
"constructive algorithms",
"trees"
] | null | null | Sasha is taking part in a programming competition. In one of the problems she should check if some rooted trees are isomorphic or not. She has never seen this problem before, but, being an experienced participant, she guessed that she should match trees to some sequences and then compare these sequences instead of trees. Sasha wants to match each tree with a sequence *a*0,<=*a*1,<=...,<=*a**h*, where *h* is the height of the tree, and *a**i* equals to the number of vertices that are at distance of *i* edges from root.
Unfortunately, this time Sasha's intuition was wrong, and there could be several trees matching the same sequence. To show it, you need to write a program that, given the sequence *a**i*, builds two non-isomorphic rooted trees that match that sequence, or determines that there is only one such tree.
Two rooted trees are isomorphic, if you can reenumerate the vertices of the first one in such a way, that the index of the root becomes equal the index of the root of the second tree, and these two trees become equal.
The height of a rooted tree is the maximum number of edges on a path from the root to any other vertex. | The first line contains a single integer *h* (2<=β€<=*h*<=β€<=105)Β β the height of the tree.
The second line contains *h*<=+<=1 integersΒ β the sequence *a*0,<=*a*1,<=...,<=*a**h* (1<=β€<=*a**i*<=β€<=2Β·105). The sum of all *a**i* does not exceed 2Β·105. It is guaranteed that there is at least one tree matching this sequence. | If there is only one tree matching this sequence, print "perfect".
Otherwise print "ambiguous" in the first line. In the second and in the third line print descriptions of two trees in the following format: in one line print integers, the *k*-th of them should be the parent of vertex *k* or be equal to zero, if the *k*-th vertex is the root.
These treese should be non-isomorphic and should match the given sequence. | [
"2\n1 1 1\n",
"2\n1 2 2\n"
] | [
"perfect\n",
"ambiguous\n0 1 1 3 3\n0 1 1 3 2\n"
] | The only tree in the first example and the two printed trees from the second example are shown on the picture:
<img class="tex-graphics" src="https://espresso.codeforces.com/ae5d1889e09854f9d8ad6e29ab7afbe690ca4702.png" style="max-width: 100.0%;max-height: 100.0%;"/> | [
{
"input": "2\n1 1 1",
"output": "perfect"
},
{
"input": "2\n1 2 2",
"output": "ambiguous\n0 1 1 3 3\n0 1 1 3 2"
},
{
"input": "10\n1 1 1 1 1 1 1 1 1 1 1",
"output": "perfect"
},
{
"input": "10\n1 1 1 1 1 2 1 1 1 1 1",
"output": "perfect"
},
{
"input": "10\n1 1 1 ... | 139 | 0 | 0 | 2,775 | |
0 | none | [
"none"
] | null | null | You are given a rebus of form ? + ? - ? + ? = n, consisting of only question marks, separated by arithmetic operation '+' and '-', equality and positive integer *n*. The goal is to replace each question mark with some positive integer from 1 to *n*, such that equality holds. | The only line of the input contains a rebus. It's guaranteed that it contains no more than 100 question marks, integer *n* is positive and doesn't exceed 1<=000<=000, all letters and integers are separated by spaces, arithmetic operations are located only between question marks. | The first line of the output should contain "Possible" (without quotes) if rebus has a solution and "Impossible" (without quotes) otherwise.
If the answer exists, the second line should contain any valid rebus with question marks replaced by integers from 1 to *n*. Follow the format given in the samples. | [
"? + ? - ? + ? + ? = 42\n",
"? - ? = 1\n",
"? = 1000000\n"
] | [
"Possible\n9 + 13 - 39 + 28 + 31 = 42\n",
"Impossible\n",
"Possible\n1000000 = 1000000\n"
] | none | [
{
"input": "? + ? - ? + ? + ? = 42",
"output": "Possible\n1 + 1 - 1 + 1 + 40 = 42"
},
{
"input": "? - ? = 1",
"output": "Impossible"
},
{
"input": "? = 1000000",
"output": "Possible\n1000000 = 1000000"
},
{
"input": "? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? + ? +... | 124 | 0 | 3 | 2,782 | |
525 | Ilya and Sticks | [
"greedy",
"math",
"sortings"
] | null | null | In the evening, after the contest Ilya was bored, and he really felt like maximizing. He remembered that he had a set of *n* sticks and an instrument. Each stick is characterized by its length *l**i*.
Ilya decided to make a rectangle from the sticks. And due to his whim, he decided to make rectangles in such a way that maximizes their total area. Each stick is used in making at most one rectangle, it is possible that some of sticks remain unused. Bending sticks is not allowed.
Sticks with lengths *a*1, *a*2, *a*3 and *a*4 can make a rectangle if the following properties are observed:
- *a*1<=β€<=*a*2<=β€<=*a*3<=β€<=*a*4 - *a*1<==<=*a*2 - *a*3<==<=*a*4
A rectangle can be made of sticks with lengths of, for example, 3Β 3Β 3Β 3 or 2Β 2Β 4Β 4. A rectangle cannot be made of, for example, sticks 5Β 5Β 5Β 7.
Ilya also has an instrument which can reduce the length of the sticks. The sticks are made of a special material, so the length of each stick can be reduced by at most one. For example, a stick with length 5 can either stay at this length or be transformed into a stick of length 4.
You have to answer the question β what maximum total area of the rectangles can Ilya get with a file if makes rectangles from the available sticks? | The first line of the input contains a positive integer *n* (1<=β€<=*n*<=β€<=105)Β βΒ the number of the available sticks.
The second line of the input contains *n* positive integers *l**i* (2<=β€<=*l**i*<=β€<=106)Β βΒ the lengths of the sticks. | The first line of the output must contain a single non-negative integerΒ βΒ the maximum total area of the rectangles that Ilya can make from the available sticks. | [
"4\n2 4 4 2\n",
"4\n2 2 3 5\n",
"4\n100003 100004 100005 100006\n"
] | [
"8\n",
"0\n",
"10000800015\n"
] | none | [
{
"input": "4\n2 4 4 2",
"output": "8"
},
{
"input": "4\n2 2 3 5",
"output": "0"
},
{
"input": "4\n100003 100004 100005 100006",
"output": "10000800015"
},
{
"input": "8\n5 3 3 3 3 4 4 4",
"output": "25"
},
{
"input": "10\n123 124 123 124 2 2 2 2 9 9",
"output... | 140 | 7,577,600 | 0 | 2,784 | |
75 | Modified GCD | [
"binary search",
"number theory"
] | C. Modified GCD | 2 | 256 | Well, here is another math class task. In mathematics, GCD is the greatest common divisor, and it's an easy task to calculate the GCD between two positive integers.
A common divisor for two positive numbers is a number which both numbers are divisible by.
But your teacher wants to give you a harder task, in this task you have to find the greatest common divisor *d* between two integers *a* and *b* that is in a given range from *low* to *high* (inclusive), i.e. *low*<=β€<=*d*<=β€<=*high*. It is possible that there is no common divisor in the given range.
You will be given the two integers *a* and *b*, then *n* queries. Each query is a range from *low* to *high* and you have to answer each query. | The first line contains two integers *a* and *b*, the two integers as described above (1<=β€<=*a*,<=*b*<=β€<=109). The second line contains one integer *n*, the number of queries (1<=β€<=*n*<=β€<=104). Then *n* lines follow, each line contains one query consisting of two integers, *low* and *high* (1<=β€<=*low*<=β€<=*high*<=β€<=109). | Print *n* lines. The *i*-th of them should contain the result of the *i*-th query in the input. If there is no common divisor in the given range for any query, you should print -1 as a result for this query. | [
"9 27\n3\n1 5\n10 11\n9 11\n"
] | [
"3\n-1\n9\n"
] | none | [
{
"input": "9 27\n3\n1 5\n10 11\n9 11",
"output": "3\n-1\n9"
},
{
"input": "48 72\n2\n8 29\n29 37",
"output": "24\n-1"
},
{
"input": "90 100\n10\n51 61\n6 72\n1 84\n33 63\n37 69\n18 21\n9 54\n49 90\n14 87\n37 90",
"output": "-1\n10\n10\n-1\n-1\n-1\n10\n-1\n-1\n-1"
},
{
"input... | 280 | 0 | 0 | 2,791 |
572 | Arrays | [
"sortings"
] | null | null | You are given two arrays *A* and *B* consisting of integers, sorted in non-decreasing order. Check whether it is possible to choose *k* numbers in array *A* and choose *m* numbers in array *B* so that any number chosen in the first array is strictly less than any number chosen in the second array. | The first line contains two integers *n**A*,<=*n**B* (1<=β€<=*n**A*,<=*n**B*<=β€<=105), separated by a space β the sizes of arrays *A* and *B*, correspondingly.
The second line contains two integers *k* and *m* (1<=β€<=*k*<=β€<=*n**A*,<=1<=β€<=*m*<=β€<=*n**B*), separated by a space.
The third line contains *n**A* numbers *a*1,<=*a*2,<=... *a**n**A* (<=-<=109<=β€<=*a*1<=β€<=*a*2<=β€<=...<=β€<=*a**n**A*<=β€<=109), separated by spaces β elements of array *A*.
The fourth line contains *n**B* integers *b*1,<=*b*2,<=... *b**n**B* (<=-<=109<=β€<=*b*1<=β€<=*b*2<=β€<=...<=β€<=*b**n**B*<=β€<=109), separated by spaces β elements of array *B*. | Print "YES" (without the quotes), if you can choose *k* numbers in array *A* and *m* numbers in array *B* so that any number chosen in array *A* was strictly less than any number chosen in array *B*. Otherwise, print "NO" (without the quotes). | [
"3 3\n2 1\n1 2 3\n3 4 5\n",
"3 3\n3 3\n1 2 3\n3 4 5\n",
"5 2\n3 1\n1 1 1 1 1\n2 2\n"
] | [
"YES\n",
"NO\n",
"YES\n"
] | In the first sample test you can, for example, choose numbers 1 and 2 from array *A* and number 3 from array *B* (1 < 3 and 2 < 3).
In the second sample test the only way to choose *k* elements in the first array and *m* elements in the second one is to choose all numbers in both arrays, but then not all the numbers chosen in *A* will be less than all the numbers chosen in *B*: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7280148ed5eab0a7d418d4f92b32061243a8ca58.png" style="max-width: 100.0%;max-height: 100.0%;"/>. | [
{
"input": "3 3\n2 1\n1 2 3\n3 4 5",
"output": "YES"
},
{
"input": "3 3\n3 3\n1 2 3\n3 4 5",
"output": "NO"
},
{
"input": "5 2\n3 1\n1 1 1 1 1\n2 2",
"output": "YES"
},
{
"input": "3 5\n1 1\n5 5 5\n5 5 5 5 5",
"output": "NO"
},
{
"input": "1 1\n1 1\n1\n1",
"ou... | 62 | 0 | 0 | 2,795 | |
804 | Minimum number of steps | [
"combinatorics",
"greedy",
"implementation",
"math"
] | null | null | We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109<=+<=7.
The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string. | The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106. | Print the minimum number of steps modulo 109<=+<=7. | [
"ab\n",
"aab\n"
] | [
"1\n",
"3\n"
] | The first example: "ab" βββ "bba".
The second example: "aab" βββ "abba" βββ "bbaba" βββ "bbbbaa". | [
{
"input": "ab",
"output": "1"
},
{
"input": "aab",
"output": "3"
},
{
"input": "aaaaabaabababaaaaaba",
"output": "17307"
},
{
"input": "abaabaaabbabaabab",
"output": "1795"
},
{
"input": "abbaa",
"output": "2"
},
{
"input": "abbaaabaabaaaaabbbbaababaa... | 30 | 0 | 0 | 2,796 | |
0 | none | [
"none"
] | null | null | There is a rectangular grid of *n* rows of *m* initially-white cells each.
Arkady performed a certain number (possibly zero) of operations on it. In the *i*-th operation, a non-empty subset of rows *R**i* and a non-empty subset of columns *C**i* are chosen. For each row *r* in *R**i* and each column *c* in *C**i*, the intersection of row *r* and column *c* is coloured black.
There's another constraint: a row or a column can only be chosen at most once among all operations. In other words, it means that no pair of (*i*,<=*j*) (*i*<=<<=*j*) exists such that or , where denotes intersection of sets, and denotes the empty set.
You are to determine whether a valid sequence of operations exists that produces a given final grid. | The first line contains two space-separated integers *n* and *m* (1<=β€<=*n*,<=*m*<=β€<=50)Β β the number of rows and columns of the grid, respectively.
Each of the following *n* lines contains a string of *m* characters, each being either '.' (denoting a white cell) or '#' (denoting a black cell), representing the desired setup. | If the given grid can be achieved by any valid sequence of operations, output "Yes"; otherwise output "No" (both without quotes).
You can print each character in any case (upper or lower). | [
"5 8\n.#.#..#.\n.....#..\n.#.#..#.\n#.#....#\n.....#..\n",
"5 5\n..#..\n..#..\n#####\n..#..\n..#..\n",
"5 9\n........#\n#........\n..##.#...\n.......#.\n....#.#.#\n"
] | [
"Yes\n",
"No\n",
"No\n"
] | For the first example, the desired setup can be produced by 3 operations, as is shown below.
For the second example, the desired setup cannot be produced, since in order to colour the center row, the third row and all columns must be selected in one operation, but after that no column can be selected again, hence it won't be possible to colour the other cells in the center column. | [
{
"input": "5 8\n.#.#..#.\n.....#..\n.#.#..#.\n#.#....#\n.....#..",
"output": "Yes"
},
{
"input": "5 5\n..#..\n..#..\n#####\n..#..\n..#..",
"output": "No"
},
{
"input": "5 9\n........#\n#........\n..##.#...\n.......#.\n....#.#.#",
"output": "No"
},
{
"input": "1 1\n#",
"o... | 46 | 0 | 0 | 2,801 | |
592 | The Monster and the Squirrel | [
"math"
] | null | null | Ari the monster always wakes up very early with the first ray of the sun and the first thing she does is feeding her squirrel.
Ari draws a regular convex polygon on the floor and numbers it's vertices 1,<=2,<=...,<=*n* in clockwise order. Then starting from the vertex 1 she draws a ray in the direction of each other vertex. The ray stops when it reaches a vertex or intersects with another ray drawn before. Ari repeats this process for vertex 2,<=3,<=...,<=*n* (in this particular order). And then she puts a walnut in each region inside the polygon.
Ada the squirrel wants to collect all the walnuts, but she is not allowed to step on the lines drawn by Ari. That means Ada have to perform a small jump if she wants to go from one region to another. Ada can jump from one region P to another region Q if and only if P and Q share a side or a corner.
Assuming that Ada starts from outside of the picture, what is the minimum number of jumps she has to perform in order to collect all the walnuts? | The first and only line of the input contains a single integer *n* (3<=β€<=*n*<=β€<=54321) - the number of vertices of the regular polygon drawn by Ari. | Print the minimum number of jumps Ada should make to collect all the walnuts. Note, that she doesn't need to leave the polygon after. | [
"5\n",
"3\n"
] | [
"9\n",
"1\n"
] | One of the possible solutions for the first sample is shown on the picture above. | [
{
"input": "5",
"output": "9"
},
{
"input": "3",
"output": "1"
},
{
"input": "54321",
"output": "2950553761"
},
{
"input": "4",
"output": "4"
},
{
"input": "6",
"output": "16"
},
{
"input": "7",
"output": "25"
},
{
"input": "8",
"output... | 77 | 1,228,800 | 3 | 2,805 | |
0 | none | [
"none"
] | null | null | Valery is very interested in magic. Magic attracts him so much that he sees it everywhere. He explains any strange and weird phenomenon through intervention of supernatural forces. But who would have thought that even in a regular array of numbers Valera manages to see something beautiful and magical.
Valera absolutely accidentally got a piece of ancient parchment on which an array of numbers was written. He immediately thought that the numbers in this array were not random. As a result of extensive research Valera worked out a wonderful property that a magical array should have: an array is defined as magic if its minimum and maximum coincide.
He decided to share this outstanding discovery with you, but he asks you for help in return. Despite the tremendous intelligence and wit, Valera counts very badly and so you will have to complete his work. All you have to do is count the number of magical subarrays of the original array of numbers, written on the parchment. Subarray is defined as non-empty sequence of consecutive elements. | The first line of the input data contains an integer *n* (1<=β€<=*n*<=β€<=105). The second line contains an array of original integers *a*1,<=*a*2,<=...,<=*a**n* (<=-<=109<=β€<=*a**i*<=β€<=109). | Print on the single line the answer to the problem: the amount of subarrays, which are magical.
Please do not use the %lld specificator to read or write 64-bit numbers in C++. It is recommended to use cin, cout streams (you can also use the %I64d specificator). | [
"4\n2 1 1 4\n",
"5\n-2 -2 -2 0 1\n"
] | [
"5\n",
"8\n"
] | Notes to sample tests:
Magical subarrays are shown with pairs of indices [a;b] of the beginning and the end.
In the first sample: [1;1], [2;2], [3;3], [4;4], [2;3].
In the second sample: [1;1], [2;2], [3;3], [4;4], [5;5], [1;2], [2;3], [1;3]. | [
{
"input": "4\n2 1 1 4",
"output": "5"
},
{
"input": "5\n-2 -2 -2 0 1",
"output": "8"
},
{
"input": "1\n10",
"output": "1"
},
{
"input": "2\n5 6",
"output": "2"
},
{
"input": "5\n5 5 4 5 5",
"output": "7"
},
{
"input": "8\n1 2 0 0 0 0 3 3",
"output... | 280 | 14,643,200 | 3 | 2,806 | |
0 | none | [
"none"
] | null | null | Stepan has the newest electronic device with a display. Different digits can be shown on it. Each digit is shown on a seven-section indicator like it is shown on the picture below.
So, for example, to show the digit 3 on the display, 5 sections must be highlighted; and for the digit 6, 6 sections must be highlighted.
The battery of the newest device allows to highlight at most *n* sections on the display.
Stepan wants to know the maximum possible integer number which can be shown on the display of his newest device. Your task is to determine this number. Note that this number must not contain leading zeros. Assume that the size of the display is enough to show any integer. | The first line contains the integer *n* (2<=β€<=*n*<=β€<=100<=000) β the maximum number of sections which can be highlighted on the display. | Print the maximum integer which can be shown on the display of Stepan's newest device. | [
"2\n",
"3\n"
] | [
"1\n",
"7\n"
] | none | [
{
"input": "2",
"output": "1"
},
{
"input": "3",
"output": "7"
},
{
"input": "4",
"output": "11"
},
{
"input": "5",
"output": "71"
},
{
"input": "6",
"output": "111"
},
{
"input": "85651",
"output": "711111111111111111111111111111111111111111111111... | 202 | 28,672,000 | 3 | 2,808 | |
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*<=Γ<=*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<=β€<=*n*<=β€<=3, 1<=β€<=*k*<=β€<=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 Β«.Β» stands for a white square, whereas Β«*Β» stands for a black one. It is guaranteed that the model has at least one white square. | Output a matrix *n**k*<=Γ<=*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.... | 154 | 307,200 | -1 | 2,810 |
675 | Tree Construction | [
"data structures",
"trees"
] | null | null | During the programming classes Vasya was assigned a difficult problem. However, he doesn't know how to code and was unable to find the solution in the Internet, so he asks you to help.
You are given a sequence $a$, consisting of $n$ distinct integers, that is used to construct the binary search tree. Below is the formal description of the construction process.
1. First element $a_1$ becomes the root of the tree. 1. Elements $a_2, a_3, \ldots, a_n$ are added one by one. To add element $a_i$ one needs to traverse the tree starting from the root and using the following rules: The pointer to the current node is set to the root. 1. If $a_i$ is greater than the value in the current node, then its right child becomes the current node. Otherwise, the left child of the current node becomes the new current node. 1. If at some point there is no required child, the new node is created, it is assigned value $a_i$ and becomes the corresponding child of the current node. | The first line of the input contains a single integer $n$ ($2 \leq n \leq 100\,000$)Β β the length of the sequence $a$.
The second line contains $n$ distinct integers $a_i$ ($1 \leq a_i \leq 10^9$)Β β the sequence $a$ itself. | Output $n - 1$ integers. For all $i > 1$ print the value written in the node that is the parent of the node with value $a_i$ in it. | [
"3\n1 2 3\n",
"5\n4 2 3 1 6\n"
] | [
"1 2\n",
"4 2 2 4\n"
] | none | [
{
"input": "3\n1 2 3",
"output": "1 2"
},
{
"input": "5\n4 2 3 1 6",
"output": "4 2 2 4"
},
{
"input": "2\n1 2",
"output": "1"
},
{
"input": "10\n991309218 517452607 870021923 978357992 136426010 10601767 302627526 883615372 163475700 600546765",
"output": "991309218 5174... | 280 | 7,884,800 | -1 | 2,821 | |
204 | Little Elephant and Cards | [
"binary search",
"data structures"
] | null | null | The Little Elephant loves to play with color cards.
He has *n* cards, each has exactly two colors (the color of the front side and the color of the back side). Initially, all the cards lay on the table with the front side up. In one move the Little Elephant can turn any card to the other side. The Little Elephant thinks that a set of cards on the table is funny if at least half of the cards have the same color (for each card the color of the upper side is considered).
Help the Little Elephant to find the minimum number of moves needed to make the set of *n* cards funny. | The first line contains a single integer *n* (1<=β€<=*n*<=β€<=105) β the number of the cards. The following *n* lines contain the description of all cards, one card per line. The cards are described by a pair of positive integers not exceeding 109 β colors of both sides. The first number in a line is the color of the front of the card, the second one β of the back. The color of the front of the card may coincide with the color of the back of the card.
The numbers in the lines are separated by single spaces. | On a single line print a single integer β the sought minimum number of moves. If it is impossible to make the set funny, print -1. | [
"3\n4 7\n4 7\n7 4\n",
"5\n4 7\n7 4\n2 11\n9 7\n1 1\n"
] | [
"0\n",
"2\n"
] | In the first sample there initially are three cards lying with colors 4, 4, 7. Since two of the three cards are of the same color 4, you do not need to change anything, so the answer is 0.
In the second sample, you can turn the first and the fourth cards. After that three of the five cards will be of color 7. | [
{
"input": "3\n4 7\n4 7\n7 4",
"output": "0"
},
{
"input": "5\n4 7\n7 4\n2 11\n9 7\n1 1",
"output": "2"
},
{
"input": "1\n1 1",
"output": "0"
},
{
"input": "2\n1 1\n1 1",
"output": "0"
},
{
"input": "7\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n7 8",
"output": "-1"
},
... | 124 | 614,400 | 0 | 2,825 | |
990 | Micro-World | [
"greedy",
"sortings"
] | null | null | You have a Petri dish with bacteria and you are preparing to dive into the harsh micro-world. But, unfortunately, you don't have any microscope nearby, so you can't watch them.
You know that you have $n$ bacteria in the Petri dish and size of the $i$-th bacteria is $a_i$. Also you know intergalactic positive integer constant $K$.
The $i$-th bacteria can swallow the $j$-th bacteria if and only if $a_i > a_j$ and $a_i \le a_j + K$. The $j$-th bacteria disappear, but the $i$-th bacteria doesn't change its size. The bacteria can perform multiple swallows. On each swallow operation any bacteria $i$ can swallow any bacteria $j$ if $a_i > a_j$ and $a_i \le a_j + K$. The swallow operations go one after another.
For example, the sequence of bacteria sizes $a=[101, 53, 42, 102, 101, 55, 54]$ and $K=1$. The one of possible sequences of swallows is: $[101, 53, 42, 102, \underline{101}, 55, 54]$ $\to$ $[101, \underline{53}, 42, 102, 55, 54]$ $\to$ $[\underline{101}, 42, 102, 55, 54]$ $\to$ $[42, 102, 55, \underline{54}]$ $\to$ $[42, 102, 55]$. In total there are $3$ bacteria remained in the Petri dish.
Since you don't have a microscope, you can only guess, what the minimal possible number of bacteria can remain in your Petri dish when you finally will find any microscope. | The first line contains two space separated positive integers $n$ and $K$ ($1 \le n \le 2 \cdot 10^5$, $1 \le K \le 10^6$) β number of bacteria and intergalactic constant $K$.
The second line contains $n$ space separated integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) β sizes of bacteria you have. | Print the only integer β minimal possible number of bacteria can remain. | [
"7 1\n101 53 42 102 101 55 54\n",
"6 5\n20 15 10 15 20 25\n",
"7 1000000\n1 1 1 1 1 1 1\n"
] | [
"3\n",
"1\n",
"7\n"
] | The first example is clarified in the problem statement.
In the second example an optimal possible sequence of swallows is: $[20, 15, 10, 15, \underline{20}, 25]$ $\to$ $[20, 15, 10, \underline{15}, 25]$ $\to$ $[20, 15, \underline{10}, 25]$ $\to$ $[20, \underline{15}, 25]$ $\to$ $[\underline{20}, 25]$ $\to$ $[25]$.
In the third example no bacteria can swallow any other bacteria. | [
{
"input": "7 1\n101 53 42 102 101 55 54",
"output": "3"
},
{
"input": "6 5\n20 15 10 15 20 25",
"output": "1"
},
{
"input": "7 1000000\n1 1 1 1 1 1 1",
"output": "7"
},
{
"input": "1 1\n1",
"output": "1"
},
{
"input": "1 4\n8",
"output": "1"
},
{
"inp... | 2,000 | 14,848,000 | 0 | 2,828 | |
471 | MUH and Sticks | [
"implementation"
] | null | null | Two polar bears Menshykov and Uslada from the St.Petersburg zoo and elephant Horace from the Kiev zoo got six sticks to play with and assess the animals' creativity. Menshykov, Uslada and Horace decided to make either an elephant or a bear from those sticks. They can make an animal from sticks in the following way:
- Four sticks represent the animal's legs, these sticks should have the same length. - Two remaining sticks represent the animal's head and body. The bear's head stick must be shorter than the body stick. The elephant, however, has a long trunk, so his head stick must be as long as the body stick. Note that there are no limits on the relations between the leg sticks and the head and body sticks.
Your task is to find out which animal can be made from the given stick set. The zoo keeper wants the sticks back after the game, so they must never be broken, even bears understand it. | The single line contains six space-separated integers *l**i* (1<=β€<=*l**i*<=β€<=9) β the lengths of the six sticks. It is guaranteed that the input is such that you cannot make both animals from the sticks. | If you can make a bear from the given set, print string "Bear" (without the quotes). If you can make an elephant, print string "Elephant" (wΔ±thout the quotes). If you can make neither a bear nor an elephant, print string "Alien" (without the quotes). | [
"4 2 5 4 4 4\n",
"4 4 5 4 4 5\n",
"1 2 3 4 5 6\n"
] | [
"Bear",
"Elephant",
"Alien"
] | If you're out of creative ideas, see instructions below which show how to make a bear and an elephant in the first two samples. The stick of length 2 is in red, the sticks of length 4 are in green, the sticks of length 5 are in blue. | [
{
"input": "4 2 5 4 4 4",
"output": "Bear"
},
{
"input": "4 4 5 4 4 5",
"output": "Elephant"
},
{
"input": "1 2 3 4 5 6",
"output": "Alien"
},
{
"input": "5 5 5 5 5 5",
"output": "Elephant"
},
{
"input": "1 1 1 2 3 5",
"output": "Alien"
},
{
"input": "... | 46 | 0 | 0 | 2,831 | |
292 | SMSC | [
"implementation"
] | null | null | Some large corporation where Polycarpus works has its own short message service center (SMSC). The center's task is to send all sorts of crucial information. Polycarpus decided to check the efficiency of the SMSC.
For that, he asked to give him the statistics of the performance of the SMSC for some period of time. In the end, Polycarpus got a list of *n* tasks that went to the SMSC of the corporation. Each task was described by the time it was received by the SMSC and the number of text messages to send. More formally, the *i*-th task was described by two integers *t**i* and *c**i* β the receiving time (the second) and the number of the text messages, correspondingly.
Polycarpus knows that the SMSC cannot send more than one text message per second. The SMSC uses a queue to organize its work. Consider a time moment *x*, the SMSC work at that moment as follows:
1. If at the time moment *x* the queue is not empty, then SMSC sends one message from the queue (SMSC gets the message from the head of the queue). Otherwise it doesn't send messages at the time moment *x*. 1. If at the time moment *x* SMSC receives a task, then it adds to the queue all the messages from this task (SMSC adds messages to the tail of the queue). Note, that the messages from the task cannot be send at time moment *x*. That's because the decision about sending message or not is made at point 1 before adding these messages to the queue.
Given the information about all *n* tasks, Polycarpus wants to count two values: the time when the last text message was sent and the maximum size of the queue at some time. Help him count these two characteristics he needs to evaluate the efficiency of the SMSC. | The first line contains a single integer *n* (1<=β€<=*n*<=β€<=103) β the number of tasks of the SMSC. Next *n* lines contain the tasks' descriptions: the *i*-th line contains two space-separated integers *t**i* and *c**i* (1<=β€<=*t**i*,<=*c**i*<=β€<=106) β the time (the second) when the *i*-th task was received and the number of messages to send, correspondingly.
It is guaranteed that all tasks were received at different moments of time. It is guaranteed that the tasks are sorted in the chronological order, that is, *t**i*<=<<=*t**i*<=+<=1 for all integer *i* (1<=β€<=*i*<=<<=*n*). | In a single line print two space-separated integers β the time when the last text message was sent and the maximum queue size at a certain moment of time. | [
"2\n1 1\n2 1\n",
"1\n1000000 10\n",
"3\n3 3\n4 3\n5 3\n"
] | [
"3 1\n",
"1000010 10\n",
"12 7\n"
] | In the first test sample:
- second 1: the first message has appeared in the queue, the queue's size is 1; - second 2: the first message is sent, the second message has been received, the queue's size is 1; - second 3: the second message is sent, the queue's size is 0,
Thus, the maximum size of the queue is 1, the last message was sent at the second 3. | [
{
"input": "2\n1 1\n2 1",
"output": "3 1"
},
{
"input": "1\n1000000 10",
"output": "1000010 10"
},
{
"input": "3\n3 3\n4 3\n5 3",
"output": "12 7"
},
{
"input": "1\n1 1",
"output": "2 1"
},
{
"input": "2\n1 11\n100 10",
"output": "110 11"
},
{
"input":... | 154 | 6,963,200 | 3 | 2,834 | |
65 | Harry Potter and Moving Staircases | [
"dfs and similar",
"implementation"
] | E. Harry Potter and Moving Staircases | 2 | 256 | Harry Potter lost his Invisibility Cloak, running from the school caretaker Filch. Finding an invisible object is not an easy task. Fortunately, Harry has friends who are willing to help. Hermione Granger had read "The Invisibility Cloaks, and Everything about Them", as well as six volumes of "The Encyclopedia of Quick Search of Shortest Paths in Graphs, Network Flows, the Maximal Increasing Subsequences and Other Magical Objects". She has already developed a search algorithm for the invisibility cloak in complex dynamic systems (Hogwarts is one of them).
Hogwarts consists of *n* floors, numbered by integers from 1 to *n*. Some pairs of floors are connected by staircases. The staircases may change its position, moving exactly one end. Formally the situation is like this: if a staircase connects the floors *a* and *b*, then in one move it may modify its position so as to connect the floors *a* and *c* or *b* and *c*, where *c* is any floor different from *a* and *b*. Under no circumstances the staircase can connect a floor with itself. At the same time there can be multiple stairs between a pair of floors.
Initially, Harry is on the floor with the number 1. He does not remember on what floor he has lost the cloak and wants to look for it on each of the floors. Therefore, his goal is to visit each of *n* floors at least once. Harry can visit the floors in any order and finish the searching at any floor.
Nowadays the staircases move quite rarely. However, Ron and Hermione are willing to put a spell on any of them to help Harry find the cloak. To cause less suspicion, the three friends plan to move the staircases one by one, and no more than once for each staircase. In between shifting the staircases Harry will be able to move about the floors, reachable at the moment from the staircases, and look for his Invisibility Cloak. It is assumed that during all this time the staircases will not move spontaneously.
Help the three friends to compose a searching plan. If there are several variants to solve the problem, any valid option (not necessarily the optimal one) will be accepted. | The first line contains integers *n* and *m* (1<=β€<=*n*<=β€<=100000, 0<=β€<=*m*<=β€<=200000), which are the number of floors and staircases in Hogwarts, respectively. The following *m* lines contain pairs of floors connected by staircases at the initial moment of time. | In the first line print "YES" (without the quotes) if Harry is able to search all the floors, and "NO" otherwise. If the answer is positive, then print on the second line the number of staircases that Ron and Hermione will have to shift. Further output should look like this:
Harry's moves
a staircase's move
Harry's moves
a staircase's move
...
a staircase's move
Harry's moves
Each "Harry's move" should be represented as a list of floors in the order in which they have been visited. The total amount of elements of these lists must not exceed 106. When you print each list, first print the number of elements in it, and then in the same line print the actual space-separated elements. The first number in the first list should be the number 1 (the floor, from which Harry begins to search). Any list except the first one might contain the zero number of elements. Note that Harry can visit some floors again, but must visit all *n* floors at least once. Two consecutively visited floors must be directly connected by a staircase (at the time Harry goes from one of them to the other one). No two floors that are visited consequtively can be equal.
In the description of a "staircase's move" indicate the number of staircase (the staircases are numbered from 1 to *m* in the order in which they are given in the input data) and its new location (two numbers of the connected floors in any order).
Any staircase can be moved at most once. If there are several solutions, output any. | [
"6 4\n1 2\n1 3\n2 3\n4 5\n",
"4 1\n1 2\n",
"5 5\n1 2\n1 3\n3 4\n3 5\n4 5\n"
] | [
"YES\n2\n3 1 2 3\n2 3 5\n3 5 4 5\n4 5 6\n3 6 5 3\n",
"NO\n",
"YES\n0\n6 1 2 1 3 4 5\n"
] | none | [] | 0 | 0 | -1 | 2,837 |
340 | Maximal Area Quadrilateral | [
"brute force",
"geometry"
] | null | null | Iahub has drawn a set of *n* points in the cartesian plane which he calls "special points". A quadrilateral is a simple polygon without self-intersections with four sides (also called edges) and four vertices (also called corners). Please note that a quadrilateral doesn't have to be convex. A special quadrilateral is one which has all four vertices in the set of special points. Given the set of special points, please calculate the maximal area of a special quadrilateral. | The first line contains integer *n* (4<=β€<=*n*<=β€<=300). Each of the next *n* lines contains two integers: *x**i*, *y**i* (<=-<=1000<=β€<=*x**i*,<=*y**i*<=β€<=1000) β the cartesian coordinates of *i*th special point. It is guaranteed that no three points are on the same line. It is guaranteed that no two points coincide. | Output a single real number β the maximal area of a special quadrilateral. The answer will be considered correct if its absolute or relative error does't exceed 10<=-<=9. | [
"5\n0 0\n0 4\n4 0\n4 4\n2 3\n"
] | [
"16.000000"
] | In the test example we can choose first 4 points to be the vertices of the quadrilateral. They form a square by side 4, so the area is 4Β·4β=β16. | [
{
"input": "5\n0 0\n0 4\n4 0\n4 4\n2 3",
"output": "16.000000"
},
{
"input": "10\n-6 -4\n-7 5\n-7 -7\n5 -7\n4 -9\n-6 7\n2 9\n-4 -6\n2 10\n-10 -4",
"output": "166.000000"
},
{
"input": "4\n-3 3\n0 3\n-2 -1\n2 2",
"output": "11.000000"
},
{
"input": "5\n-4 -3\n-3 -2\n3 3\n-1 2\... | 1,000 | 307,200 | 0 | 2,838 | |
5 | Center Alignment | [
"implementation",
"strings"
] | B. Center Alignment | 1 | 64 | Almost every text editor has a built-in function of center text alignment. The developers of the popular in Berland text editor Β«TextpadΒ» decided to introduce this functionality into the fourth release of the product.
You are to implement the alignment in the shortest possible time. Good luck! | The input file consists of one or more lines, each of the lines contains Latin letters, digits and/or spaces. The lines cannot start or end with a space. It is guaranteed that at least one of the lines has positive length. The length of each line and the total amount of the lines do not exceed 1000. | Format the given text, aligning it center. Frame the whole text with characters Β«*Β» of the minimum size. If a line cannot be aligned perfectly (for example, the line has even length, while the width of the block is uneven), you should place such lines rounding down the distance to the left or to the right edge and bringing them closer left or right alternatively (you should start with bringing left). Study the sample tests carefully to understand the output format better. | [
"This is\n\nCodeforces\nBeta\nRound\n5\n",
"welcome to the\nCodeforces\nBeta\nRound 5\n\nand\ngood luck\n"
] | [
"************\n* This is *\n* *\n*Codeforces*\n* Beta *\n* Round *\n* 5 *\n************\n",
"****************\n*welcome to the*\n* Codeforces *\n* Beta *\n* Round 5 *\n* *\n* and *\n* good luck *\n****************\n"
] | none | [
{
"input": "This is\n\nCodeforces\nBeta\nRound\n5",
"output": "************\n* This is *\n* *\n*Codeforces*\n* Beta *\n* Round *\n* 5 *\n************"
},
{
"input": "welcome to the\nCodeforces\nBeta\nRound 5\n\nand\ngood luck",
"output": "****************\n*welcome to th... | 92 | 0 | 0 | 2,839 |
476 | Dreamoon and WiFi | [
"bitmasks",
"brute force",
"combinatorics",
"dp",
"math",
"probabilities"
] | null | null | Dreamoon is standing at the position 0 on a number line. Drazil is sending a list of commands through Wi-Fi to Dreamoon's smartphone and Dreamoon follows them.
Each command is one of the following two types:
1. Go 1 unit towards the positive direction, denoted as '+' 1. Go 1 unit towards the negative direction, denoted as '-'
But the Wi-Fi condition is so poor that Dreamoon's smartphone reports some of the commands can't be recognized and Dreamoon knows that some of them might even be wrong though successfully recognized. Dreamoon decides to follow every recognized command and toss a fair coin to decide those unrecognized ones (that means, he moves to the 1 unit to the negative or positive direction with the same probability 0.5).
You are given an original list of commands sent by Drazil and list received by Dreamoon. What is the probability that Dreamoon ends in the position originally supposed to be final by Drazil's commands? | The first line contains a string *s*1 β the commands Drazil sends to Dreamoon, this string consists of only the characters in the set {'+', '-'}.
The second line contains a string *s*2 β the commands Dreamoon's smartphone recognizes, this string consists of only the characters in the set {'+', '-', '?'}. '?' denotes an unrecognized command.
Lengths of two strings are equal and do not exceed 10. | Output a single real number corresponding to the probability. The answer will be considered correct if its relative or absolute error doesn't exceed 10<=-<=9. | [
"++-+-\n+-+-+\n",
"+-+-\n+-??\n",
"+++\n??-\n"
] | [
"1.000000000000\n",
"0.500000000000\n",
"0.000000000000\n"
] | For the first sample, both *s*<sub class="lower-index">1</sub> and *s*<sub class="lower-index">2</sub> will lead Dreamoon to finish at the same position β+β1.
For the second sample, *s*<sub class="lower-index">1</sub> will lead Dreamoon to finish at position 0, while there are four possibilites for *s*<sub class="lower-index">2</sub>: {"+-++", "+-+-", "+--+", "+---"} with ending position {+2, 0, 0, -2} respectively. So there are 2 correct cases out of 4, so the probability of finishing at the correct position is 0.5.
For the third sample, *s*<sub class="lower-index">2</sub> could only lead us to finish at positions {+1, -1, -3}, so the probability to finish at the correct position β+β3 is 0. | [
{
"input": "++-+-\n+-+-+",
"output": "1.000000000000"
},
{
"input": "+-+-\n+-??",
"output": "0.500000000000"
},
{
"input": "+++\n??-",
"output": "0.000000000000"
},
{
"input": "++++++++++\n+++??++?++",
"output": "0.125000000000"
},
{
"input": "--+++---+-\n????????... | 218 | 9,420,800 | 0 | 2,844 | |
840 | In a Trap | [
"trees"
] | null | null | Lech got into a tree consisting of *n* vertices with a root in vertex number 1. At each vertex *i* written integer *a**i*. He will not get out until he answers *q* queries of the form *u* *v*. Answer for the query is maximal value among all vertices *i* on path from *u* to *v* including *u* and *v*, where *dist*(*i*,<=*v*) is number of edges on path from *i* to *v*. Also guaranteed that vertex *u* is ancestor of vertex *v*. Leha's tastes are very singular: he believes that vertex is ancestor of itself.
Help Leha to get out.
The expression means the bitwise exclusive OR to the numbers *x* and *y*.
Note that vertex *u* is ancestor of vertex *v* if vertex *u* lies on the path from root to the vertex *v*. | First line of input data contains two integers *n* and *q* (1<=β€<=*n*<=β€<=5Β·104, 1<=β€<=*q*<=β€<=150<=000) β number of vertices in the tree and number of queries respectively.
Next line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (0<=β€<=*a**i*<=β€<=*n*) β numbers on vertices.
Each of next *n*<=-<=1 lines contains two integers *u* and *v* (1<=β€<=*u*,<=*v*<=β€<=*n*) β description of the edges in tree.
Guaranteed that given graph is a tree.
Each of next *q* lines contains two integers *u* and *v* (1<=β€<=*u*,<=*v*<=β€<=*n*) β description of queries. Guaranteed that vertex *u* is ancestor of vertex *v*. | Output *q* lines β answers for a queries. | [
"5 3\n0 3 2 1 4\n1 2\n2 3\n3 4\n3 5\n1 4\n1 5\n2 4\n",
"5 4\n1 2 3 4 5\n1 2\n2 3\n3 4\n4 5\n1 5\n2 5\n1 4\n3 3\n"
] | [
"3\n4\n3\n",
"5\n5\n4\n3\n"
] | none | [] | 30 | 0 | 0 | 2,860 | |
915 | Garden | [
"implementation"
] | null | null | Luba thinks about watering her garden. The garden can be represented as a segment of length *k*. Luba has got *n* buckets, the *i*-th bucket allows her to water some continuous subsegment of garden of length exactly *a**i* each hour. Luba can't water any parts of the garden that were already watered, also she can't water the ground outside the garden.
Luba has to choose one of the buckets in order to water the garden as fast as possible (as mentioned above, each hour she will water some continuous subsegment of length *a**i* if she chooses the *i*-th bucket). Help her to determine the minimum number of hours she has to spend watering the garden. It is guaranteed that Luba can always choose a bucket so it is possible water the garden.
See the examples for better understanding. | The first line of input contains two integer numbers *n* and *k* (1<=β€<=*n*,<=*k*<=β€<=100) β the number of buckets and the length of the garden, respectively.
The second line of input contains *n* integer numbers *a**i* (1<=β€<=*a**i*<=β€<=100) β the length of the segment that can be watered by the *i*-th bucket in one hour.
It is guaranteed that there is at least one bucket such that it is possible to water the garden in integer number of hours using only this bucket. | Print one integer number β the minimum number of hours required to water the garden. | [
"3 6\n2 3 5\n",
"6 7\n1 2 3 4 5 6\n"
] | [
"2\n",
"7\n"
] | In the first test the best option is to choose the bucket that allows to water the segment of length 3. We can't choose the bucket that allows to water the segment of length 5 because then we can't water the whole garden.
In the second test we can choose only the bucket that allows us to water the segment of length 1. | [
{
"input": "3 6\n2 3 5",
"output": "2"
},
{
"input": "6 7\n1 2 3 4 5 6",
"output": "7"
},
{
"input": "5 97\n1 10 50 97 2",
"output": "1"
},
{
"input": "5 97\n1 10 50 100 2",
"output": "97"
},
{
"input": "100 100\n2 46 24 18 86 90 31 38 84 49 58 28 15 80 14 24 87 5... | 109 | 0 | 3 | 2,875 | |
818 | Multicolored Cars | [
"data structures",
"implementation"
] | null | null | Alice and Bob got very bored during a long car trip so they decided to play a game. From the window they can see cars of different colors running past them. Cars are going one after another.
The game rules are like this. Firstly Alice chooses some color *A*, then Bob chooses some color *B* (*A*<=β <=*B*). After each car they update the number of cars of their chosen color that have run past them. Let's define this numbers after *i*-th car *cnt**A*(*i*) and *cnt**B*(*i*).
- If *cnt**A*(*i*)<=><=*cnt**B*(*i*) for every *i* then the winner is Alice. - If *cnt**B*(*i*)<=β₯<=*cnt**A*(*i*) for every *i* then the winner is Bob. - Otherwise it's a draw.
Bob knows all the colors of cars that they will encounter and order of their appearance. Alice have already chosen her color *A* and Bob now wants to choose such color *B* that he will win the game (draw is not a win). Help him find this color.
If there are multiple solutions, print any of them. If there is no such color then print -1. | The first line contains two integer numbers *n* and *A* (1<=β€<=*n*<=β€<=105,<=1<=β€<=*A*<=β€<=106) β number of cars and the color chosen by Alice.
The second line contains *n* integer numbers *c*1,<=*c*2,<=...,<=*c**n* (1<=β€<=*c**i*<=β€<=106) β colors of the cars that Alice and Bob will encounter in the order of their appearance. | Output such color *B* (1<=β€<=*B*<=β€<=106) that if Bob chooses it then he will win the game. If there are multiple solutions, print any of them. If there is no such color then print -1.
It is guaranteed that if there exists any solution then there exists solution with (1<=β€<=*B*<=β€<=106). | [
"4 1\n2 1 4 2\n",
"5 2\n2 2 4 5 3\n",
"3 10\n1 2 3\n"
] | [
"2\n",
"-1\n",
"4\n"
] | Let's consider availability of colors in the first example:
- *cnt*<sub class="lower-index">2</sub>(*i*)ββ₯β*cnt*<sub class="lower-index">1</sub>(*i*) for every *i*, and color 2 can be the answer. - *cnt*<sub class="lower-index">4</sub>(2)β<β*cnt*<sub class="lower-index">1</sub>(2), so color 4 isn't the winning one for Bob. - All the other colors also have *cnt*<sub class="lower-index">*j*</sub>(2)β<β*cnt*<sub class="lower-index">1</sub>(2), thus they are not available.
In the third example every color is acceptable except for 10. | [
{
"input": "4 1\n2 1 4 2",
"output": "2"
},
{
"input": "5 2\n2 2 4 5 3",
"output": "-1"
},
{
"input": "3 10\n1 2 3",
"output": "4"
},
{
"input": "1 1\n2",
"output": "3"
},
{
"input": "1 2\n2",
"output": "-1"
},
{
"input": "10 6\n8 5 1 6 6 5 10 6 9 8",
... | 62 | 5,529,600 | 0 | 2,888 | |
869 | The Eternal Immortality | [
"math"
] | null | null | Even if the world is full of counterfeits, I still regard it as wonderful.
Pile up herbs and incense, and arise again from the flames and ashes of its predecessorΒ β as is known to many, the phoenix does it like this.
The phoenix has a rather long lifespan, and reincarnates itself once every *a*! years. Here *a*! denotes the factorial of integer *a*, that is, *a*!<==<=1<=Γ<=2<=Γ<=...<=Γ<=*a*. Specifically, 0!<==<=1.
Koyomi doesn't care much about this, but before he gets into another mess with oddities, he is interested in the number of times the phoenix will reincarnate in a timespan of *b*! years, that is, . Note that when *b*<=β₯<=*a* this value is always integer.
As the answer can be quite large, it would be enough for Koyomi just to know the last digit of the answer in decimal representation. And you're here to provide Koyomi with this knowledge. | The first and only line of input contains two space-separated integers *a* and *b* (0<=β€<=*a*<=β€<=*b*<=β€<=1018). | Output one line containing a single decimal digitΒ β the last digit of the value that interests Koyomi. | [
"2 4\n",
"0 10\n",
"107 109\n"
] | [
"2\n",
"0\n",
"2\n"
] | In the first example, the last digit of <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/99c47ca8b182f097e38094d12f0c06ce0b081b76.png" style="max-width: 100.0%;max-height: 100.0%;"/> is 2;
In the second example, the last digit of <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/9642ef11a23e7c5a3f3c2b1255c1b1b3533802a4.png" style="max-width: 100.0%;max-height: 100.0%;"/> is 0;
In the third example, the last digit of <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/844938cef52ee264c183246d2a9df05cca94dc60.png" style="max-width: 100.0%;max-height: 100.0%;"/> is 2. | [
{
"input": "2 4",
"output": "2"
},
{
"input": "0 10",
"output": "0"
},
{
"input": "107 109",
"output": "2"
},
{
"input": "10 13",
"output": "6"
},
{
"input": "998244355 998244359",
"output": "4"
},
{
"input": "999999999000000000 1000000000000000000",
... | 61 | 5,529,600 | 0 | 2,901 | |
914 | Substrings in a String | [
"bitmasks",
"brute force",
"data structures",
"string suffix structures",
"strings"
] | null | null | Given a string *s*, process *q* queries, each having one of the following forms:
- 1<=*i*<=*c* β Change the *i*-th character in the string to *c*. - 2<=*l*<=*r*<=*y* β Consider the substring of *s* starting at position *l* and ending at position *r*. Output the number of times *y* occurs as a substring in it. | The first line of the input contains the string *s* (1<=β€<=|*s*|<=β€<=105) of lowercase English letters.
The second line contains an integer *q* (1<=β€<=*q*<=β€<=105) Β β the number of queries to process.
The next *q* lines describe the queries and may have one of the following forms:
- 1<=*i*<=*c* (1<=β€<=*i*<=β€<=|*s*|) - 2<=*l*<=*r*<=*y* (1<=β€<=*l*<=β€<=*r*<=β€<=|*s*|)
*c* is a lowercase English letter and *y* is a non-empty string consisting of only lowercase English letters.
The sum of |*y*| over all queries of second type is at most 105.
It is guaranteed that there is at least one query of second type.
All strings are 1-indexed.
|*s*| is the length of the string *s*. | For each query of type 2, output the required answer in a separate line. | [
"ababababa\n3\n2 1 7 aba\n1 5 c\n2 1 7 aba\n",
"abcdcbc\n5\n2 1 7 bc\n1 4 b\n2 4 7 bc\n1 2 a\n2 1 4 aa\n"
] | [
"3\n1\n",
"2\n2\n1\n"
] | Consider the first sample case. Initially, the string aba occurs 3 times in the range [1,β7]. Note that two occurrences may overlap.
After the update, the string becomes ababcbaba and now aba occurs only once in the range [1,β7]. | [] | 30 | 0 | -1 | 2,905 | |
981 | Bookshelves | [
"bitmasks",
"dp",
"greedy"
] | null | null | Mr Keks is a typical white-collar in Byteland.
He has a bookshelf in his office with some books on it, each book has an integer positive price.
Mr Keks defines the value of a shelf as the sum of books prices on it.
Miraculously, Mr Keks was promoted and now he is moving into a new office.
He learned that in the new office he will have not a single bookshelf, but exactly $k$ bookshelves. He decided that the beauty of the $k$ shelves is the [bitwise AND](https://en.wikipedia.org/wiki/Bitwise_operation#AND) of the values of all the shelves.
He also decided that he won't spend time on reordering the books, so he will place several first books on the first shelf, several next books on the next shelf and so on. Of course, he will place at least one book on each shelf. This way he will put all his books on $k$ shelves in such a way that the beauty of the shelves is as large as possible. Compute this maximum possible beauty. | The first line contains two integers $n$ and $k$ ($1 \leq k \leq n \leq 50$)Β β the number of books and the number of shelves in the new office.
The second line contains $n$ integers $a_1, a_2, \ldots a_n$, ($0 < a_i < 2^{50}$)Β β the prices of the books in the order they stand on the old shelf. | Print the maximum possible beauty of $k$ shelves in the new office. | [
"10 4\n9 14 28 1 7 13 15 29 2 31\n",
"7 3\n3 14 15 92 65 35 89\n"
] | [
"24\n",
"64\n"
] | In the first example you can split the books as follows:
$$(9 + 14 + 28 + 1 + 7) \& (13 + 15) \& (29 + 2) \& (31) = 24.$$
In the second example you can split the books as follows:
$$(3 + 14 + 15 + 92) \& (65) \& (35 + 89) = 64.$$ | [
{
"input": "10 4\n9 14 28 1 7 13 15 29 2 31",
"output": "24"
},
{
"input": "7 3\n3 14 15 92 65 35 89",
"output": "64"
},
{
"input": "40 5\n6 18 24 5 14 16 31 9 15 5 25 2 18 12 19 27 10 23 23 18 22 14 1 14 6 14 17 28 11 21 8 23 10 30 21 5 17 11 26 16",
"output": "80"
},
{
"inp... | 639 | 9,420,800 | 3 | 2,912 | |
965 | Greedy Arkady | [
"math"
] | null | null | $k$ people want to split $n$ candies between them. Each candy should be given to exactly one of them or be thrown away.
The people are numbered from $1$ to $k$, and Arkady is the first of them. To split the candies, Arkady will choose an integer $x$ and then give the first $x$ candies to himself, the next $x$ candies to the second person, the next $x$ candies to the third person and so on in a cycle. The leftover (the remainder that is not divisible by $x$) will be thrown away.
Arkady can't choose $x$ greater than $M$ as it is considered greedy. Also, he can't choose such a small $x$ that some person will receive candies more than $D$ times, as it is considered a slow splitting.
Please find what is the maximum number of candies Arkady can receive by choosing some valid $x$. | The only line contains four integers $n$, $k$, $M$ and $D$ ($2 \le n \le 10^{18}$, $2 \le k \le n$, $1 \le M \le n$, $1 \le D \le \min{(n, 1000)}$, $M \cdot D \cdot k \ge n$)Β β the number of candies, the number of people, the maximum number of candies given to a person at once, the maximum number of times a person can receive candies. | Print a single integerΒ β the maximum possible number of candies Arkady can give to himself.
Note that it is always possible to choose some valid $x$. | [
"20 4 5 2\n",
"30 9 4 1\n"
] | [
"8\n",
"4\n"
] | In the first example Arkady should choose $x = 4$. He will give $4$ candies to himself, $4$ candies to the second person, $4$ candies to the third person, then $4$ candies to the fourth person and then again $4$ candies to himself. No person is given candies more than $2$ times, and Arkady receives $8$ candies in total.
Note that if Arkady chooses $x = 5$, he will receive only $5$ candies, and if he chooses $x = 3$, he will receive only $3 + 3 = 6$ candies as well as the second person, the third and the fourth persons will receive $3$ candies, and $2$ candies will be thrown away. He can't choose $x = 1$ nor $x = 2$ because in these cases he will receive candies more than $2$ times.
In the second example Arkady has to choose $x = 4$, because any smaller value leads to him receiving candies more than $1$ time. | [
{
"input": "20 4 5 2",
"output": "8"
},
{
"input": "30 9 4 1",
"output": "4"
},
{
"input": "2 2 1 1",
"output": "1"
},
{
"input": "42 20 5 29",
"output": "5"
},
{
"input": "1000000000000000000 135 1000000000000000 1000",
"output": "8325624421831635"
},
{
... | 124 | 0 | 0 | 2,914 | |
101 | Homework | [
"greedy"
] | A. Homework | 2 | 256 | Once when Gerald studied in the first year at school, his teacher gave the class the following homework. She offered the students a string consisting of *n* small Latin letters; the task was to learn the way the letters that the string contains are written. However, as Gerald is too lazy, he has no desire whatsoever to learn those letters. That's why he decided to lose some part of the string (not necessarily a connected part). The lost part can consist of any number of segments of any length, at any distance from each other. However, Gerald knows that if he loses more than *k* characters, it will be very suspicious.
Find the least number of distinct characters that can remain in the string after no more than *k* characters are deleted. You also have to find any possible way to delete the characters. | The first input data line contains a string whose length is equal to *n* (1<=β€<=*n*<=β€<=105). The string consists of lowercase Latin letters. The second line contains the number *k* (0<=β€<=*k*<=β€<=105). | Print on the first line the only number *m* β the least possible number of different characters that could remain in the given string after it loses no more than *k* characters.
Print on the second line the string that Gerald can get after some characters are lost. The string should have exactly *m* distinct characters. The final string should be the subsequence of the initial string. If Gerald can get several different strings with exactly *m* distinct characters, print any of them. | [
"aaaaa\n4\n",
"abacaba\n4\n",
"abcdefgh\n10\n"
] | [
"1\naaaaa\n",
"1\naaaa\n",
"0\n\n"
] | In the first sample the string consists of five identical letters but you are only allowed to delete 4 of them so that there was at least one letter left. Thus, the right answer is 1 and any string consisting of characters "a" from 1 to 5 in length.
In the second sample you are allowed to delete 4 characters. You cannot delete all the characters, because the string has length equal to 7. However, you can delete all characters apart from "a" (as they are no more than four), which will result in the "aaaa" string.
In the third sample you are given a line whose length is equal to 8, and *k*β=β10, so that the whole line can be deleted. The correct answer is 0 and an empty string. | [
{
"input": "aaaaa\n4",
"output": "1\naaaaa"
},
{
"input": "abacaba\n4",
"output": "1\naaaa"
},
{
"input": "abcdefgh\n10",
"output": "0"
},
{
"input": "aaaaaaaaaaaaaaaaaaaa\n19",
"output": "1\naaaaaaaaaaaaaaaaaaaa"
},
{
"input": "abcdefghijjihgedcba\n0",
"outpu... | 186 | 921,600 | 3.951783 | 2,928 |
1,009 | Game Shopping | [
"implementation"
] | null | null | Maxim wants to buy some games at the local game shop. There are $n$ games in the shop, the $i$-th game costs $c_i$.
Maxim has a wallet which can be represented as an array of integers. His wallet contains $m$ bills, the $j$-th bill has value $a_j$.
Games in the shop are ordered from left to right, Maxim tries to buy every game in that order.
When Maxim stands at the position $i$ in the shop, he takes the first bill from his wallet (if his wallet is empty then he proceeds to the next position immediately) and tries to buy the $i$-th game using this bill. After Maxim tried to buy the $n$-th game, he leaves the shop.
Maxim buys the $i$-th game if and only if the value of the first bill (which he takes) from his wallet is greater or equal to the cost of the $i$-th game. If he successfully buys the $i$-th game, the first bill from his wallet disappears and the next bill becomes first. Otherwise Maxim leaves the first bill in his wallet (this bill still remains the first one) and proceeds to the next game.
For example, for array $c = [2, 4, 5, 2, 4]$ and array $a = [5, 3, 4, 6]$ the following process takes place: Maxim buys the first game using the first bill (its value is $5$), the bill disappears, after that the second bill (with value $3$) becomes the first one in Maxim's wallet, then Maxim doesn't buy the second game because $c_2 > a_2$, the same with the third game, then he buys the fourth game using the bill of value $a_2$ (the third bill becomes the first one in Maxim's wallet) and buys the fifth game using the bill of value $a_3$.
Your task is to get the number of games Maxim will buy. | The first line of the input contains two integers $n$ and $m$ ($1 \le n, m \le 1000$) β the number of games and the number of bills in Maxim's wallet.
The second line of the input contains $n$ integers $c_1, c_2, \dots, c_n$ ($1 \le c_i \le 1000$), where $c_i$ is the cost of the $i$-th game.
The third line of the input contains $m$ integers $a_1, a_2, \dots, a_m$ ($1 \le a_j \le 1000$), where $a_j$ is the value of the $j$-th bill from the Maxim's wallet. | Print a single integer β the number of games Maxim will buy. | [
"5 4\n2 4 5 2 4\n5 3 4 6\n",
"5 2\n20 40 50 20 40\n19 20\n",
"6 4\n4 8 15 16 23 42\n1000 1000 1000 1000\n"
] | [
"3\n",
"0\n",
"4\n"
] | The first example is described in the problem statement.
In the second example Maxim cannot buy any game because the value of the first bill in his wallet is smaller than the cost of any game in the shop.
In the third example the values of the bills in Maxim's wallet are large enough to buy any game he encounter until he runs out of bills in his wallet. | [
{
"input": "5 4\n2 4 5 2 4\n5 3 4 6",
"output": "3"
},
{
"input": "5 2\n20 40 50 20 40\n19 20",
"output": "0"
},
{
"input": "6 4\n4 8 15 16 23 42\n1000 1000 1000 1000",
"output": "4"
},
{
"input": "5 1\n1 1 1 1 1\n5",
"output": "1"
},
{
"input": "5 1\n10 1 1 1 1\n... | 46 | 716,800 | 3 | 2,941 | |
828 | Restaurant Tables | [
"implementation"
] | null | null | In a small restaurant there are *a* tables for one person and *b* tables for two persons.
It it known that *n* groups of people come today, each consisting of one or two people.
If a group consist of one person, it is seated at a vacant one-seater table. If there are none of them, it is seated at a vacant two-seater table. If there are none of them, it is seated at a two-seater table occupied by single person. If there are still none of them, the restaurant denies service to this group.
If a group consist of two people, it is seated at a vacant two-seater table. If there are none of them, the restaurant denies service to this group.
You are given a chronological order of groups coming. You are to determine the total number of people the restaurant denies service to. | The first line contains three integers *n*, *a* and *b* (1<=β€<=*n*<=β€<=2Β·105, 1<=β€<=*a*,<=*b*<=β€<=2Β·105) β the number of groups coming to the restaurant, the number of one-seater and the number of two-seater tables.
The second line contains a sequence of integers *t*1,<=*t*2,<=...,<=*t**n* (1<=β€<=*t**i*<=β€<=2) β the description of clients in chronological order. If *t**i* is equal to one, then the *i*-th group consists of one person, otherwise the *i*-th group consists of two people. | Print the total number of people the restaurant denies service to. | [
"4 1 2\n1 2 1 1\n",
"4 1 1\n1 1 2 1\n"
] | [
"0\n",
"2\n"
] | In the first example the first group consists of one person, it is seated at a vacant one-seater table. The next group occupies a whole two-seater table. The third group consists of one person, it occupies one place at the remaining two-seater table. The fourth group consists of one person, he is seated at the remaining seat at the two-seater table. Thus, all clients are served.
In the second example the first group consists of one person, it is seated at the vacant one-seater table. The next group consists of one person, it occupies one place at the two-seater table. It's impossible to seat the next group of two people, so the restaurant denies service to them. The fourth group consists of one person, he is seated at the remaining seat at the two-seater table. Thus, the restaurant denies service to 2 clients. | [
{
"input": "4 1 2\n1 2 1 1",
"output": "0"
},
{
"input": "4 1 1\n1 1 2 1",
"output": "2"
},
{
"input": "1 1 1\n1",
"output": "0"
},
{
"input": "2 1 2\n2 2",
"output": "0"
},
{
"input": "5 1 3\n1 2 2 2 1",
"output": "1"
},
{
"input": "7 6 1\n1 1 1 1 1 1... | 218 | 3,481,600 | 0 | 2,943 | |
888 | Local Extrema | [
"brute force",
"implementation"
] | null | null | You are given an array *a*. Some element of this array *a**i* is a local minimum iff it is strictly less than both of its neighbours (that is, *a**i*<=<<=*a**i*<=-<=1 and *a**i*<=<<=*a**i*<=+<=1). Also the element can be called local maximum iff it is strictly greater than its neighbours (that is, *a**i*<=><=*a**i*<=-<=1 and *a**i*<=><=*a**i*<=+<=1). Since *a*1 and *a**n* have only one neighbour each, they are neither local minima nor local maxima.
An element is called a local extremum iff it is either local maximum or local minimum. Your task is to calculate the number of local extrema in the given array. | The first line contains one integer *n* (1<=β€<=*n*<=β€<=1000) β the number of elements in array *a*.
The second line contains *n* integers *a*1, *a*2, ..., *a**n* (1<=β€<=*a**i*<=β€<=1000) β the elements of array *a*. | Print the number of local extrema in the given array. | [
"3\n1 2 3\n",
"4\n1 5 2 5\n"
] | [
"0\n",
"2\n"
] | none | [
{
"input": "3\n1 2 3",
"output": "0"
},
{
"input": "4\n1 5 2 5",
"output": "2"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "1\n548",
"output": "0"
},
{
"input": "2\n1 1",
"output": "0"
},
{
"input": "3\n3 2 3",
"output": "1"
},
{
"inp... | 61 | 6,963,200 | 3 | 2,966 | |
120 | Winnie-the-Pooh and honey | [
"implementation",
"math"
] | null | null | As we all know, Winnie-the-Pooh just adores honey. Ones he and the Piglet found out that the Rabbit has recently gotten hold of an impressive amount of this sweet and healthy snack. As you may guess, Winnie and the Piglet asked to come at the Rabbit's place. Thus, there are *n* jars of honey lined up in front of Winnie-the-Pooh, jar number *i* contains *a**i* kilos of honey. Winnie-the-Pooh eats the honey like that: each time he chooses a jar containing most honey. If the jar has less that *k* kilos of honey or if Winnie-the-Pooh has already eaten from it three times, he gives the jar to Piglet. Otherwise he eats exactly *k* kilos of honey from the jar and puts it back. Winnie does so until he gives all jars to the Piglet. Count how much honey Piglet will overall get after Winnie satisfies his hunger. | The first line contains two integers *n* and *k* (1<=β€<=*n*<=β€<=100,<=1<=β€<=*k*<=β€<=100). The second line contains *n* integers *a*1, *a*2, ..., *a**n*, separated by spaces (1<=β€<=*a**i*<=β€<=100). | Print a single number β how many kilos of honey gets Piglet. | [
"3 3\n15 8 10\n"
] | [
"9\n"
] | none | [
{
"input": "3 3\n15 8 10",
"output": "9"
},
{
"input": "1 3\n3",
"output": "0"
},
{
"input": "3 4\n3 8 2",
"output": "5"
},
{
"input": "3 2\n95 25 49",
"output": "151"
},
{
"input": "3 1\n8 3 2",
"output": "5"
},
{
"input": "5 1\n4 7 9 5 7",
"outpu... | 186 | 0 | -1 | 2,968 | |
805 | Fake NP | [
"greedy",
"math"
] | null | null | Tavak and Seyyed are good friends. Seyyed is very funny and he told Tavak to solve the following problem instead of longest-path.
You are given *l* and *r*. For all integers from *l* to *r*, inclusive, we wrote down all of their integer divisors except 1. Find the integer that we wrote down the maximum number of times.
Solve the problem to show that it's not a NP problem. | The first line contains two integers *l* and *r* (2<=β€<=*l*<=β€<=*r*<=β€<=109). | Print single integer, the integer that appears maximum number of times in the divisors.
If there are multiple answers, print any of them. | [
"19 29\n",
"3 6\n"
] | [
"2\n",
"3\n"
] | Definition of a divisor: [https://www.mathsisfun.com/definitions/divisor-of-an-integer-.html](https://www.mathsisfun.com/definitions/divisor-of-an-integer-.html)
The first example: from 19 to 29 these numbers are divisible by 2: {20,β22,β24,β26,β28}.
The second example: from 3 to 6 these numbers are divisible by 3: {3,β6}. | [
{
"input": "19 29",
"output": "2"
},
{
"input": "3 6",
"output": "2"
},
{
"input": "39 91",
"output": "2"
},
{
"input": "76 134",
"output": "2"
},
{
"input": "93 95",
"output": "2"
},
{
"input": "17 35",
"output": "2"
},
{
"input": "94 95",... | 109 | 0 | 3 | 2,976 | |
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<=β€<=*n*,<=*d*,<=*m*,<=*l*<=β€<=106,<=*l*<=<<=*m*) β 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"... | 528 | 20,889,600 | 3.71236 | 2,987 |
994 | Fingerprints | [
"implementation"
] | null | null | You are locked in a room with a door that has a keypad with 10 keys corresponding to digits from 0 to 9. To escape from the room, you need to enter a correct code. You also have a sequence of digits.
Some keys on the keypad have fingerprints. You believe the correct code is the longest not necessarily contiguous subsequence of the sequence you have that only contains digits with fingerprints on the corresponding keys. Find such code. | The first line contains two integers $n$ and $m$ ($1 \le n, m \le 10$) representing the number of digits in the sequence you have and the number of keys on the keypad that have fingerprints.
The next line contains $n$ distinct space-separated integers $x_1, x_2, \ldots, x_n$ ($0 \le x_i \le 9$) representing the sequence.
The next line contains $m$ distinct space-separated integers $y_1, y_2, \ldots, y_m$ ($0 \le y_i \le 9$) β the keys with fingerprints. | In a single line print a space-separated sequence of integers representing the code. If the resulting sequence is empty, both printing nothing and printing a single line break is acceptable. | [
"7 3\n3 5 7 1 6 2 8\n1 2 7\n",
"4 4\n3 4 1 0\n0 1 7 9\n"
] | [
"7 1 2\n",
"1 0\n"
] | In the first example, the only digits with fingerprints are $1$, $2$ and $7$. All three of them appear in the sequence you know, $7$ first, then $1$ and then $2$. Therefore the output is 7 1 2. Note that the order is important, and shall be the same as the order in the original sequence.
In the second example digits $0$, $1$, $7$ and $9$ have fingerprints, however only $0$ and $1$ appear in the original sequence. $1$ appears earlier, so the output is 1 0. Again, the order is important. | [
{
"input": "7 3\n3 5 7 1 6 2 8\n1 2 7",
"output": "7 1 2"
},
{
"input": "4 4\n3 4 1 0\n0 1 7 9",
"output": "1 0"
},
{
"input": "9 4\n9 8 7 6 5 4 3 2 1\n2 4 6 8",
"output": "8 6 4 2"
},
{
"input": "10 5\n3 7 1 2 4 6 9 0 5 8\n4 3 0 7 9",
"output": "3 7 4 9 0"
},
{
"... | 109 | 0 | 3 | 2,990 | |
44 | Anfisa the Monkey | [
"dp"
] | E. Anfisa the Monkey | 2 | 256 | Anfisa the monkey learns to type. She is yet unfamiliar with the "space" key and can only type in lower-case Latin letters. Having typed for a fairly long line, Anfisa understood that it would be great to divide what she has written into *k* lines not shorter than *a* and not longer than *b*, for the text to resemble human speech more. Help Anfisa. | The first line contains three integers *k*, *a* and *b* (1<=β€<=*k*<=β€<=200, 1<=β€<=*a*<=β€<=*b*<=β€<=200). The second line contains a sequence of lowercase Latin letters β the text typed by Anfisa. It is guaranteed that the given line is not empty and its length does not exceed 200 symbols. | Print *k* lines, each of which contains no less than *a* and no more than *b* symbols β Anfisa's text divided into lines. It is not allowed to perform any changes in the text, such as: deleting or adding symbols, changing their order, etc. If the solution is not unique, print any of them. If there is no solution, print "No solution" (without quotes). | [
"3 2 5\nabrakadabra\n",
"4 1 2\nabrakadabra\n"
] | [
"ab\nrakad\nabra\n",
"No solution\n"
] | none | [
{
"input": "3 2 5\nabrakadabra",
"output": "abra\nkada\nbra"
},
{
"input": "4 1 2\nabrakadabra",
"output": "No solution"
},
{
"input": "3 1 2\nvgnfpo",
"output": "vg\nnf\npo"
},
{
"input": "5 3 4\nvrrdnhazvexzjfv",
"output": "vrr\ndnh\nazv\nexz\njfv"
},
{
"input":... | 592 | 0 | 0 | 2,994 |
616 | Comparing Two Long Integers | [
"implementation",
"strings"
] | null | null | You are given two very long integers *a*,<=*b* (leading zeroes are allowed). You should check what number *a* or *b* is greater or determine that they are equal.
The input size is very large so don't use the reading of symbols one by one. Instead of that use the reading of a whole line or token.
As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use scanf/printf instead of cin/cout in C++, prefer to use BufferedReader/PrintWriter instead of Scanner/System.out in Java. Don't use the function input() in Python2 instead of it use the function raw_input(). | The first line contains a non-negative integer *a*.
The second line contains a non-negative integer *b*.
The numbers *a*,<=*b* may contain leading zeroes. Each of them contains no more than 106 digits. | Print the symbol "<" if *a*<=<<=*b* and the symbol ">" if *a*<=><=*b*. If the numbers are equal print the symbol "=". | [
"9\n10\n",
"11\n10\n",
"00012345\n12345\n",
"0123\n9\n",
"0123\n111\n"
] | [
"<\n",
">\n",
"=\n",
">\n",
">\n"
] | none | [
{
"input": "9\n10",
"output": "<"
},
{
"input": "11\n10",
"output": ">"
},
{
"input": "00012345\n12345",
"output": "="
},
{
"input": "0123\n9",
"output": ">"
},
{
"input": "0123\n111",
"output": ">"
},
{
"input": "9\n9",
"output": "="
},
{
... | 2,000 | 2,867,200 | 0 | 3,006 | |
883 | Quadcopter Competition | [
"greedy",
"math"
] | null | null | Polycarp takes part in a quadcopter competition. According to the rules a flying robot should:
- start the race from some point of a field, - go around the flag, - close cycle returning back to the starting point.
Polycarp knows the coordinates of the starting point (*x*1,<=*y*1) and the coordinates of the point where the flag is situated (*x*2,<=*y*2). Polycarpβs quadcopter can fly only parallel to the sides of the field each tick changing exactly one coordinate by 1. It means that in one tick the quadcopter can fly from the point (*x*,<=*y*) to any of four points: (*x*<=-<=1,<=*y*), (*x*<=+<=1,<=*y*), (*x*,<=*y*<=-<=1) or (*x*,<=*y*<=+<=1).
Thus the quadcopter path is a closed cycle starting and finishing in (*x*1,<=*y*1) and containing the point (*x*2,<=*y*2) strictly inside.
What is the minimal length of the quadcopter path? | The first line contains two integer numbers *x*1 and *y*1 (<=-<=100<=β€<=*x*1,<=*y*1<=β€<=100) β coordinates of the quadcopter starting (and finishing) point.
The second line contains two integer numbers *x*2 and *y*2 (<=-<=100<=β€<=*x*2,<=*y*2<=β€<=100) β coordinates of the flag.
It is guaranteed that the quadcopter starting point and the flag do not coincide. | Print the length of minimal path of the quadcopter to surround the flag and return back. | [
"1 5\n5 2\n",
"0 1\n0 0\n"
] | [
"18\n",
"8\n"
] | none | [
{
"input": "1 5\n5 2",
"output": "18"
},
{
"input": "0 1\n0 0",
"output": "8"
},
{
"input": "-100 -100\n100 100",
"output": "804"
},
{
"input": "-100 -100\n-100 100",
"output": "406"
},
{
"input": "-100 -100\n100 -100",
"output": "406"
},
{
"input": "1... | 77 | 0 | 3 | 3,007 | |
408 | Garland | [
"implementation"
] | null | null | Once little Vasya read an article in a magazine on how to make beautiful handmade garland from colored paper. Vasya immediately went to the store and bought *n* colored sheets of paper, the area of each sheet is 1 square meter.
The garland must consist of exactly *m* pieces of colored paper of arbitrary area, each piece should be of a certain color. To make the garland, Vasya can arbitrarily cut his existing colored sheets into pieces. Vasya is not obliged to use all the sheets to make the garland.
Vasya wants the garland to be as attractive as possible, so he wants to maximize the total area of ββ*m* pieces of paper in the garland. Calculate what the maximum total area of ββthe pieces of paper in the garland Vasya can get. | The first line contains a non-empty sequence of *n* (1<=β€<=*n*<=β€<=1000) small English letters ("a"..."z"). Each letter means that Vasya has a sheet of paper of the corresponding color.
The second line contains a non-empty sequence of *m* (1<=β€<=*m*<=β€<=1000) small English letters that correspond to the colors of the pieces of paper in the garland that Vasya wants to make. | Print an integer that is the maximum possible total area of the pieces of paper in the garland Vasya wants to get or -1, if it is impossible to make the garland from the sheets he's got. It is guaranteed that the answer is always an integer. | [
"aaabbac\naabbccac\n",
"a\nz\n"
] | [
"6\n",
"-1"
] | In the first test sample Vasya can make an garland of area 6: he can use both sheets of color *b*, three (but not four) sheets of color *a* and cut a single sheet of color *c* in three, for example, equal pieces. Vasya can use the resulting pieces to make a garland of area 6.
In the second test sample Vasya cannot make a garland at all β he doesn't have a sheet of color *z*. | [
{
"input": "aaabbac\naabbccac",
"output": "6"
},
{
"input": "a\nz",
"output": "-1"
},
{
"input": "r\nr",
"output": "1"
},
{
"input": "stnsdn\nndnndsn",
"output": "4"
},
{
"input": "yqfqfp\ntttwtqq",
"output": "-1"
},
{
"input": "zzbbrrtrtzr\ntbbtrrrzr"... | 46 | 0 | 0 | 3,016 | |
547 | Mike and Fish | [
"constructive algorithms",
"dfs and similar",
"graphs"
] | null | null | As everyone knows, bears love fish. But Mike is a strange bear; He hates fish! The even more strange thing about him is he has an infinite number of blue and red fish.
He has marked *n* distinct points in the plane. *i*-th point is point (*x**i*,<=*y**i*). He wants to put exactly one fish in each of these points such that the difference between the number of red fish and the blue fish on each horizontal or vertical line is at most 1.
He can't find a way to perform that! Please help him. | The first line of input contains integer *n* (1<=β€<=*n*<=β€<=2<=Γ<=105).
The next *n* lines contain the information about the points, *i*-th line contains two integers *x**i* and *y**i* (1<=β€<=*x**i*,<=*y**i*<=β€<=2<=Γ<=105), the *i*-th point coordinates.
It is guaranteed that there is at least one valid answer. | Print the answer as a sequence of *n* characters 'r' (for red) or 'b' (for blue) where *i*-th character denotes the color of the fish in the *i*-th point. | [
"4\n1 1\n1 2\n2 1\n2 2\n",
"3\n1 1\n1 2\n2 1\n"
] | [
"brrb\n",
"brr\n"
] | none | [
{
"input": "4\n1 1\n1 2\n2 1\n2 2",
"output": "brrb"
},
{
"input": "3\n1 1\n1 2\n2 1",
"output": "brr"
},
{
"input": "3\n157210 22861\n175396 39466\n40933 17093",
"output": "rrr"
},
{
"input": "5\n55599 84144\n169207 98421\n1909 186625\n31525 147710\n7781 82078",
"output"... | 0 | 0 | -1 | 3,019 | |
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<=β€<=*n*<=β€<=106). The second line contains *n* integers *x*1,<=*x*2,<=...,<=*x**n* (2<=β€<=*x**i*<=β€<=107). The numbers are not necessarily distinct.
The third line contains integer *m* (1<=β€<=*m*<=β€<=50000). Each of the following *m* lines contains a pair of space-separated integers, *l**i* and *r**i* (2<=β€<=*l**i*<=β€<=*r**i*<=β€<=2Β·109) β the numbers that characterize the current query. | Print *m* integers β 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*β=β2, *r*β=β11 comes. You need to count *f*(2)β+β*f*(3)β+β*f*(5)β+β*f*(7)β+β*f*(11)β=β2β+β1β+β4β+β2β+β0β=β9. 1. The second query comes *l*β=β3, *r*β=β12. You need to count *f*(3)β+β*f*(5)β+β*f*(7)β+β*f*(11)β=β1β+β4β+β2β+β0β=β7. 1. The third query comes *l*β=β4, *r*β=β4. 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"
},
{
"... | 1,700 | 264,396,800 | 0 | 3,024 | |
554 | Ohana Cleans Up | [
"brute force",
"greedy",
"strings"
] | null | null | Ohana Matsumae is trying to clean a room, which is divided up into an *n* by *n* grid of squares. Each square is initially either clean or dirty. Ohana can sweep her broom over columns of the grid. Her broom is very strange: if she sweeps over a clean square, it will become dirty, and if she sweeps over a dirty square, it will become clean. She wants to sweep some columns of the room to maximize the number of rows that are completely clean. It is not allowed to sweep over the part of the column, Ohana can only sweep the whole column.
Return the maximum number of rows that she can make completely clean. | The first line of input will be a single integer *n* (1<=β€<=*n*<=β€<=100).
The next *n* lines will describe the state of the room. The *i*-th line will contain a binary string with *n* characters denoting the state of the *i*-th row of the room. The *j*-th character on this line is '1' if the *j*-th square in the *i*-th row is clean, and '0' if it is dirty. | The output should be a single line containing an integer equal to a maximum possible number of rows that are completely clean. | [
"4\n0101\n1000\n1111\n0101\n",
"3\n111\n111\n111\n"
] | [
"2\n",
"3\n"
] | In the first sample, Ohana can sweep the 1st and 3rd columns. This will make the 1st and 4th row be completely clean.
In the second sample, everything is already clean, so Ohana doesn't need to do anything. | [
{
"input": "4\n0101\n1000\n1111\n0101",
"output": "2"
},
{
"input": "3\n111\n111\n111",
"output": "3"
},
{
"input": "10\n0100000000\n0000000000\n0000000000\n0000000000\n0000000000\n0000000000\n0000000000\n0000000000\n0000000000\n0000000000",
"output": "9"
},
{
"input": "1\n1"... | 46 | 0 | 3 | 3,029 | |
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<=β€<=*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<=β€<=*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 | 3,046 | |
913 | Too Easy Problems | [
"binary search",
"brute force",
"data structures",
"greedy",
"sortings"
] | null | null | You are preparing for an exam on scheduling theory. The exam will last for exactly *T* milliseconds and will consist of *n* problems. You can either solve problem *i* in exactly *t**i* milliseconds or ignore it and spend no time. You don't need time to rest after solving a problem, either.
Unfortunately, your teacher considers some of the problems too easy for you. Thus, he assigned an integer *a**i* to every problem *i* meaning that the problem *i* can bring you a point to the final score only in case you have solved no more than *a**i* problems overall (including problem *i*).
Formally, suppose you solve problems *p*1,<=*p*2,<=...,<=*p**k* during the exam. Then, your final score *s* will be equal to the number of values of *j* between 1 and *k* such that *k*<=β€<=*a**p**j*.
You have guessed that the real first problem of the exam is already in front of you. Therefore, you want to choose a set of problems to solve during the exam maximizing your final score in advance. Don't forget that the exam is limited in time, and you must have enough time to solve all chosen problems. If there exist different sets of problems leading to the maximum final score, any of them will do. | The first line contains two integers *n* and *T* (1<=β€<=*n*<=β€<=2Β·105; 1<=β€<=*T*<=β€<=109)Β β the number of problems in the exam and the length of the exam in milliseconds, respectively.
Each of the next *n* lines contains two integers *a**i* and *t**i* (1<=β€<=*a**i*<=β€<=*n*; 1<=β€<=*t**i*<=β€<=104). The problems are numbered from 1 to *n*. | In the first line, output a single integer *s*Β β your maximum possible final score.
In the second line, output a single integer *k* (0<=β€<=*k*<=β€<=*n*)Β β the number of problems you should solve.
In the third line, output *k* distinct integers *p*1,<=*p*2,<=...,<=*p**k* (1<=β€<=*p**i*<=β€<=*n*)Β β the indexes of problems you should solve, in any order.
If there are several optimal sets of problems, you may output any of them. | [
"5 300\n3 100\n4 150\n4 80\n2 90\n2 300\n",
"2 100\n1 787\n2 788\n",
"2 100\n2 42\n2 58\n"
] | [
"2\n3\n3 1 4\n",
"0\n0\n\n",
"2\n2\n1 2\n"
] | In the first example, you should solve problems 3, 1, and 4. In this case you'll spend 80β+β100β+β90β=β270 milliseconds, falling within the length of the exam, 300 milliseconds (and even leaving yourself 30 milliseconds to have a rest). Problems 3 and 1 will bring you a point each, while problem 4 won't. You'll score two points.
In the second example, the length of the exam is catastrophically not enough to solve even a single problem.
In the third example, you have just enough time to solve both problems in 42β+β58β=β100 milliseconds and hand your solutions to the teacher with a smile. | [
{
"input": "5 300\n3 100\n4 150\n4 80\n2 90\n2 300",
"output": "2\n2\n3 4"
},
{
"input": "2 100\n1 787\n2 788",
"output": "0\n0"
},
{
"input": "2 100\n2 42\n2 58",
"output": "2\n2\n1 2"
},
{
"input": "1 1\n1 1",
"output": "1\n1\n1"
},
{
"input": "10 481\n4 25\n3 8... | 2,000 | 24,678,400 | 0 | 3,060 | |
336 | Vasily the Bear and Fly | [
"math"
] | null | null | One beautiful day Vasily the bear painted 2*m* circles of the same radius *R* on a coordinate plane. Circles with numbers from 1 to *m* had centers at points (2*R*<=-<=*R*,<=0), (4*R*<=-<=*R*,<=0), ..., (2*Rm*<=-<=*R*,<=0), respectively. Circles with numbers from *m*<=+<=1 to 2*m* had centers at points (2*R*<=-<=*R*,<=2*R*), (4*R*<=-<=*R*,<=2*R*), ..., (2*Rm*<=-<=*R*,<=2*R*), respectively.
Naturally, the bear painted the circles for a simple experiment with a fly. The experiment continued for *m*2 days. Each day of the experiment got its own unique number from 0 to *m*2<=-<=1, inclusive.
On the day number *i* the following things happened:
1. The fly arrived at the coordinate plane at the center of the circle with number ( is the result of dividing number *x* by number *y*, rounded down to an integer). 1. The fly went along the coordinate plane to the center of the circle number ( is the remainder after dividing number *x* by number *y*). The bear noticed that the fly went from the center of circle *v* to the center of circle *u* along the shortest path with all points lying on the border or inside at least one of the 2*m* circles. After the fly reached the center of circle *u*, it flew away in an unknown direction.
Help Vasily, count the average distance the fly went along the coordinate plane during each of these *m*2 days. | The first line contains two integers *m*,<=*R* (1<=β€<=*m*<=β€<=105, 1<=β€<=*R*<=β€<=10). | In a single line print a single real number β the answer to the problem. The answer will be considered correct if its absolute or relative error doesn't exceed 10<=-<=6. | [
"1 1\n",
"2 2\n"
] | [
"2.0000000000\n",
"5.4142135624\n"
] | <img class="tex-graphics" src="https://espresso.codeforces.com/9fe384073741e20965ddc4bf162afd3a604b6b39.png" style="max-width: 100.0%;max-height: 100.0%;"/>
Figure to the second sample | [
{
"input": "1 1",
"output": "2.0000000000"
},
{
"input": "2 2",
"output": "5.4142135624"
},
{
"input": "100000 3",
"output": "200002.4853316681"
},
{
"input": "2344 5",
"output": "7817.4790439982"
},
{
"input": "999 10",
"output": "6668.3010410807"
},
{
... | 186 | 21,811,200 | 0 | 3,066 | |
621 | Wet Shark and Blocks | [
"dp",
"matrices"
] | null | null | There are *b* blocks of digits. Each one consisting of the same *n* digits, which are given to you in the input. Wet Shark must choose exactly one digit from each block and concatenate all of those digits together to form one large integer. For example, if he chooses digit 1 from the first block and digit 2 from the second block, he gets the integer 12.
Wet Shark then takes this number modulo *x*. Please, tell him how many ways he can choose one digit from each block so that he gets exactly *k* as the final result. As this number may be too large, print it modulo 109<=+<=7.
Note, that the number of ways to choose some digit in the block is equal to the number of it's occurrences. For example, there are 3 ways to choose digit 5 from block 3 5 6 7 8 9 5 1 1 1 1 5. | The first line of the input contains four space-separated integers, *n*, *b*, *k* and *x* (2<=β€<=*n*<=β€<=50<=000,<=1<=β€<=*b*<=β€<=109,<=0<=β€<=*k*<=<<=*x*<=β€<=100,<=*x*<=β₯<=2)Β β the number of digits in one block, the number of blocks, interesting remainder modulo *x* and modulo *x* itself.
The next line contains *n* space separated integers *a**i* (1<=β€<=*a**i*<=β€<=9), that give the digits contained in each block. | Print the number of ways to pick exactly one digit from each blocks, such that the resulting integer equals *k* modulo *x*. | [
"12 1 5 10\n3 5 6 7 8 9 5 1 1 1 1 5\n",
"3 2 1 2\n6 2 2\n",
"3 2 1 2\n3 1 2\n"
] | [
"3\n",
"0\n",
"6\n"
] | In the second sample possible integers are 22, 26, 62 and 66. None of them gives the remainder 1 modulo 2.
In the third sample integers 11, 13, 21, 23, 31 and 33 have remainder 1 modulo 2. There is exactly one way to obtain each of these integers, so the total answer is 6. | [
{
"input": "12 1 5 10\n3 5 6 7 8 9 5 1 1 1 1 5",
"output": "3"
},
{
"input": "3 2 1 2\n6 2 2",
"output": "0"
},
{
"input": "3 2 1 2\n3 1 2",
"output": "6"
},
{
"input": "3 2 1 2\n6 3 2",
"output": "3"
},
{
"input": "3 2 1 2\n3 6 3",
"output": "6"
},
{
... | 0 | 0 | -1 | 3,077 | |
938 | Constructing Tests | [
"binary search",
"brute force",
"constructive algorithms"
] | null | null | Let's denote a *m*-free matrix as a binary (that is, consisting of only 1's and 0's) matrix such that every square submatrix of size *m*<=Γ<=*m* of this matrix contains at least one zero.
Consider the following problem:
You are given two integers *n* and *m*. You have to construct an *m*-free square matrix of size *n*<=Γ<=*n* such that the number of 1's in this matrix is maximum possible. Print the maximum possible number of 1's in such matrix.
You don't have to solve this problem. Instead, you have to construct a few tests for it.
You will be given *t* numbers *x*1, *x*2, ..., *x**t*. For every , find two integers *n**i* and *m**i* (*n**i*<=β₯<=*m**i*) such that the answer for the aforementioned problem is exactly *x**i* if we set *n*<==<=*n**i* and *m*<==<=*m**i*. | The first line contains one integer *t* (1<=β€<=*t*<=β€<=100) β the number of tests you have to construct.
Then *t* lines follow, *i*-th line containing one integer *x**i* (0<=β€<=*x**i*<=β€<=109).
Note that in hacks you have to set *t*<==<=1. | For each test you have to construct, output two positive numbers *n**i* and *m**i* (1<=β€<=*m**i*<=β€<=*n**i*<=β€<=109) such that the maximum number of 1's in a *m**i*-free *n**i*<=Γ<=*n**i* matrix is exactly *x**i*. If there are multiple solutions, you may output any of them; and if this is impossible to construct a test, output a single integer <=-<=1. | [
"3\n21\n0\n1\n"
] | [
"5 2\n1 1\n-1\n"
] | none | [
{
"input": "3\n21\n0\n1",
"output": "5 2\n1 1\n-1"
},
{
"input": "1\n420441920",
"output": "-1"
},
{
"input": "1\n4",
"output": "-1"
},
{
"input": "1\n297540",
"output": "546 22"
},
{
"input": "1\n9",
"output": "-1"
},
{
"input": "1\n144",
"output"... | 1,000 | 20,377,600 | 0 | 3,078 | |
192 | Walking in the Rain | [
"brute force",
"implementation"
] | null | null | In Berland the opposition is going to arrange mass walking on the boulevard. The boulevard consists of *n* tiles that are lain in a row and are numbered from 1 to *n* from right to left. The opposition should start walking on the tile number 1 and the finish on the tile number *n*. During the walk it is allowed to move from right to left between adjacent tiles in a row, and jump over a tile. More formally, if you are standing on the tile number *i* (*i*<=<<=*n*<=-<=1), you can reach the tiles number *i*<=+<=1 or the tile number *i*<=+<=2 from it (if you stand on the tile number *n*<=-<=1, you can only reach tile number *n*). We can assume that all the opposition movements occur instantaneously.
In order to thwart an opposition rally, the Berland bloody regime organized the rain. The tiles on the boulevard are of poor quality and they are rapidly destroyed in the rain. We know that the *i*-th tile is destroyed after *a**i* days of rain (on day *a**i* tile isn't destroyed yet, and on day *a**i*<=+<=1 it is already destroyed). Of course, no one is allowed to walk on the destroyed tiles! So the walk of the opposition is considered thwarted, if either the tile number 1 is broken, or the tile number *n* is broken, or it is impossible to reach the tile number *n* from the tile number 1 if we can walk on undestroyed tiles.
The opposition wants to gather more supporters for their walk. Therefore, the more time they have to pack, the better. Help the opposition to calculate how much time they still have and tell us for how many days the walk from the tile number 1 to the tile number *n* will be possible. | The first line contains integer *n* (1<=β€<=*n*<=β€<=103) β the boulevard's length in tiles.
The second line contains *n* space-separated integers *a**i* β the number of days after which the *i*-th tile gets destroyed (1<=β€<=*a**i*<=β€<=103). | Print a single number β the sought number of days. | [
"4\n10 3 5 10\n",
"5\n10 2 8 3 5\n"
] | [
"5\n",
"5\n"
] | In the first sample the second tile gets destroyed after day three, and the only path left is 1βββ3βββ4. After day five there is a two-tile gap between the first and the last tile, you can't jump over it.
In the second sample path 1βββ3βββ5 is available up to day five, inclusive. On day six the last tile is destroyed and the walk is thwarted. | [
{
"input": "4\n10 3 5 10",
"output": "5"
},
{
"input": "5\n10 2 8 3 5",
"output": "5"
},
{
"input": "10\n10 3 1 6 7 1 3 3 8 1",
"output": "1"
},
{
"input": "10\n26 72 10 52 2 5 61 2 39 64",
"output": "5"
},
{
"input": "100\n8 2 1 2 8 3 5 8 5 1 9 3 4 1 5 6 4 2 9 10... | 124 | 0 | 3 | 3,081 | |
723 | Text Document Analysis | [
"expression parsing",
"implementation",
"strings"
] | null | null | Modern text editors usually show some information regarding the document being edited. For example, the number of words, the number of pages, or the number of characters.
In this problem you should implement the similar functionality.
You are given a string which only consists of:
- uppercase and lowercase English letters, - underscore symbols (they are used as separators), - parentheses (both opening and closing).
It is guaranteed that each opening parenthesis has a succeeding closing parenthesis. Similarly, each closing parentheses has a preceding opening parentheses matching it. For each pair of matching parentheses there are no other parenthesis between them. In other words, each parenthesis in the string belongs to a matching "opening-closing" pair, and such pairs can't be nested.
For example, the following string is valid: "_Hello_Vasya(and_Petya)__bye_(and_OK)".
Word is a maximal sequence of consecutive letters, i.e. such sequence that the first character to the left and the first character to the right of it is an underscore, a parenthesis, or it just does not exist. For example, the string above consists of seven words: "Hello", "Vasya", "and", "Petya", "bye", "and" and "OK". Write a program that finds:
- the length of the longest word outside the parentheses (print 0, if there is no word outside the parentheses), - the number of words inside the parentheses (print 0, if there is no word inside the parentheses). | The first line of the input contains a single integer *n* (1<=β€<=*n*<=β€<=255)Β β the length of the given string. The second line contains the string consisting of only lowercase and uppercase English letters, parentheses and underscore symbols. | Print two space-separated integers:
- the length of the longest word outside the parentheses (print 0, if there is no word outside the parentheses), - the number of words inside the parentheses (print 0, if there is no word inside the parentheses). | [
"37\n_Hello_Vasya(and_Petya)__bye_(and_OK)\n",
"37\n_a_(_b___c)__de_f(g_)__h__i(j_k_l)m__\n",
"27\n(LoooonG)__shOrt__(LoooonG)\n",
"5\n(___)\n"
] | [
"5 4",
"2 6",
"5 2",
"0 0\n"
] | In the first sample, the words "Hello", "Vasya" and "bye" are outside any of the parentheses, and the words "and", "Petya", "and" and "OK" are inside. Note, that the word "and" is given twice and you should count it twice in the answer. | [
{
"input": "37\n_Hello_Vasya(and_Petya)__bye_(and_OK)",
"output": "5 4"
},
{
"input": "37\n_a_(_b___c)__de_f(g_)__h__i(j_k_l)m__",
"output": "2 6"
},
{
"input": "27\n(LoooonG)__shOrt__(LoooonG)",
"output": "5 2"
},
{
"input": "5\n(___)",
"output": "0 0"
},
{
"inpu... | 62 | 0 | 3 | 3,085 | |
0 | none | [
"none"
] | null | null | Limak is a little polar bear. He doesn't have many toys and thus he often plays with polynomials.
He considers a polynomial valid if its degree is *n* and its coefficients are integers not exceeding *k* by the absolute value. More formally:
Let *a*0,<=*a*1,<=...,<=*a**n* denote the coefficients, so . Then, a polynomial *P*(*x*) is valid if all the following conditions are satisfied:
- *a**i* is integer for every *i*; - |*a**i*|<=β€<=*k* for every *i*; - *a**n*<=β <=0.
Limak has recently got a valid polynomial *P* with coefficients *a*0,<=*a*1,<=*a*2,<=...,<=*a**n*. He noticed that *P*(2)<=β <=0 and he wants to change it. He is going to change one coefficient to get a valid polynomial *Q* of degree *n* that *Q*(2)<==<=0. Count the number of ways to do so. You should count two ways as a distinct if coefficients of target polynoms differ. | The first line contains two integers *n* and *k* (1<=β€<=*n*<=β€<=200<=000,<=1<=β€<=*k*<=β€<=109)Β β the degree of the polynomial and the limit for absolute values of coefficients.
The second line contains *n*<=+<=1 integers *a*0,<=*a*1,<=...,<=*a**n* (|*a**i*|<=β€<=*k*,<=*a**n*<=β <=0)Β β describing a valid polynomial . It's guaranteed that *P*(2)<=β <=0. | Print the number of ways to change one coefficient to get a valid polynomial *Q* that *Q*(2)<==<=0. | [
"3 1000000000\n10 -9 -3 5\n",
"3 12\n10 -9 -3 5\n",
"2 20\n14 -7 19\n"
] | [
"3\n",
"2\n",
"0\n"
] | In the first sample, we are given a polynomial *P*(*x*)β=β10β-β9*x*β-β3*x*<sup class="upper-index">2</sup>β+β5*x*<sup class="upper-index">3</sup>.
Limak can change one coefficient in three ways:
1. He can set *a*<sub class="lower-index">0</sub>β=ββ-β10. Then he would get *Q*(*x*)β=ββ-β10β-β9*x*β-β3*x*<sup class="upper-index">2</sup>β+β5*x*<sup class="upper-index">3</sup> and indeed *Q*(2)β=ββ-β10β-β18β-β12β+β40β=β0. 1. Or he can set *a*<sub class="lower-index">2</sub>β=ββ-β8. Then *Q*(*x*)β=β10β-β9*x*β-β8*x*<sup class="upper-index">2</sup>β+β5*x*<sup class="upper-index">3</sup> and indeed *Q*(2)β=β10β-β18β-β32β+β40β=β0. 1. Or he can set *a*<sub class="lower-index">1</sub>β=ββ-β19. Then *Q*(*x*)β=β10β-β19*x*β-β3*x*<sup class="upper-index">2</sup>β+β5*x*<sup class="upper-index">3</sup> and indeed *Q*(2)β=β10β-β38β-β12β+β40β=β0.
In the second sample, we are given the same polynomial. This time though, *k* is equal to 12 instead of 10<sup class="upper-index">9</sup>. Two first of ways listed above are still valid but in the third way we would get |*a*<sub class="lower-index">1</sub>|β>β*k* what is not allowed. Thus, the answer is 2 this time. | [] | 30 | 0 | 0 | 3,087 | |
555 | Case of Matryoshkas | [
"implementation"
] | null | null | Andrewid the Android is a galaxy-famous detective. He is now investigating the case of vandalism at the exhibition of contemporary art.
The main exhibit is a construction of *n* matryoshka dolls that can be nested one into another. The matryoshka dolls are numbered from 1 to *n*. A matryoshka with a smaller number can be nested in a matryoshka with a higher number, two matryoshkas can not be directly nested in the same doll, but there may be chain nestings, for example, 1<=β<=2<=β<=4<=β<=5.
In one second, you can perform one of the two following operations:
- Having a matryoshka *a* that isn't nested in any other matryoshka and a matryoshka *b*, such that *b* doesn't contain any other matryoshka and is not nested in any other matryoshka, you may put *a* in *b*; - Having a matryoshka *a* directly contained in matryoshka *b*, such that *b* is not nested in any other matryoshka, you may get *a* out of *b*.
According to the modern aesthetic norms the matryoshka dolls on display were assembled in a specific configuration, i.e. as several separate chains of nested matryoshkas, but the criminal, following the mysterious plan, took out all the dolls and assembled them into a single large chain (1<=β<=2<=β<=...<=β<=*n*). In order to continue the investigation Andrewid needs to know in what minimum time it is possible to perform this action. | The first line contains integers *n* (1<=β€<=*n*<=β€<=105) and *k* (1<=β€<=*k*<=β€<=105) β the number of matryoshkas and matryoshka chains in the initial configuration.
The next *k* lines contain the descriptions of the chains: the *i*-th line first contains number *m**i* (1<=β€<=*m**i*<=β€<=*n*), and then *m**i* numbers *a**i*1,<=*a**i*2,<=...,<=*a**im**i* β the numbers of matryoshkas in the chain (matryoshka *a**i*1 is nested into matryoshka *a**i*2, that is nested into matryoshka *a**i*3, and so on till the matryoshka *a**im**i* that isn't nested into any other matryoshka).
It is guaranteed that *m*1<=+<=*m*2<=+<=...<=+<=*m**k*<==<=*n*, the numbers of matryoshkas in all the chains are distinct, in each chain the numbers of matryoshkas follow in the ascending order. | In the single line print the minimum number of seconds needed to assemble one large chain from the initial configuration. | [
"3 2\n2 1 2\n1 3\n",
"7 3\n3 1 3 7\n2 2 5\n2 4 6\n"
] | [
"1\n",
"10\n"
] | In the first sample test there are two chains: 1βββ2 and 3. In one second you can nest the first chain into the second one and get 1βββ2βββ3.
In the second sample test you need to disassemble all the three chains into individual matryoshkas in 2 + 1 + 1 = 4 seconds and then assemble one big chain in 6 seconds. | [
{
"input": "3 2\n2 1 2\n1 3",
"output": "1"
},
{
"input": "7 3\n3 1 3 7\n2 2 5\n2 4 6",
"output": "10"
},
{
"input": "1 1\n1 1",
"output": "0"
},
{
"input": "3 2\n1 2\n2 1 3",
"output": "3"
},
{
"input": "5 3\n1 4\n3 1 2 3\n1 5",
"output": "2"
},
{
"in... | 46 | 4,608,000 | 0 | 3,090 | |
0 | none | [
"none"
] | null | null | An infinitely long railway has a train consisting of *n* cars, numbered from 1 to *n* (the numbers of all the cars are distinct) and positioned in arbitrary order. David Blaine wants to sort the railway cars in the order of increasing numbers. In one move he can make one of the cars disappear from its place and teleport it either to the beginning of the train, or to the end of the train, at his desire. What is the minimum number of actions David Blaine needs to perform in order to sort the train? | The first line of the input contains integer *n* (1<=β€<=*n*<=β€<=100<=000)Β β the number of cars in the train.
The second line contains *n* integers *p**i* (1<=β€<=*p**i*<=β€<=*n*, *p**i*<=β <=*p**j* if *i*<=β <=*j*)Β β the sequence of the numbers of the cars in the train. | Print a single integerΒ β the minimum number of actions needed to sort the railway cars. | [
"5\n4 1 2 5 3\n",
"4\n4 1 3 2\n"
] | [
"2\n",
"2\n"
] | In the first sample you need first to teleport the 4-th car, and then the 5-th car to the end of the train. | [
{
"input": "5\n4 1 2 5 3",
"output": "2"
},
{
"input": "4\n4 1 3 2",
"output": "2"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "2\n1 2",
"output": "0"
},
{
"input": "2\n2 1",
"output": "1"
},
{
"input": "6\n5 3 6 1 4 2",
"output": "4"
},
... | 62 | 0 | 0 | 3,095 | |
977 | Wrong Subtraction | [
"implementation"
] | null | null | Little girl Tanya is learning how to decrease a number by one, but she does it wrong with a number consisting of two or more digits. Tanya subtracts one from a number by the following algorithm:
- if the last digit of the number is non-zero, she decreases the number by one; - if the last digit of the number is zero, she divides the number by 10 (i.e. removes the last digit).
You are given an integer number $n$. Tanya will subtract one from it $k$ times. Your task is to print the result after all $k$ subtractions.
It is guaranteed that the result will be positive integer number. | The first line of the input contains two integer numbers $n$ and $k$ ($2 \le n \le 10^9$, $1 \le k \le 50$) β the number from which Tanya will subtract and the number of subtractions correspondingly. | Print one integer number β the result of the decreasing $n$ by one $k$ times.
It is guaranteed that the result will be positive integer number. | [
"512 4\n",
"1000000000 9\n"
] | [
"50\n",
"1\n"
] | The first example corresponds to the following sequence: $512 \rightarrow 511 \rightarrow 510 \rightarrow 51 \rightarrow 50$. | [
{
"input": "512 4",
"output": "50"
},
{
"input": "1000000000 9",
"output": "1"
},
{
"input": "131203 11",
"output": "12"
},
{
"input": "999999999 50",
"output": "9999"
},
{
"input": "999999999 49",
"output": "99990"
},
{
"input": "131203 9",
"outpu... | 62 | 0 | 3 | 3,096 | |
934 | A Prosperous Lot | [
"constructive algorithms",
"implementation"
] | null | null | Apart from Nian, there is a daemon named Sui, which terrifies children and causes them to become sick. Parents give their children money wrapped in red packets and put them under the pillow, so that when Sui tries to approach them, it will be driven away by the fairies inside.
Big Banban is hesitating over the amount of money to give out. He considers loops to be lucky since it symbolizes unity and harmony.
He would like to find a positive integer *n* not greater than 1018, such that there are exactly *k* loops in the decimal representation of *n*, or determine that such *n* does not exist.
A loop is a planar area enclosed by lines in the digits' decimal representation written in Arabic numerals. For example, there is one loop in digit 4, two loops in 8 and no loops in 5. Refer to the figure below for all exact forms. | The first and only line contains an integer *k* (1<=β€<=*k*<=β€<=106)Β β the desired number of loops. | Output an integerΒ β if no such *n* exists, output -1; otherwise output any such *n*. In the latter case, your output should be a positive decimal integer not exceeding 1018. | [
"2\n",
"6\n"
] | [
"462",
"8080"
] | none | [
{
"input": "2",
"output": "8"
},
{
"input": "6",
"output": "888"
},
{
"input": "3",
"output": "86"
},
{
"input": "4",
"output": "88"
},
{
"input": "5",
"output": "886"
},
{
"input": "1000000",
"output": "-1"
},
{
"input": "1",
"output":... | 77 | 1,024,000 | 3 | 3,114 | |
288 | Polo the Penguin and Houses | [
"combinatorics"
] | null | null | Little penguin Polo loves his home village. The village has *n* houses, indexed by integers from 1 to *n*. Each house has a plaque containing an integer, the *i*-th house has a plaque containing integer *p**i* (1<=β€<=*p**i*<=β€<=*n*).
Little penguin Polo loves walking around this village. The walk looks like that. First he stands by a house number *x*. Then he goes to the house whose number is written on the plaque of house *x* (that is, to house *p**x*), then he goes to the house whose number is written on the plaque of house *p**x* (that is, to house *p**p**x*), and so on.
We know that:
1. When the penguin starts walking from any house indexed from 1 to *k*, inclusive, he can walk to house number 1. 1. When the penguin starts walking from any house indexed from *k*<=+<=1 to *n*, inclusive, he definitely cannot walk to house number 1. 1. When the penguin starts walking from house number 1, he can get back to house number 1 after some non-zero number of walks from a house to a house.
You need to find the number of ways you may write the numbers on the houses' plaques so as to fulfill the three above described conditions. Print the remainder after dividing this number by 1000000007 (109<=+<=7). | The single line contains two space-separated integers *n* and *k* (1<=β€<=*n*<=β€<=1000,<=1<=β€<=*k*<=β€<=*min*(8,<=*n*)) β the number of the houses and the number *k* from the statement. | In a single line print a single integer β the answer to the problem modulo 1000000007 (109<=+<=7). | [
"5 2\n",
"7 4\n"
] | [
"54\n",
"1728\n"
] | none | [
{
"input": "5 2",
"output": "54"
},
{
"input": "7 4",
"output": "1728"
},
{
"input": "8 5",
"output": "16875"
},
{
"input": "8 1",
"output": "823543"
},
{
"input": "10 7",
"output": "3176523"
},
{
"input": "12 8",
"output": "536870912"
},
{
... | 31 | 0 | 0 | 3,115 | |
290 | HQ | [
"*special",
"constructive algorithms"
] | null | null | The famous joke programming language HQ9+ has only 4 commands. In this problem we will explore its subset β a language called HQ... | The only line of the input is a string between 1 and 106 characters long. | Output "Yes" or "No". | [
"HHHH\n",
"HQHQH\n",
"HHQHHQH\n",
"HHQQHHQQHH\n"
] | [
"Yes\n",
"No\n",
"No\n",
"Yes\n"
] | The rest of the problem statement was destroyed by a stray raccoon. We are terribly sorry for the inconvenience. | [
{
"input": "HHHH",
"output": "Yes"
},
{
"input": "HQHQH",
"output": "No"
},
{
"input": "HHQHHQH",
"output": "No"
},
{
"input": "HHQQHHQQHH",
"output": "Yes"
},
{
"input": "Q",
"output": "Yes"
},
{
"input": "HHHHHHHHHHQHHH",
"output": "No"
},
{
... | 124 | 0 | 0 | 3,118 | |
739 | Alyona and a tree | [
"binary search",
"data structures",
"dfs and similar",
"graphs",
"trees"
] | null | null | Alyona has a tree with *n* vertices. The root of the tree is the vertex 1. In each vertex Alyona wrote an positive integer, in the vertex *i* she wrote *a**i*. Moreover, the girl wrote a positive integer to every edge of the tree (possibly, different integers on different edges).
Let's define *dist*(*v*,<=*u*) as the sum of the integers written on the edges of the simple path from *v* to *u*.
The vertex *v* controls the vertex *u* (*v*<=β <=*u*) if and only if *u* is in the subtree of *v* and *dist*(*v*,<=*u*)<=β€<=*a**u*.
Alyona wants to settle in some vertex. In order to do this, she wants to know for each vertex *v* what is the number of vertices *u* such that *v* controls *u*. | The first line contains single integer *n* (1<=β€<=*n*<=β€<=2Β·105).
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=β€<=*a**i*<=β€<=109)Β β the integers written in the vertices.
The next (*n*<=-<=1) lines contain two integers each. The *i*-th of these lines contains integers *p**i* and *w**i* (1<=β€<=*p**i*<=β€<=*n*, 1<=β€<=*w**i*<=β€<=109)Β β the parent of the (*i*<=+<=1)-th vertex in the tree and the number written on the edge between *p**i* and (*i*<=+<=1).
It is guaranteed that the given graph is a tree. | Print *n* integersΒ β the *i*-th of these numbers should be equal to the number of vertices that the *i*-th vertex controls. | [
"5\n2 5 1 4 6\n1 7\n1 1\n3 5\n3 6\n",
"5\n9 7 8 6 5\n1 1\n2 1\n3 1\n4 1\n"
] | [
"1 0 1 0 0\n",
"4 3 2 1 0\n"
] | In the example test case the vertex 1 controls the vertex 3, the vertex 3 controls the vertex 5 (note that is doesn't mean the vertex 1 controls the vertex 5). | [
{
"input": "5\n2 5 1 4 6\n1 7\n1 1\n3 5\n3 6",
"output": "1 0 1 0 0"
},
{
"input": "5\n9 7 8 6 5\n1 1\n2 1\n3 1\n4 1",
"output": "4 3 2 1 0"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "2\n1 1\n1 1",
"output": "1 0"
},
{
"input": "10\n40 77 65 14 86 16 2 51 ... | 61 | 0 | 0 | 3,121 | |
691 | Fashion in Berland | [
"implementation"
] | null | null | According to rules of the Berland fashion, a jacket should be fastened by all the buttons except only one, but not necessarily it should be the last one. Also if the jacket has only one button, it should be fastened, so the jacket will not swinging open.
You are given a jacket with *n* buttons. Determine if it is fastened in a right way. | The first line contains integer *n* (1<=β€<=*n*<=β€<=1000) β the number of buttons on the jacket.
The second line contains *n* integers *a**i* (0<=β€<=*a**i*<=β€<=1). The number *a**i*<==<=0 if the *i*-th button is not fastened. Otherwise *a**i*<==<=1. | In the only line print the word "YES" if the jacket is fastened in a right way. Otherwise print the word "NO". | [
"3\n1 0 1\n",
"3\n1 0 0\n"
] | [
"YES\n",
"NO\n"
] | none | [
{
"input": "3\n1 0 1",
"output": "YES"
},
{
"input": "3\n1 0 0",
"output": "NO"
},
{
"input": "3\n1 1 0",
"output": "YES"
},
{
"input": "3\n1 1 1",
"output": "NO"
},
{
"input": "3\n0 0 1",
"output": "NO"
},
{
"input": "3\n0 0 0",
"output": "NO"
}... | 31 | 0 | 0 | 3,122 | |
638 | Home Numbers | [
"*special",
"constructive algorithms",
"math"
] | null | null | The main street of Berland is a straight line with *n* houses built along it (*n* is an even number). The houses are located at both sides of the street. The houses with odd numbers are at one side of the street and are numbered from 1 to *n*<=-<=1 in the order from the beginning of the street to the end (in the picture: from left to right). The houses with even numbers are at the other side of the street and are numbered from 2 to *n* in the order from the end of the street to its beginning (in the picture: from right to left). The corresponding houses with even and odd numbers are strictly opposite each other, that is, house 1 is opposite house *n*, house 3 is opposite house *n*<=-<=2, house 5 is opposite house *n*<=-<=4 and so on.
Vasya needs to get to house number *a* as quickly as possible. He starts driving from the beginning of the street and drives his car to house *a*. To get from the beginning of the street to houses number 1 and *n*, he spends exactly 1 second. He also spends exactly one second to drive the distance between two neighbouring houses. Vasya can park at any side of the road, so the distance between the beginning of the street at the houses that stand opposite one another should be considered the same.
Your task is: find the minimum time Vasya needs to reach house *a*. | The first line of the input contains two integers, *n* and *a* (1<=β€<=*a*<=β€<=*n*<=β€<=100<=000)Β β the number of houses on the street and the number of the house that Vasya needs to reach, correspondingly. It is guaranteed that number *n* is even. | Print a single integer β the minimum time Vasya needs to get from the beginning of the street to house *a*. | [
"4 2\n",
"8 5\n"
] | [
"2\n",
"3\n"
] | In the first sample there are only four houses on the street, two houses at each side. House 2 will be the last at Vasya's right.
The second sample corresponds to picture with *n*β=β8. House 5 is the one before last at Vasya's left. | [
{
"input": "4 2",
"output": "2"
},
{
"input": "8 5",
"output": "3"
},
{
"input": "2 1",
"output": "1"
},
{
"input": "2 2",
"output": "1"
},
{
"input": "10 1",
"output": "1"
},
{
"input": "10 10",
"output": "1"
},
{
"input": "100000 100000",... | 62 | 5,120,000 | 3 | 3,129 | |
414 | Mashmokh and ACM | [
"combinatorics",
"dp",
"number theory"
] | null | null | Mashmokh's boss, Bimokh, didn't like Mashmokh. So he fired him. Mashmokh decided to go to university and participate in ACM instead of finding a new job. He wants to become a member of Bamokh's team. In order to join he was given some programming tasks and one week to solve them. Mashmokh is not a very experienced programmer. Actually he is not a programmer at all. So he wasn't able to solve them. That's why he asked you to help him with these tasks. One of these tasks is the following.
A sequence of *l* integers *b*1,<=*b*2,<=...,<=*b**l* (1<=β€<=*b*1<=β€<=*b*2<=β€<=...<=β€<=*b**l*<=β€<=*n*) is called good if each number divides (without a remainder) by the next number in the sequence. More formally for all *i* (1<=β€<=*i*<=β€<=*l*<=-<=1).
Given *n* and *k* find the number of good sequences of length *k*. As the answer can be rather large print it modulo 1000000007 (109<=+<=7). | The first line of input contains two space-separated integers *n*,<=*k*Β (1<=β€<=*n*,<=*k*<=β€<=2000). | Output a single integer β the number of good sequences of length *k* modulo 1000000007 (109<=+<=7). | [
"3 2\n",
"6 4\n",
"2 1\n"
] | [
"5\n",
"39\n",
"2\n"
] | In the first sample the good sequences are: [1,β1],β[2,β2],β[3,β3],β[1,β2],β[1,β3]. | [
{
"input": "3 2",
"output": "5"
},
{
"input": "6 4",
"output": "39"
},
{
"input": "2 1",
"output": "2"
},
{
"input": "1478 194",
"output": "312087753"
},
{
"input": "1415 562",
"output": "953558593"
},
{
"input": "1266 844",
"output": "735042656"
... | 389 | 39,936,000 | 3 | 3,130 | |
707 | Bakery | [
"graphs"
] | null | null | Masha wants to open her own bakery and bake muffins in one of the *n* cities numbered from 1 to *n*. There are *m* bidirectional roads, each of whose connects some pair of cities.
To bake muffins in her bakery, Masha needs to establish flour supply from some storage. There are only *k* storages, located in different cities numbered *a*1,<=*a*2,<=...,<=*a**k*.
Unforunately the law of the country Masha lives in prohibits opening bakery in any of the cities which has storage located in it. She can open it only in one of another *n*<=-<=*k* cities, and, of course, flour delivery should be paidΒ β for every kilometer of path between storage and bakery Masha should pay 1 ruble.
Formally, Masha will pay *x* roubles, if she will open the bakery in some city *b* (*a**i*<=β <=*b* for every 1<=β€<=*i*<=β€<=*k*) and choose a storage in some city *s* (*s*<==<=*a**j* for some 1<=β€<=*j*<=β€<=*k*) and *b* and *s* are connected by some path of roads of summary length *x* (if there are more than one path, Masha is able to choose which of them should be used).
Masha is very thrifty and rational. She is interested in a city, where she can open her bakery (and choose one of *k* storages and one of the paths between city with bakery and city with storage) and pay minimum possible amount of rubles for flour delivery. Please help Masha find this amount. | The first line of the input contains three integers *n*, *m* and *k* (1<=β€<=*n*,<=*m*<=β€<=105, 0<=β€<=*k*<=β€<=*n*)Β β the number of cities in country Masha lives in, the number of roads between them and the number of flour storages respectively.
Then *m* lines follow. Each of them contains three integers *u*, *v* and *l* (1<=β€<=*u*,<=*v*<=β€<=*n*, 1<=β€<=*l*<=β€<=109, *u*<=β <=*v*) meaning that there is a road between cities *u* and *v* of length of *l* kilometers .
If *k*<=><=0, then the last line of the input contains *k* distinct integers *a*1,<=*a*2,<=...,<=*a**k* (1<=β€<=*a**i*<=β€<=*n*)Β β the number of cities having flour storage located in. If *k*<==<=0 then this line is not presented in the input. | Print the minimum possible amount of rubles Masha should pay for flour delivery in the only line.
If the bakery can not be opened (while satisfying conditions) in any of the *n* cities, print <=-<=1 in the only line. | [
"5 4 2\n1 2 5\n1 2 3\n2 3 4\n1 4 10\n1 5\n",
"3 1 1\n1 2 3\n3\n"
] | [
"3",
"-1"
] | Image illustrates the first sample case. Cities with storage located in and the road representing the answer are darkened. | [
{
"input": "5 4 2\n1 2 5\n1 2 3\n2 3 4\n1 4 10\n1 5",
"output": "3"
},
{
"input": "3 1 1\n1 2 3\n3",
"output": "-1"
},
{
"input": "2 3 1\n1 2 3\n1 2 18\n1 2 13\n2",
"output": "3"
},
{
"input": "3 7 0\n1 3 9\n1 2 5\n1 2 21\n1 2 12\n1 2 13\n2 3 19\n2 3 8",
"output": "-1"
... | 327 | 36,659,200 | 3 | 3,131 | |
749 | Parallelogram is Back | [
"brute force",
"constructive algorithms",
"geometry"
] | null | null | Long time ago Alex created an interesting problem about parallelogram. The input data for this problem contained four integer points on the Cartesian plane, that defined the set of vertices of some non-degenerate (positive area) parallelogram. Points not necessary were given in the order of clockwise or counterclockwise traversal.
Alex had very nice test for this problem, but is somehow happened that the last line of the input was lost and now he has only three out of four points of the original parallelogram. He remembers that test was so good that he asks you to restore it given only these three points. | The input consists of three lines, each containing a pair of integer coordinates *x**i* and *y**i* (<=-<=1000<=β€<=*x**i*,<=*y**i*<=β€<=1000). It's guaranteed that these three points do not lie on the same line and no two of them coincide. | First print integer *k*Β β the number of ways to add one new integer point such that the obtained set defines some parallelogram of positive area. There is no requirement for the points to be arranged in any special order (like traversal), they just define the set of vertices.
Then print *k* lines, each containing a pair of integerΒ β possible coordinates of the fourth point. | [
"0 0\n1 0\n0 1\n"
] | [
"3\n1 -1\n-1 1\n1 1\n"
] | If you need clarification of what parallelogram is, please check Wikipedia page:
https://en.wikipedia.org/wiki/Parallelogram | [
{
"input": "0 0\n1 0\n0 1",
"output": "3\n1 -1\n-1 1\n1 1"
},
{
"input": "0 -1\n-1 0\n1 1",
"output": "3\n-2 -2\n2 0\n0 2"
},
{
"input": "-1 -1\n0 1\n1 1",
"output": "3\n-2 -1\n0 -1\n2 3"
},
{
"input": "1000 1000\n-1000 -1000\n-1000 1000",
"output": "3\n1000 -1000\n1000 3... | 1,000 | 2,662,400 | 0 | 3,140 | |
127 | Canvas Frames | [
"implementation"
] | null | null | Nicholas, a painter is going to paint several new canvases. Nicholas is sure that the canvases will turn out so great that each one will need framing and being hung on the wall. Frames are what Nicholas decided to begin with.
Nicholas has *n* sticks whose lengths equal *a*1,<=*a*2,<=... *a**n*. Nicholas does not want to break the sticks or glue them together. To make a *h*<=Γ<=*w*-sized frame, he needs two sticks whose lengths equal *h* and two sticks whose lengths equal *w*. Specifically, to make a square frame (when *h*<==<=*w*), he needs four sticks of the same length.
Now Nicholas wants to make from the sticks that he has as many frames as possible; to be able to paint as many canvases as possible to fill the frames. Help him in this uneasy task. Note that it is not necessary to use all the sticks Nicholas has. | The first line contains an integer *n* (1<=β€<=*n*<=β€<=100) β the number of sticks. The second line contains *n* space-separated integers. The *i*-th integer equals the length of the *i*-th stick *a**i* (1<=β€<=*a**i*<=β€<=100). | Print the single number β the maximum number of frames Nicholas can make for his future canvases. | [
"5\n2 4 3 2 3\n",
"13\n2 2 4 4 4 4 6 6 6 7 7 9 9\n",
"4\n3 3 3 5\n"
] | [
"1",
"3",
"0"
] | none | [
{
"input": "5\n2 4 3 2 3",
"output": "1"
},
{
"input": "13\n2 2 4 4 4 4 6 6 6 7 7 9 9",
"output": "3"
},
{
"input": "4\n3 3 3 5",
"output": "0"
},
{
"input": "2\n3 5",
"output": "0"
},
{
"input": "9\n1 2 3 4 5 6 7 8 9",
"output": "0"
},
{
"input": "14\... | 77 | 102,400 | 3 | 3,141 | |
65 | Harry Potter and the History of Magic | [
"brute force",
"greedy",
"implementation"
] | B. Harry Potter and the History of Magic | 1 | 256 | The History of Magic is perhaps the most boring subject in the Hogwarts school of Witchcraft and Wizardry. Harry Potter is usually asleep during history lessons, and his magical quill writes the lectures for him. Professor Binns, the history of magic teacher, lectures in such a boring and monotonous voice, that he has a soporific effect even on the quill. That's why the quill often makes mistakes, especially in dates.
So, at the end of the semester Professor Binns decided to collect the students' parchments with notes and check them. Ron Weasley is in a panic: Harry's notes may contain errors, but at least he has some notes, whereas Ron does not have any. Ronald also has been sleeping during the lectures and his quill had been eaten by his rat Scabbers. Hermione Granger refused to give Ron her notes, because, in her opinion, everyone should learn on their own. Therefore, Ron has no choice but to copy Harry's notes.
Due to the quill's errors Harry's dates are absolutely confused: the years of goblin rebellions and other important events for the wizarding world do not follow in order, and sometimes even dates from the future occur. Now Ron wants to change some of the digits while he copies the notes so that the dates were in the chronological (i.e. non-decreasing) order and so that the notes did not have any dates strictly later than 2011, or strictly before than 1000. To make the resulting sequence as close as possible to the one dictated by Professor Binns, Ron will change no more than one digit in each date into other digit. Help him do it. | The first input line contains an integer *n* (1<=β€<=*n*<=β€<=1000). It represents the number of dates in Harry's notes. Next *n* lines contain the actual dates *y*1, *y*2, ..., *y**n*, each line contains a date. Each date is a four-digit integer (1000<=β€<=*y**i*<=β€<=9999). | Print *n* numbers *z*1, *z*2, ..., *z**n* (1000<=β€<=*z**i*<=β€<=2011). They are Ron's resulting dates. Print each number on a single line. Numbers *z**i* must form the non-decreasing sequence. Each number *z**i* should differ from the corresponding date *y**i* in no more than one digit. It is not allowed to change the first digit of a number into 0. If there are several possible solutions, print any of them. If there's no solution, print "No solution" (without the quotes). | [
"3\n1875\n1936\n1721\n",
"4\n9999\n2000\n3000\n3011\n",
"3\n1999\n5055\n2000\n"
] | [
"1835\n1836\n1921\n",
"1999\n2000\n2000\n2011\n",
"No solution\n"
] | none | [
{
"input": "3\n1875\n1936\n1721",
"output": "1075\n1136\n1221"
},
{
"input": "4\n9999\n2000\n3000\n3011",
"output": "1999\n2000\n2000\n2011"
},
{
"input": "3\n1999\n5055\n2000",
"output": "No solution"
},
{
"input": "2\n2037\n2025",
"output": "1037\n2005"
},
{
"in... | 124 | 0 | 3.938 | 3,142 |
678 | Iterated Linear Function | [
"math",
"number theory"
] | null | null | Consider a linear function *f*(*x*)<==<=*Ax*<=+<=*B*. Let's define *g*(0)(*x*)<==<=*x* and *g*(*n*)(*x*)<==<=*f*(*g*(*n*<=-<=1)(*x*)) for *n*<=><=0. For the given integer values *A*, *B*, *n* and *x* find the value of *g*(*n*)(*x*) modulo 109<=+<=7. | The only line contains four integers *A*, *B*, *n* and *x* (1<=β€<=*A*,<=*B*,<=*x*<=β€<=109,<=1<=β€<=*n*<=β€<=1018) β the parameters from the problem statement.
Note that the given value *n* can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type. | Print the only integer *s* β the value *g*(*n*)(*x*) modulo 109<=+<=7. | [
"3 4 1 1\n",
"3 4 2 1\n",
"3 4 3 1\n"
] | [
"7\n",
"25\n",
"79\n"
] | none | [
{
"input": "3 4 1 1",
"output": "7"
},
{
"input": "3 4 2 1",
"output": "25"
},
{
"input": "3 4 3 1",
"output": "79"
},
{
"input": "1 1 1 1",
"output": "2"
},
{
"input": "3 10 723 6",
"output": "443623217"
},
{
"input": "14 81 51 82",
"output": "908... | 93 | 0 | 0 | 3,144 | |
788 | Functions again | [
"dp",
"two pointers"
] | null | null | Something happened in Uzhlyandia again... There are riots on the streets... Famous Uzhlyandian superheroes Shean the Sheep and Stas the Giraffe were called in order to save the situation. Upon the arriving, they found that citizens are worried about maximum values of the Main Uzhlyandian Function *f*, which is defined as follows:
In the above formula, 1<=β€<=*l*<=<<=*r*<=β€<=*n* must hold, where *n* is the size of the Main Uzhlyandian Array *a*, and |*x*| means absolute value of *x*. But the heroes skipped their math lessons in school, so they asked you for help. Help them calculate the maximum value of *f* among all possible values of *l* and *r* for the given array *a*. | The first line contains single integer *n* (2<=β€<=*n*<=β€<=105)Β β the size of the array *a*.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (-109<=β€<=*a**i*<=β€<=109)Β β the array elements. | Print the only integerΒ β the maximum value of *f*. | [
"5\n1 4 2 3 1\n",
"4\n1 5 4 7\n"
] | [
"3",
"6"
] | In the first sample case, the optimal value of *f* is reached on intervals [1,β2] and [2,β5].
In the second case maximal value of *f* is reachable only on the whole array. | [
{
"input": "5\n1 4 2 3 1",
"output": "3"
},
{
"input": "4\n1 5 4 7",
"output": "6"
},
{
"input": "8\n16 14 12 10 8 100 50 0",
"output": "92"
},
{
"input": "2\n1 1",
"output": "0"
},
{
"input": "50\n-5 -9 0 44 -10 37 34 -49 11 -22 -26 44 8 -13 23 -46 34 12 -24 2 -4... | 296 | 20,480,000 | 3 | 3,145 | |
240 | TorCoder | [
"data structures"
] | null | null | A boy named Leo doesn't miss a single TorCoder contest round. On the last TorCoder round number 100666 Leo stumbled over the following problem. He was given a string *s*, consisting of *n* lowercase English letters, and *m* queries. Each query is characterised by a pair of integers *l**i*,<=*r**i* (1<=β€<=*l**i*<=β€<=*r**i*<=β€<=*n*).
We'll consider the letters in the string numbered from 1 to *n* from left to right, that is, *s*<==<=*s*1*s*2... *s**n*.
After each query he must swap letters with indexes from *l**i* to *r**i* inclusive in string *s* so as to make substring (*l**i*,<=*r**i*) a palindrome. If there are multiple such letter permutations, you should choose the one where string (*l**i*,<=*r**i*) will be lexicographically minimum. If no such permutation exists, you should ignore the query (that is, not change string *s*).
Everybody knows that on TorCoder rounds input line and array size limits never exceed 60, so Leo solved this problem easily. Your task is to solve the problem on a little bit larger limits. Given string *s* and *m* queries, print the string that results after applying all *m* queries to string *s*. | The first input line contains two integers *n* and *m* (1<=β€<=*n*,<=*m*<=β€<=105) β the string length and the number of the queries.
The second line contains string *s*, consisting of *n* lowercase Latin letters.
Each of the next *m* lines contains a pair of integers *l**i*,<=*r**i* (1<=β€<=*l**i*<=β€<=*r**i*<=β€<=*n*) β a query to apply to the string. | In a single line print the result of applying *m* queries to string *s*. Print the queries in the order in which they are given in the input. | [
"7 2\naabcbaa\n1 3\n5 7\n",
"3 2\nabc\n1 2\n2 3\n"
] | [
"abacaba\n",
"abc\n"
] | A substring (*l*<sub class="lower-index">*i*</sub>,β*r*<sub class="lower-index">*i*</sub>) 1ββ€β*l*<sub class="lower-index">*i*</sub>ββ€β*r*<sub class="lower-index">*i*</sub>ββ€β*n*) of string *s*β=β*s*<sub class="lower-index">1</sub>*s*<sub class="lower-index">2</sub>... *s*<sub class="lower-index">*n*</sub> of length *n* is a sequence of characters *s*<sub class="lower-index">*l*<sub class="lower-index">*i*</sub></sub>*s*<sub class="lower-index">*l*<sub class="lower-index">*i*β+β1</sub></sub>...*s*<sub class="lower-index">*r*<sub class="lower-index">*i*</sub></sub>.
A string is a palindrome, if it reads the same from left to right and from right to left.
String *x*<sub class="lower-index">1</sub>*x*<sub class="lower-index">2</sub>... *x*<sub class="lower-index">*p*</sub> is lexicographically smaller than string *y*<sub class="lower-index">1</sub>*y*<sub class="lower-index">2</sub>... *y*<sub class="lower-index">*q*</sub>, if either *p*β<β*q* and *x*<sub class="lower-index">1</sub>β=β*y*<sub class="lower-index">1</sub>,β*x*<sub class="lower-index">2</sub>β=β*y*<sub class="lower-index">2</sub>,β... ,β*x*<sub class="lower-index">*p*</sub>β=β*y*<sub class="lower-index">*p*</sub>, or exists such number *r* (*r*β<β*p*,β*r*β<β*q*), that *x*<sub class="lower-index">1</sub>β=β*y*<sub class="lower-index">1</sub>,β*x*<sub class="lower-index">2</sub>β=β*y*<sub class="lower-index">2</sub>,β... ,β*x*<sub class="lower-index">*r*</sub>β=β*y*<sub class="lower-index">*r*</sub> and *x*<sub class="lower-index">*r*β+β1</sub>β<β*y*<sub class="lower-index">*r*β+β1</sub>. | [] | 30 | 0 | 0 | 3,146 | |
289 | Polo the Penguin and Matrix | [
"brute force",
"dp",
"implementation",
"sortings",
"ternary search"
] | null | null | Little penguin Polo has an *n*<=Γ<=*m* matrix, consisting of integers. Let's index the matrix rows from 1 to *n* from top to bottom and let's index the columns from 1 to *m* from left to right. Let's represent the matrix element on the intersection of row *i* and column *j* as *a**ij*.
In one move the penguin can add or subtract number *d* from some matrix element. Find the minimum number of moves needed to make all matrix elements equal. If the described plan is impossible to carry out, say so. | The first line contains three integers *n*, *m* and *d* (1<=β€<=*n*,<=*m*<=β€<=100,<=1<=β€<=*d*<=β€<=104) β the matrix sizes and the *d* parameter. Next *n* lines contain the matrix: the *j*-th integer in the *i*-th row is the matrix element *a**ij* (1<=β€<=*a**ij*<=β€<=104). | In a single line print a single integer β the minimum number of moves the penguin needs to make all matrix elements equal. If that is impossible, print "-1" (without the quotes). | [
"2 2 2\n2 4\n6 8\n",
"1 2 7\n6 7\n"
] | [
"4\n",
"-1\n"
] | none | [
{
"input": "2 2 2\n2 4\n6 8",
"output": "4"
},
{
"input": "1 2 7\n6 7",
"output": "-1"
},
{
"input": "3 2 1\n5 7\n1 2\n5 100",
"output": "104"
},
{
"input": "3 3 3\n5 8 5\n11 11 17\n14 5 2",
"output": "12"
},
{
"input": "3 3 3\n5 8 5\n11 11 17\n14 5 3",
"outpu... | 124 | 6,963,200 | 0 | 3,147 | |
964 | Messages | [
"math"
] | null | null | There are *n* incoming messages for Vasya. The *i*-th message is going to be received after *t**i* minutes. Each message has a cost, which equals to *A* initially. After being received, the cost of a message decreases by *B* each minute (it can become negative). Vasya can read any message after receiving it at any moment of time. After reading the message, Vasya's bank account receives the current cost of this message. Initially, Vasya's bank account is at 0.
Also, each minute Vasya's bank account receives *C*Β·*k*, where *k* is the amount of received but unread messages.
Vasya's messages are very important to him, and because of that he wants to have all messages read after *T* minutes.
Determine the maximum amount of money Vasya's bank account can hold after *T* minutes. | The first line contains five integers *n*, *A*, *B*, *C* and *T* (1<=β€<=*n*,<=*A*,<=*B*,<=*C*,<=*T*<=β€<=1000).
The second string contains *n* integers *t**i* (1<=β€<=*t**i*<=β€<=*T*). | Output one integer Β β the answer to the problem. | [
"4 5 5 3 5\n1 5 5 4\n",
"5 3 1 1 3\n2 2 2 1 1\n",
"5 5 3 4 5\n1 2 3 4 5\n"
] | [
"20\n",
"15\n",
"35\n"
] | In the first sample the messages must be read immediately after receiving, Vasya receives *A* points for each message, *n*Β·*A*β=β20 in total.
In the second sample the messages can be read at any integer moment.
In the third sample messages must be read at the moment T. This way Vasya has 1, 2, 3, 4 and 0 unread messages at the corresponding minutes, he gets 40 points for them. When reading messages, he receives (5β-β4Β·3)β+β(5β-β3Β·3)β+β(5β-β2Β·3)β+β(5β-β1Β·3)β+β5β=ββ-β5 points. This is 35 in total. | [
{
"input": "4 5 5 3 5\n1 5 5 4",
"output": "20"
},
{
"input": "5 3 1 1 3\n2 2 2 1 1",
"output": "15"
},
{
"input": "5 5 3 4 5\n1 2 3 4 5",
"output": "35"
},
{
"input": "1 6 4 3 9\n2",
"output": "6"
},
{
"input": "10 9 7 5 3\n3 3 3 3 2 3 2 2 3 3",
"output": "90... | 139 | 1,536,000 | 0 | 3,161 | |
467 | Fedor and New Game | [
"bitmasks",
"brute force",
"constructive algorithms",
"implementation"
] | null | null | After you had helped George and Alex to move in the dorm, they went to help their friend Fedor play a new computer game Β«Call of Soldiers 3Β».
The game has (*m*<=+<=1) players and *n* types of soldiers in total. Players Β«Call of Soldiers 3Β» are numbered form 1 to (*m*<=+<=1). Types of soldiers are numbered from 0 to *n*<=-<=1. Each player has an army. Army of the *i*-th player can be described by non-negative integer *x**i*. Consider binary representation of *x**i*: if the *j*-th bit of number *x**i* equal to one, then the army of the *i*-th player has soldiers of the *j*-th type.
Fedor is the (*m*<=+<=1)-th player of the game. He assume that two players can become friends if their armies differ in at most *k* types of soldiers (in other words, binary representations of the corresponding numbers differ in at most *k* bits). Help Fedor and count how many players can become his friends. | The first line contains three integers *n*, *m*, *k* (1<=β€<=*k*<=β€<=*n*<=β€<=20;Β 1<=β€<=*m*<=β€<=1000).
The *i*-th of the next (*m*<=+<=1) lines contains a single integer *x**i* (1<=β€<=*x**i*<=β€<=2*n*<=-<=1), that describes the *i*-th player's army. We remind you that Fedor is the (*m*<=+<=1)-th player. | Print a single integer β the number of Fedor's potential friends. | [
"7 3 1\n8\n5\n111\n17\n",
"3 3 3\n1\n2\n3\n4\n"
] | [
"0\n",
"3\n"
] | none | [
{
"input": "7 3 1\n8\n5\n111\n17",
"output": "0"
},
{
"input": "3 3 3\n1\n2\n3\n4",
"output": "3"
},
{
"input": "4 2 2\n5\n6\n7",
"output": "2"
},
{
"input": "4 7 4\n9\n10\n5\n12\n4\n12\n7\n10",
"output": "7"
},
{
"input": "2 7 2\n1\n1\n1\n1\n1\n1\n1\n1",
"out... | 62 | 0 | 3 | 3,164 | |
415 | Mashmokh and Lights | [
"implementation"
] | null | null | Mashmokh works in a factory. At the end of each day he must turn off all of the lights.
The lights on the factory are indexed from 1 to *n*. There are *n* buttons in Mashmokh's room indexed from 1 to *n* as well. If Mashmokh pushes button with index *i*, then each light with index not less than *i* that is still turned on turns off.
Mashmokh is not very clever. So instead of pushing the first button he pushes some of the buttons randomly each night. He pushed *m* distinct buttons *b*1,<=*b*2,<=...,<=*b**m* (the buttons were pushed consecutively in the given order) this night. Now he wants to know for each light the index of the button that turned this light off. Please note that the index of button *b**i* is actually *b**i*, not *i*.
Please, help Mashmokh, print these indices. | The first line of the input contains two space-separated integers *n* and *m* (1<=β€<=*n*,<=*m*<=β€<=100), the number of the factory lights and the pushed buttons respectively. The next line contains *m* distinct space-separated integers *b*1,<=*b*2,<=...,<=*b**m*Β (1<=β€<=*b**i*<=β€<=*n*).
It is guaranteed that all lights will be turned off after pushing all buttons. | Output *n* space-separated integers where the *i*-th number is index of the button that turns the *i*-th light off. | [
"5 4\n4 3 1 2\n",
"5 5\n5 4 3 2 1\n"
] | [
"1 1 3 4 4 \n",
"1 2 3 4 5 \n"
] | In the first sample, after pressing button number 4, lights 4 and 5 are turned off and lights 1, 2 and 3 are still on. Then after pressing button number 3, light number 3 is turned off as well. Pressing button number 1 turns off lights number 1 and 2 as well so pressing button number 2 in the end has no effect. Thus button number 4 turned lights 4 and 5 off, button number 3 turned light 3 off and button number 1 turned light 1 and 2 off. | [
{
"input": "5 4\n4 3 1 2",
"output": "1 1 3 4 4 "
},
{
"input": "5 5\n5 4 3 2 1",
"output": "1 2 3 4 5 "
},
{
"input": "16 11\n8 5 12 10 14 2 6 3 15 9 1",
"output": "1 2 2 2 5 5 5 8 8 8 8 8 8 8 8 8 "
},
{
"input": "79 22\n76 32 48 28 33 44 58 59 1 51 77 13 15 64 49 72 74 21 6... | 61 | 0 | 3 | 3,169 | |
366 | Dima and Salad | [
"dp"
] | null | null | Dima, Inna and Seryozha have gathered in a room. That's right, someone's got to go. To cheer Seryozha up and inspire him to have a walk, Inna decided to cook something.
Dima and Seryozha have *n* fruits in the fridge. Each fruit has two parameters: the taste and the number of calories. Inna decided to make a fruit salad, so she wants to take some fruits from the fridge for it. Inna follows a certain principle as she chooses the fruits: the total taste to the total calories ratio of the chosen fruits must equal *k*. In other words, , where *a**j* is the taste of the *j*-th chosen fruit and *b**j* is its calories.
Inna hasn't chosen the fruits yet, she is thinking: what is the maximum taste of the chosen fruits if she strictly follows her principle? Help Inna solve this culinary problem β now the happiness of a young couple is in your hands!
Inna loves Dima very much so she wants to make the salad from at least one fruit. | The first line of the input contains two integers *n*, *k* (1<=β€<=*n*<=β€<=100,<=1<=β€<=*k*<=β€<=10). The second line of the input contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=β€<=*a**i*<=β€<=100) β the fruits' tastes. The third line of the input contains *n* integers *b*1,<=*b*2,<=...,<=*b**n* (1<=β€<=*b**i*<=β€<=100) β the fruits' calories. Fruit number *i* has taste *a**i* and calories *b**i*. | If there is no way Inna can choose the fruits for the salad, print in the single line number -1. Otherwise, print a single integer β the maximum possible sum of the taste values of the chosen fruits. | [
"3 2\n10 8 1\n2 7 1\n",
"5 3\n4 4 4 4 4\n2 2 2 2 2\n"
] | [
"18\n",
"-1\n"
] | In the first test sample we can get the total taste of the fruits equal to 18 if we choose fruit number 1 and fruit number 2, then the total calories will equal 9. The condition <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/f7429bb0084a26268b364ce919a5231a4d9e38a9.png" style="max-width: 100.0%;max-height: 100.0%;"/> fulfills, that's exactly what Inna wants.
In the second test sample we cannot choose the fruits so as to follow Inna's principle. | [
{
"input": "3 2\n10 8 1\n2 7 1",
"output": "18"
},
{
"input": "5 3\n4 4 4 4 4\n2 2 2 2 2",
"output": "-1"
},
{
"input": "1 1\n1\n1",
"output": "1"
},
{
"input": "1 1\n1\n2",
"output": "-1"
},
{
"input": "2 1\n75 65\n16 60",
"output": "-1"
},
{
"input":... | 62 | 2,764,800 | -1 | 3,171 | |
145 | Lucky Conversion | [
"greedy",
"implementation"
] | null | null | Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
Petya has two strings *a* and *b* of the same length *n*. The strings consist only of lucky digits. Petya can perform operations of two types:
- replace any one digit from string *a* by its opposite (i.e., replace 4 by 7 and 7 by 4); - swap any pair of digits in string *a*.
Petya is interested in the minimum number of operations that are needed to make string *a* equal to string *b*. Help him with the task. | The first and the second line contains strings *a* and *b*, correspondingly. Strings *a* and *b* have equal lengths and contain only lucky digits. The strings are not empty, their length does not exceed 105. | Print on the single line the single number β the minimum number of operations needed to convert string *a* into string *b*. | [
"47\n74\n",
"774\n744\n",
"777\n444\n"
] | [
"1\n",
"1\n",
"3\n"
] | In the first sample it is enough simply to swap the first and the second digit.
In the second sample we should replace the second digit with its opposite.
In the third number we should replace all three digits with their opposites. | [
{
"input": "47\n74",
"output": "1"
},
{
"input": "774\n744",
"output": "1"
},
{
"input": "777\n444",
"output": "3"
},
{
"input": "74747474\n77777777",
"output": "4"
},
{
"input": "444444444444\n777777777777",
"output": "12"
},
{
"input": "4744744447774... | 310 | 307,200 | 3 | 3,172 | |
610 | Vika and Squares | [
"constructive algorithms",
"implementation"
] | null | null | Vika has *n* jars with paints of distinct colors. All the jars are numbered from 1 to *n* and the *i*-th jar contains *a**i* liters of paint of color *i*.
Vika also has an infinitely long rectangular piece of paper of width 1, consisting of squares of size 1<=Γ<=1. Squares are numbered 1, 2, 3 and so on. Vika decided that she will start painting squares one by one from left to right, starting from the square number 1 and some arbitrary color. If the square was painted in color *x*, then the next square will be painted in color *x*<=+<=1. In case of *x*<==<=*n*, next square is painted in color 1. If there is no more paint of the color Vika wants to use now, then she stops.
Square is always painted in only one color, and it takes exactly 1 liter of paint. Your task is to calculate the maximum number of squares that might be painted, if Vika chooses right color to paint the first square. | The first line of the input contains a single integer *n* (1<=β€<=*n*<=β€<=200<=000)Β β the number of jars with colors Vika has.
The second line of the input contains a sequence of integers *a*1,<=*a*2,<=...,<=*a**n* (1<=β€<=*a**i*<=β€<=109), where *a**i* is equal to the number of liters of paint in the *i*-th jar, i.e. the number of liters of color *i* that Vika has. | The only line of the output should contain a single integerΒ β the maximum number of squares that Vika can paint if she follows the rules described above. | [
"5\n2 4 2 3 3\n",
"3\n5 5 5\n",
"6\n10 10 10 1 10 10\n"
] | [
"12\n",
"15\n",
"11\n"
] | In the first sample the best strategy is to start painting using color 4. Then the squares will be painted in the following colors (from left to right): 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5.
In the second sample Vika can start to paint using any color.
In the third sample Vika should start painting using color number 5. | [
{
"input": "5\n2 4 2 3 3",
"output": "12"
},
{
"input": "3\n5 5 5",
"output": "15"
},
{
"input": "6\n10 10 10 1 10 10",
"output": "11"
},
{
"input": "1\n167959139",
"output": "167959139"
},
{
"input": "10\n896619242 805194919 844752453 848347723 816995848 85681361... | 280 | 20,172,800 | 0 | 3,185 | |
431 | Shower Line | [
"brute force",
"implementation"
] | null | null | Many students live in a dormitory. A dormitory is a whole new world of funny amusements and possibilities but it does have its drawbacks.
There is only one shower and there are multiple students who wish to have a shower in the morning. That's why every morning there is a line of five people in front of the dormitory shower door. As soon as the shower opens, the first person from the line enters the shower. After a while the first person leaves the shower and the next person enters the shower. The process continues until everybody in the line has a shower.
Having a shower takes some time, so the students in the line talk as they wait. At each moment of time the students talk in pairs: the (2*i*<=-<=1)-th man in the line (for the current moment) talks with the (2*i*)-th one.
Let's look at this process in more detail. Let's number the people from 1 to 5. Let's assume that the line initially looks as 23154 (person number 2 stands at the beginning of the line). Then, before the shower opens, 2 talks with 3, 1 talks with 5, 4 doesn't talk with anyone. Then 2 enters the shower. While 2 has a shower, 3 and 1 talk, 5 and 4 talk too. Then, 3 enters the shower. While 3 has a shower, 1 and 5 talk, 4 doesn't talk to anyone. Then 1 enters the shower and while he is there, 5 and 4 talk. Then 5 enters the shower, and then 4 enters the shower.
We know that if students *i* and *j* talk, then the *i*-th student's happiness increases by *g**ij* and the *j*-th student's happiness increases by *g**ji*. Your task is to find such initial order of students in the line that the total happiness of all students will be maximum in the end. Please note that some pair of students may have a talk several times. In the example above students 1 and 5 talk while they wait for the shower to open and while 3 has a shower. | The input consists of five lines, each line contains five space-separated integers: the *j*-th number in the *i*-th line shows *g**ij* (0<=β€<=*g**ij*<=β€<=105). It is guaranteed that *g**ii*<==<=0 for all *i*.
Assume that the students are numbered from 1 to 5. | Print a single integer β the maximum possible total happiness of the students. | [
"0 0 0 0 9\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n7 0 0 0 0\n",
"0 43 21 18 2\n3 0 21 11 65\n5 2 0 1 4\n54 62 12 0 99\n87 64 81 33 0\n"
] | [
"32\n",
"620\n"
] | In the first sample, the optimal arrangement of the line is 23154. In this case, the total happiness equals: | [
{
"input": "0 0 0 0 9\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n7 0 0 0 0",
"output": "32"
},
{
"input": "0 43 21 18 2\n3 0 21 11 65\n5 2 0 1 4\n54 62 12 0 99\n87 64 81 33 0",
"output": "620"
},
{
"input": "0 4 2 4 9\n6 0 2 5 0\n2 5 0 6 3\n6 3 3 0 10\n0 3 1 3 0",
"output": "63"
},
{
... | 77 | 2,969,600 | 3 | 3,199 | |
1,006 | Three Parts of the Array | [
"binary search",
"data structures",
"two pointers"
] | null | null | You are given an array $d_1, d_2, \dots, d_n$ consisting of $n$ integer numbers.
Your task is to split this array into three parts (some of which may be empty) in such a way that each element of the array belongs to exactly one of the three parts, and each of the parts forms a consecutive contiguous subsegment (possibly, empty) of the original array.
Let the sum of elements of the first part be $sum_1$, the sum of elements of the second part be $sum_2$ and the sum of elements of the third part be $sum_3$. Among all possible ways to split the array you have to choose a way such that $sum_1 = sum_3$ and $sum_1$ is maximum possible.
More formally, if the first part of the array contains $a$ elements, the second part of the array contains $b$ elements and the third part contains $c$ elements, then:
$$sum_1 = \sum\limits_{1 \le i \le a}d_i,$$ $$sum_2 = \sum\limits_{a + 1 \le i \le a + b}d_i,$$ $$sum_3 = \sum\limits_{a + b + 1 \le i \le a + b + c}d_i.$$
The sum of an empty array is $0$.
Your task is to find a way to split the array such that $sum_1 = sum_3$ and $sum_1$ is maximum possible. | The first line of the input contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) β the number of elements in the array $d$.
The second line of the input contains $n$ integers $d_1, d_2, \dots, d_n$ ($1 \le d_i \le 10^9$) β the elements of the array $d$. | Print a single integer β the maximum possible value of $sum_1$, considering that the condition $sum_1 = sum_3$ must be met.
Obviously, at least one valid way to split the array exists (use $a=c=0$ and $b=n$). | [
"5\n1 3 1 1 4\n",
"5\n1 3 2 1 4\n",
"3\n4 1 2\n"
] | [
"5\n",
"4\n",
"0\n"
] | In the first example there is only one possible splitting which maximizes $sum_1$: $[1, 3, 1], [~], [1, 4]$.
In the second example the only way to have $sum_1=4$ is: $[1, 3], [2, 1], [4]$.
In the third example there is only one way to split the array: $[~], [4, 1, 2], [~]$. | [
{
"input": "5\n1 3 1 1 4",
"output": "5"
},
{
"input": "5\n1 3 2 1 4",
"output": "4"
},
{
"input": "3\n4 1 2",
"output": "0"
},
{
"input": "1\n1000000000",
"output": "0"
},
{
"input": "2\n1 1",
"output": "1"
},
{
"input": "5\n1 3 5 4 5",
"output": ... | 421 | 34,713,600 | 3 | 3,200 | |
844 | Rectangles | [
"combinatorics",
"math"
] | null | null | You are given *n*<=Γ<=*m* table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color. 1. Every two cells in a set share row or column. | The first line of input contains integers *n* and *m* (1<=β€<=*n*,<=*m*<=β€<=50)Β β the number of rows and the number of columns correspondingly.
The next *n* lines of input contain descriptions of rows. There are *m* integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black. | Output single integer Β β the number of non-empty sets from the problem description. | [
"1 1\n0\n",
"2 3\n1 0 1\n0 1 0\n"
] | [
"1\n",
"8\n"
] | In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. | [
{
"input": "1 1\n0",
"output": "1"
},
{
"input": "2 3\n1 0 1\n0 1 0",
"output": "8"
},
{
"input": "2 2\n1 1\n1 1",
"output": "8"
},
{
"input": "1 10\n0 0 0 0 0 0 0 0 0 0",
"output": "1023"
},
{
"input": "11 1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1",
"output": "2047"... | 62 | 0 | 3 | 3,211 | |
792 | Divide by Three | [
"dp",
"greedy",
"math",
"number theory"
] | null | null | A positive integer number *n* is written on a blackboard. It consists of not more than 105 digits. You have to transform it into a beautiful number by erasing some of the digits, and you want to erase as few digits as possible.
The number is called beautiful if it consists of at least one digit, doesn't have leading zeroes and is a multiple of 3. For example, 0, 99, 10110 are beautiful numbers, and 00, 03, 122 are not.
Write a program which for the given *n* will find a beautiful number such that *n* can be transformed into this number by erasing as few digits as possible. You can erase an arbitraty set of digits. For example, they don't have to go one after another in the number *n*.
If it's impossible to obtain a beautiful number, print -1. If there are multiple answers, print any of them. | The first line of input contains *n* β a positive integer number without leading zeroes (1<=β€<=*n*<=<<=10100000). | Print one number β any beautiful number obtained by erasing as few as possible digits. If there is no answer, print <=-<=1. | [
"1033\n",
"10\n",
"11\n"
] | [
"33\n",
"0\n",
"-1\n"
] | In the first example it is enough to erase only the first digit to obtain a multiple of 3. But if we erase the first digit, then we obtain a number with a leading zero. So the minimum number of digits to be erased is two. | [
{
"input": "1033",
"output": "33"
},
{
"input": "10",
"output": "0"
},
{
"input": "11",
"output": "-1"
},
{
"input": "3",
"output": "3"
},
{
"input": "1",
"output": "-1"
},
{
"input": "117",
"output": "117"
},
{
"input": "518",
"output"... | 124 | 102,400 | 0 | 3,212 | |
292 | Copying Data | [
"data structures"
] | null | null | We often have to copy large volumes of information. Such operation can take up many computer resources. Therefore, in this problem you are advised to come up with a way to copy some part of a number array into another one, quickly.
More formally, you've got two arrays of integers *a*1,<=*a*2,<=...,<=*a**n* and *b*1,<=*b*2,<=...,<=*b**n* of length *n*. Also, you've got *m* queries of two types:
1. Copy the subsegment of array *a* of length *k*, starting from position *x*, into array *b*, starting from position *y*, that is, execute *b**y*<=+<=*q*<==<=*a**x*<=+<=*q* for all integer *q* (0<=β€<=*q*<=<<=*k*). The given operation is correct β both subsegments do not touch unexistent elements. 1. Determine the value in position *x* of array *b*, that is, find value *b**x*.
For each query of the second type print the result β the value of the corresponding element of array *b*. | The first line contains two space-separated integers *n* and *m* (1<=β€<=*n*,<=*m*<=β€<=105) β the number of elements in the arrays and the number of queries, correspondingly. The second line contains an array of integers *a*1,<=*a*2,<=...,<=*a**n* (|*a**i*|<=β€<=109). The third line contains an array of integers *b*1,<=*b*2,<=...,<=*b**n* (|*b**i*|<=β€<=109).
Next *m* lines contain the descriptions of the queries. The *i*-th line first contains integer *t**i* β the type of the *i*-th query (1<=β€<=*t**i*<=β€<=2). If *t**i*<==<=1, then the *i*-th query means the copying operation. If *t**i*<==<=2, then the *i*-th query means taking the value in array *b*. If *t**i*<==<=1, then the query type is followed by three integers *x**i*,<=*y**i*,<=*k**i* (1<=β€<=*x**i*,<=*y**i*,<=*k**i*<=β€<=*n*) β the parameters of the copying query. If *t**i*<==<=2, then the query type is followed by integer *x**i* (1<=β€<=*x**i*<=β€<=*n*) β the position in array *b*.
All numbers in the lines are separated with single spaces. It is guaranteed that all the queries are correct, that is, the copying borders fit into the borders of arrays *a* and *b*. | For each second type query print the result on a single line. | [
"5 10\n1 2 0 -1 3\n3 1 5 -2 0\n2 5\n1 3 3 3\n2 5\n2 4\n2 1\n1 2 1 4\n2 1\n2 4\n1 4 2 1\n2 2\n"
] | [
"0\n3\n-1\n3\n2\n3\n-1\n"
] | none | [
{
"input": "5 10\n1 2 0 -1 3\n3 1 5 -2 0\n2 5\n1 3 3 3\n2 5\n2 4\n2 1\n1 2 1 4\n2 1\n2 4\n1 4 2 1\n2 2",
"output": "0\n3\n-1\n3\n2\n3\n-1"
},
{
"input": "1 4\n-2\n1\n1 1 1 1\n2 1\n1 1 1 1\n1 1 1 1",
"output": "-2"
},
{
"input": "2 5\n-3 2\n3 -4\n1 1 1 2\n2 1\n2 1\n1 2 2 1\n2 1",
"out... | 2,000 | 7,987,200 | 0 | 3,224 | |
755 | PolandBall and Forest | [
"dfs and similar",
"dsu",
"graphs",
"interactive",
"trees"
] | null | null | PolandBall lives in a forest with his family. There are some trees in the forest. Trees are undirected acyclic graphs with *k* vertices and *k*<=-<=1 edges, where *k* is some integer. Note that one vertex is a valid tree.
There is exactly one relative living in each vertex of each tree, they have unique ids from 1 to *n*. For each Ball *i* we know the id of its most distant relative living on the same tree. If there are several such vertices, we only know the value of the one with smallest id among those.
How many trees are there in the forest? | The first line contains single integer *n* (1<=β€<=*n*<=β€<=104)Β β the number of Balls living in the forest.
The second line contains a sequence *p*1,<=*p*2,<=...,<=*p**n* of length *n*, where (1<=β€<=*p**i*<=β€<=*n*) holds and *p**i* denotes the most distant from Ball *i* relative living on the same tree. If there are several most distant relatives living on the same tree, *p**i* is the id of one with the smallest id.
It's guaranteed that the sequence *p* corresponds to some valid forest.
Hacking: To hack someone, you should provide a correct forest as a test. The sequence *p* will be calculated according to the forest and given to the solution you try to hack as input. Use the following format:
In the first line, output the integer *n* (1<=β€<=*n*<=β€<=104)Β β the number of Balls and the integer *m* (0<=β€<=*m*<=<<=*n*)Β β the total number of edges in the forest. Then *m* lines should follow. The *i*-th of them should contain two integers *a**i* and *b**i* and represent an edge between vertices in which relatives *a**i* and *b**i* live. For example, the first sample is written as follows: | You should output the number of trees in the forest where PolandBall lives. | [
"5\n2 1 5 3 3",
"1\n1\n"
] | [
"2",
"1"
] | In the first sample testcase, possible forest is: 1-2 3-4-5.
There are 2 trees overall.
In the second sample testcase, the only possible graph is one vertex and no edges. Therefore, there is only one tree. | [
{
"input": "5 3\n1 2\n3 4\n4 5",
"output": "2"
},
{
"input": "1 0",
"output": "1"
},
{
"input": "5 1\n4 5",
"output": "4"
},
{
"input": "10 3\n2 8\n5 9\n6 10",
"output": "7"
},
{
"input": "18 2\n9 17\n1 18",
"output": "16"
},
{
"input": "1 0",
"out... | 93 | 22,323,200 | -1 | 3,226 | |
103 | Cthulhu | [
"dfs and similar",
"dsu",
"graphs"
] | B. Cthulhu | 2 | 256 | ...Once upon a time a man came to the sea. The sea was stormy and dark. The man started to call for the little mermaid to appear but alas, he only woke up Cthulhu...
Whereas on the other end of the world Pentagon is actively collecting information trying to predict the monster's behavior and preparing the secret super weapon. Due to high seismic activity and poor weather conditions the satellites haven't yet been able to make clear shots of the monster. The analysis of the first shot resulted in an undirected graph with *n* vertices and *m* edges. Now the world's best minds are about to determine whether this graph can be regarded as Cthulhu or not.
To add simplicity, let's suppose that Cthulhu looks from the space like some spherical body with tentacles attached to it. Formally, we shall regard as Cthulhu such an undirected graph that can be represented as a set of three or more rooted trees, whose roots are connected by a simple cycle.
It is guaranteed that the graph contains no multiple edges and self-loops. | The first line contains two integers β the number of vertices *n* and the number of edges *m* of the graph (1<=β€<=*n*<=β€<=100, 0<=β€<=*m*<=β€<=).
Each of the following *m* lines contains a pair of integers *x* and *y*, that show that an edge exists between vertices *x* and *y* (1<=β€<=*x*,<=*y*<=β€<=*n*,<=*x*<=β <=*y*). For each pair of vertices there will be at most one edge between them, no edge connects a vertex to itself. | Print "NO", if the graph is not Cthulhu and "FHTAGN!" if it is. | [
"6 6\n6 3\n6 4\n5 1\n2 5\n1 4\n5 4\n",
"6 5\n5 6\n4 6\n3 1\n5 1\n1 2\n"
] | [
"FHTAGN!",
"NO"
] | Let us denote as a simple cycle a set of *v* vertices that can be numbered so that the edges will only exist between vertices number 1 and 2, 2 and 3, ..., *v*β-β1 and *v*, *v* and 1.
A tree is a connected undirected graph consisting of *n* vertices and *n*β-β1 edges (*n*β>β0).
A rooted tree is a tree where one vertex is selected to be the root. | [
{
"input": "6 6\n6 3\n6 4\n5 1\n2 5\n1 4\n5 4",
"output": "FHTAGN!"
},
{
"input": "6 5\n5 6\n4 6\n3 1\n5 1\n1 2",
"output": "NO"
},
{
"input": "10 10\n4 10\n8 5\n2 8\n4 9\n9 3\n2 7\n10 6\n10 2\n9 8\n1 8",
"output": "FHTAGN!"
},
{
"input": "5 4\n1 5\n1 3\n1 4\n3 2",
"outpu... | 186 | 6,656,000 | 0 | 3,227 |
990 | Bracket Sequences Concatenation Problem | [
"implementation"
] | null | null | A bracket sequence is a string containing only characters "(" and ")".
A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example, bracket sequences "()()", "(())" are regular (the resulting expressions are: "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.
You are given $n$ bracket sequences $s_1, s_2, \dots , s_n$. Calculate the number of pairs $i, j \, (1 \le i, j \le n)$ such that the bracket sequence $s_i + s_j$ is a regular bracket sequence. Operation $+$ means concatenation i.e. "()(" + ")()" = "()()()".
If $s_i + s_j$ and $s_j + s_i$ are regular bracket sequences and $i \ne j$, then both pairs $(i, j)$ and $(j, i)$ must be counted in the answer. Also, if $s_i + s_i$ is a regular bracket sequence, the pair $(i, i)$ must be counted in the answer. | The first line contains one integer $n \, (1 \le n \le 3 \cdot 10^5)$ β the number of bracket sequences. The following $n$ lines contain bracket sequences β non-empty strings consisting only of characters "(" and ")". The sum of lengths of all bracket sequences does not exceed $3 \cdot 10^5$. | In the single line print a single integer β the number of pairs $i, j \, (1 \le i, j \le n)$ such that the bracket sequence $s_i + s_j$ is a regular bracket sequence. | [
"3\n)\n()\n(\n",
"2\n()\n()\n"
] | [
"2\n",
"4\n"
] | In the first example, suitable pairs are $(3, 1)$ and $(2, 2)$.
In the second example, any pair is suitable, namely $(1, 1), (1, 2), (2, 1), (2, 2)$. | [
{
"input": "3\n)\n()\n(",
"output": "2"
},
{
"input": "2\n()\n()",
"output": "4"
},
{
"input": "7\n()(\n)\n)(\n())\n(((\n()()()\n()",
"output": "6"
},
{
"input": "6\n(\n((\n(((\n))))\n)))))\n))))))",
"output": "0"
},
{
"input": "9\n(()\n((())\n(\n)\n(()()(()())))\... | 2,000 | 5,324,800 | 0 | 3,228 | |
837 | Round Subset | [
"dp",
"math"
] | null | null | Let's call the roundness of the number the number of zeros to which it ends.
You have an array of *n* numbers. You need to choose a subset of exactly *k* numbers so that the roundness of the product of the selected numbers will be maximum possible. | The first line contains two integer numbers *n* and *k* (1<=β€<=*n*<=β€<=200,<=1<=β€<=*k*<=β€<=*n*).
The second line contains *n* space-separated integer numbers *a*1,<=*a*2,<=...,<=*a**n* (1<=β€<=*a**i*<=β€<=1018). | Print maximal roundness of product of the chosen subset of length *k*. | [
"3 2\n50 4 20\n",
"5 3\n15 16 3 25 9\n",
"3 3\n9 77 13\n"
] | [
"3\n",
"3\n",
"0\n"
] | In the first example there are 3 subsets of 2 numbers. [50,β4] has product 200 with roundness 2, [4,β20] β product 80, roundness 1, [50,β20] β product 1000, roundness 3.
In the second example subset [15,β16,β25] has product 6000, roundness 3.
In the third example all subsets has product with roundness 0. | [
{
"input": "3 2\n50 4 20",
"output": "3"
},
{
"input": "5 3\n15 16 3 25 9",
"output": "3"
},
{
"input": "3 3\n9 77 13",
"output": "0"
},
{
"input": "1 1\n200000000",
"output": "8"
},
{
"input": "1 1\n3",
"output": "0"
},
{
"input": "3 1\n10000000000000... | 30 | 0 | 0 | 3,234 | |
533 | Work Group | [
"dfs and similar",
"dp",
"graphs",
"strings",
"trees"
] | null | null | One Big Software Company has *n* employees numbered from 1 to *n*. The director is assigned number 1. Every employee of the company except the director has exactly one immediate superior. The director, of course, doesn't have a superior.
We will call person *a* a subordinates of another person *b*, if either *b* is an immediate supervisor of *a*, or the immediate supervisor of *a* is a subordinate to person *b*. In particular, subordinates of the head are all other employees of the company.
To solve achieve an Important Goal we need to form a workgroup. Every person has some efficiency, expressed by a positive integer *a**i*, where *i* is the person's number. The efficiency of the workgroup is defined as the total efficiency of all the people included in it.
The employees of the big software company are obsessed with modern ways of work process organization. Today pair programming is at the peak of popularity, so the workgroup should be formed with the following condition. Each person entering the workgroup should be able to sort all of his subordinates who are also in the workgroup into pairs. In other words, for each of the members of the workgroup the number of his subordinates within the workgroup should be even.
Your task is to determine the maximum possible efficiency of the workgroup formed at observing the given condition. Any person including the director of company can enter the workgroup. | The first line contains integer *n* (1<=β€<=*n*<=β€<=2Β·105) β the number of workers of the Big Software Company.
Then *n* lines follow, describing the company employees. The *i*-th line contains two integers *p**i*,<=*a**i* (1<=β€<=*a**i*<=β€<=105) β the number of the person who is the *i*-th employee's immediate superior and *i*-th employee's efficiency. For the director *p*1<==<=<=-<=1, for all other people the condition 1<=β€<=*p**i*<=<<=*i* is fulfilled. | Print a single integer β the maximum possible efficiency of the workgroup. | [
"7\n-1 3\n1 2\n1 1\n1 4\n4 5\n4 3\n5 2\n"
] | [
"17\n"
] | In the sample test the most effective way is to make a workgroup from employees number 1,β2,β4,β5,β6. | [
{
"input": "7\n-1 3\n1 2\n1 1\n1 4\n4 5\n4 3\n5 2",
"output": "17"
},
{
"input": "1\n-1 42",
"output": "42"
},
{
"input": "2\n-1 3\n1 2",
"output": "3"
},
{
"input": "3\n-1 3\n1 1\n1 2",
"output": "6"
},
{
"input": "3\n-1 1\n1 2\n1 3",
"output": "6"
},
{
... | 0 | 0 | -1 | 3,247 | |
919 | Perfect Number | [
"binary search",
"brute force",
"dp",
"implementation",
"number theory"
] | null | null | We consider a positive integer perfect, if and only if the sum of its digits is exactly $10$. Given a positive integer $k$, your task is to find the $k$-th smallest perfect positive integer. | A single line with a positive integer $k$ ($1 \leq k \leq 10\,000$). | A single number, denoting the $k$-th smallest perfect integer. | [
"1\n",
"2\n"
] | [
"19\n",
"28\n"
] | The first perfect integer is $19$ and the second one is $28$. | [
{
"input": "1",
"output": "19"
},
{
"input": "2",
"output": "28"
},
{
"input": "13",
"output": "136"
},
{
"input": "101",
"output": "1432"
},
{
"input": "1023",
"output": "100270"
},
{
"input": "9999",
"output": "10800010"
},
{
"input": "10... | 186 | 1,740,800 | 3 | 3,262 | |
713 | Sonya and Problem Wihtout a Legend | [
"dp",
"sortings"
] | null | null | Sonya was unable to think of a story for this problem, so here comes the formal description.
You are given the array containing *n* positive integers. At one turn you can pick any element and increase or decrease it by 1. The goal is the make the array strictly increasing by making the minimum possible number of operations. You are allowed to change elements in any way, they can become negative or equal to 0. | The first line of the input contains a single integer *n* (1<=β€<=*n*<=β€<=3000)Β β the length of the array.
Next line contains *n* integer *a**i* (1<=β€<=*a**i*<=β€<=109). | Print the minimum number of operation required to make the array strictly increasing. | [
"7\n2 1 5 11 5 9 11\n",
"5\n5 4 3 2 1\n"
] | [
"9\n",
"12\n"
] | In the first sample, the array is going to look as follows:
2 3 5 6 7 9 11
|2β-β2|β+β|1β-β3|β+β|5β-β5|β+β|11β-β6|β+β|5β-β7|β+β|9β-β9|β+β|11β-β11|β=β9
And for the second sample:
1 2 3 4 5
|5β-β1|β+β|4β-β2|β+β|3β-β3|β+β|2β-β4|β+β|1β-β5|β=β12 | [
{
"input": "7\n2 1 5 11 5 9 11",
"output": "9"
},
{
"input": "5\n5 4 3 2 1",
"output": "12"
},
{
"input": "2\n1 1000",
"output": "0"
},
{
"input": "2\n1000 1",
"output": "1000"
},
{
"input": "5\n100 80 60 70 90",
"output": "54"
},
{
"input": "10\n10 16... | 140 | 204,800 | 3 | 3,270 | |
701 | They Are Everywhere | [
"binary search",
"strings",
"two pointers"
] | null | null | Sergei B., the young coach of Pokemons, has found the big house which consists of *n* flats ordered in a row from left to right. It is possible to enter each flat from the street. It is possible to go out from each flat. Also, each flat is connected with the flat to the left and the flat to the right. Flat number 1 is only connected with the flat number 2 and the flat number *n* is only connected with the flat number *n*<=-<=1.
There is exactly one Pokemon of some type in each of these flats. Sergei B. asked residents of the house to let him enter their flats in order to catch Pokemons. After consulting the residents of the house decided to let Sergei B. enter one flat from the street, visit several flats and then go out from some flat. But they won't let him visit the same flat more than once.
Sergei B. was very pleased, and now he wants to visit as few flats as possible in order to collect Pokemons of all types that appear in this house. Your task is to help him and determine this minimum number of flats he has to visit. | The first line contains the integer *n* (1<=β€<=*n*<=β€<=100<=000) β the number of flats in the house.
The second line contains the row *s* with the length *n*, it consists of uppercase and lowercase letters of English alphabet, the *i*-th letter equals the type of Pokemon, which is in the flat number *i*. | Print the minimum number of flats which Sergei B. should visit in order to catch Pokemons of all types which there are in the house. | [
"3\nAaA\n",
"7\nbcAAcbc\n",
"6\naaBCCe\n"
] | [
"2\n",
"3\n",
"5\n"
] | In the first test Sergei B. can begin, for example, from the flat number 1 and end in the flat number 2.
In the second test Sergei B. can begin, for example, from the flat number 4 and end in the flat number 6.
In the third test Sergei B. must begin from the flat number 2 and end in the flat number 6. | [
{
"input": "3\nAaA",
"output": "2"
},
{
"input": "7\nbcAAcbc",
"output": "3"
},
{
"input": "6\naaBCCe",
"output": "5"
},
{
"input": "1\nA",
"output": "1"
},
{
"input": "1\ng",
"output": "1"
},
{
"input": "52\nabcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQ... | 171 | 4,710,400 | 3 | 3,278 | |
44 | Cola | [
"implementation"
] | B. Cola | 2 | 256 | To celebrate the opening of the Winter Computer School the organizers decided to buy in *n* liters of cola. However, an unexpected difficulty occurred in the shop: it turned out that cola is sold in bottles 0.5, 1 and 2 liters in volume. At that, there are exactly *a* bottles 0.5 in volume, *b* one-liter bottles and *c* of two-liter ones. The organizers have enough money to buy any amount of cola. What did cause the heated arguments was how many bottles of every kind to buy, as this question is pivotal for the distribution of cola among the participants (and organizers as well).
Thus, while the organizers are having the argument, discussing different variants of buying cola, the Winter School can't start. Your task is to count the number of all the possible ways to buy exactly *n* liters of cola and persuade the organizers that this number is too large, and if they keep on arguing, then the Winter Computer School will have to be organized in summer.
All the bottles of cola are considered indistinguishable, i.e. two variants of buying are different from each other only if they differ in the number of bottles of at least one kind. | The first line contains four integers β *n*, *a*, *b*, *c* (1<=β€<=*n*<=β€<=10000, 0<=β€<=*a*,<=*b*,<=*c*<=β€<=5000). | Print the unique number β the solution to the problem. If it is impossible to buy exactly *n* liters of cola, print 0. | [
"10 5 5 5\n",
"3 0 0 2\n"
] | [
"9\n",
"0\n"
] | none | [
{
"input": "10 5 5 5",
"output": "9"
},
{
"input": "3 0 0 2",
"output": "0"
},
{
"input": "1 0 0 0",
"output": "0"
},
{
"input": "1 1 0 0",
"output": "0"
},
{
"input": "1 2 0 0",
"output": "1"
},
{
"input": "1 0 1 0",
"output": "1"
},
{
"in... | 746 | 2,252,800 | 3.809304 | 3,300 |
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<=β€<=*n*<=β€<=2Β·104;Β 1<=β€<=*m*<=β€<=10;Β 1<=β€<=*k*<=β€<=2Β·105) β 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*<=Γ<=*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<=β€<=*x**i*<=β€<=*n*;Β 1<=β€<=*y**i*<=β€<=*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 | 15,052,800 | 0 | 3,303 | |
841 | Godsend | [
"games",
"math"
] | null | null | Leha somehow found an array consisting of *n* integers. Looking at it, he came up with a task. Two players play the game on the array. Players move one by one. The first player can choose for his move a subsegment of non-zero length with an odd sum of numbers and remove it from the array, after that the remaining parts are glued together into one array and the game continues. The second player can choose a subsegment of non-zero length with an even sum and remove it. Loses the one who can not make a move. Who will win if both play optimally? | First line of input data contains single integer *n* (1<=β€<=*n*<=β€<=106) β length of the array.
Next line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (0<=β€<=*a**i*<=β€<=109). | Output answer in single line. "First", if first player wins, and "Second" otherwise (without quotes). | [
"4\n1 3 2 3\n",
"2\n2 2\n"
] | [
"First\n",
"Second\n"
] | In first sample first player remove whole array in one move and win.
In second sample first player can't make a move and lose. | [
{
"input": "4\n1 3 2 3",
"output": "First"
},
{
"input": "2\n2 2",
"output": "Second"
},
{
"input": "4\n2 4 6 8",
"output": "Second"
},
{
"input": "5\n1 1 1 1 1",
"output": "First"
},
{
"input": "4\n720074544 345031254 849487632 80870826",
"output": "Second"
... | 467 | 57,446,400 | 3 | 3,311 | |
995 | Leaving the Bar | [
"brute force",
"data structures",
"geometry",
"greedy",
"math",
"sortings"
] | null | null | For a vector $\vec{v} = (x, y)$, define $|v| = \sqrt{x^2 + y^2}$.
Allen had a bit too much to drink at the bar, which is at the origin. There are $n$ vectors $\vec{v_1}, \vec{v_2}, \cdots, \vec{v_n}$. Allen will make $n$ moves. As Allen's sense of direction is impaired, during the $i$-th move he will either move in the direction $\vec{v_i}$ or $-\vec{v_i}$. In other words, if his position is currently $p = (x, y)$, he will either move to $p + \vec{v_i}$ or $p - \vec{v_i}$.
Allen doesn't want to wander too far from home (which happens to also be the bar). You need to help him figure out a sequence of moves (a sequence of signs for the vectors) such that his final position $p$ satisfies $|p| \le 1.5 \cdot 10^6$ so that he can stay safe. | The first line contains a single integer $n$ ($1 \le n \le 10^5$)Β β the number of moves.
Each of the following lines contains two space-separated integers $x_i$ and $y_i$, meaning that $\vec{v_i} = (x_i, y_i)$. We have that $|v_i| \le 10^6$ for all $i$. | Output a single line containing $n$ integers $c_1, c_2, \cdots, c_n$, each of which is either $1$ or $-1$. Your solution is correct if the value of $p = \sum_{i = 1}^n c_i \vec{v_i}$, satisfies $|p| \le 1.5 \cdot 10^6$.
It can be shown that a solution always exists under the given constraints. | [
"3\n999999 0\n0 999999\n999999 0\n",
"1\n-824590 246031\n",
"8\n-67761 603277\n640586 -396671\n46147 -122580\n569609 -2112\n400 914208\n131792 309779\n-850150 -486293\n5272 721899\n"
] | [
"1 1 -1 \n",
"1 \n",
"1 1 1 1 1 1 1 -1 \n"
] | none | [
{
"input": "3\n999999 0\n0 999999\n999999 0",
"output": "1 1 -1 "
},
{
"input": "1\n-824590 246031",
"output": "1 "
},
{
"input": "8\n-67761 603277\n640586 -396671\n46147 -122580\n569609 -2112\n400 914208\n131792 309779\n-850150 -486293\n5272 721899",
"output": "1 1 1 1 1 1 1 -1 "
... | 1,154 | 15,872,000 | 0 | 3,319 | |
38 | Blinds | [
"brute force"
] | C. Blinds | 2 | 256 | The blinds are known to consist of opaque horizontal stripes that can be rotated thus regulating the amount of light flowing in the room. There are *n* blind stripes with the width of 1 in the factory warehouse for blind production. The problem is that all of them are spare details from different orders, that is, they may not have the same length (it is even possible for them to have different lengths)
Every stripe can be cut into two or more parts. The cuttings are made perpendicularly to the side along which the length is measured. Thus the cuttings do not change the width of a stripe but each of the resulting pieces has a lesser length (the sum of which is equal to the length of the initial stripe)
After all the cuttings the blinds are constructed through consecutive joining of several parts, similar in length, along sides, along which length is measured. Also, apart from the resulting pieces an initial stripe can be used as a blind if it hasn't been cut. It is forbidden to construct blinds in any other way.
Thus, if the blinds consist of *k* pieces each *d* in length, then they are of form of a rectangle of *k*<=Γ<=*d* bourlemeters.
Your task is to find for what window possessing the largest possible area the blinds can be made from the given stripes if on technical grounds it is forbidden to use pieces shorter than *l* bourlemeter. The window is of form of a rectangle with side lengths as positive integers. | The first output line contains two space-separated integers *n* and *l* (1<=β€<=*n*,<=*l*<=β€<=100). They are the number of stripes in the warehouse and the minimal acceptable length of a blind stripe in bourlemeters. The second line contains space-separated *n* integers *a**i*. They are the lengths of initial stripes in bourlemeters (1<=β€<=*a**i*<=β€<=100). | Print the single number β the maximal area of the window in square bourlemeters that can be completely covered. If no window with a positive area that can be covered completely without breaking any of the given rules exist, then print the single number 0. | [
"4 2\n1 2 3 4\n",
"5 3\n5 5 7 3 1\n",
"2 3\n1 2\n"
] | [
"8\n",
"15\n",
"0\n"
] | In the first sample test the required window is 2βΓβ4 in size and the blinds for it consist of 4 parts, each 2 bourlemeters long. One of the parts is the initial stripe with the length of 2, the other one is a part of a cut stripe with the length of 3 and the two remaining stripes are parts of a stripe with the length of 4 cut in halves. | [
{
"input": "4 2\n1 2 3 4",
"output": "8"
},
{
"input": "5 3\n5 5 7 3 1",
"output": "15"
},
{
"input": "2 3\n1 2",
"output": "0"
},
{
"input": "2 2\n3 3",
"output": "6"
},
{
"input": "5 2\n2 4 1 1 3",
"output": "8"
},
{
"input": "7 4\n3 2 1 1 1 3 2",
... | 124 | 0 | 0 | 3,325 |
493 | Vasya and Wrestling | [
"implementation"
] | null | null | Vasya has become interested in wrestling. In wrestling wrestlers use techniques for which they are awarded points by judges. The wrestler who gets the most points wins.
When the numbers of points of both wrestlers are equal, the wrestler whose sequence of points is lexicographically greater, wins.
If the sequences of the awarded points coincide, the wrestler who performed the last technique wins. Your task is to determine which wrestler won. | The first line contains number *n* β the number of techniques that the wrestlers have used (1<=β€<=*n*<=β€<=2Β·105).
The following *n* lines contain integer numbers *a**i* (|*a**i*|<=β€<=109, *a**i*<=β <=0). If *a**i* is positive, that means that the first wrestler performed the technique that was awarded with *a**i* points. And if *a**i* is negative, that means that the second wrestler performed the technique that was awarded with (<=-<=*a**i*) points.
The techniques are given in chronological order. | If the first wrestler wins, print string "first", otherwise print "second" | [
"5\n1\n2\n-3\n-4\n3\n",
"3\n-1\n-2\n3\n",
"2\n4\n-4\n"
] | [
"second\n",
"first\n",
"second\n"
] | Sequence *x*ββ=ββ*x*<sub class="lower-index">1</sub>*x*<sub class="lower-index">2</sub>... *x*<sub class="lower-index">|*x*|</sub> is lexicographically larger than sequence *y*ββ=ββ*y*<sub class="lower-index">1</sub>*y*<sub class="lower-index">2</sub>... *y*<sub class="lower-index">|*y*|</sub>, if either |*x*|ββ>ββ|*y*| and *x*<sub class="lower-index">1</sub>ββ=ββ*y*<sub class="lower-index">1</sub>,ββ*x*<sub class="lower-index">2</sub>ββ=ββ*y*<sub class="lower-index">2</sub>,β... ,ββ*x*<sub class="lower-index">|*y*|</sub>ββ=ββ*y*<sub class="lower-index">|*y*|</sub>, or there is such number *r* (*r*ββ<ββ|*x*|,β*r*ββ<ββ|*y*|), that *x*<sub class="lower-index">1</sub>ββ=ββ*y*<sub class="lower-index">1</sub>,ββ*x*<sub class="lower-index">2</sub>ββ=ββ*y*<sub class="lower-index">2</sub>,ββ... ,ββ*x*<sub class="lower-index">*r*</sub>ββ=ββ*y*<sub class="lower-index">*r*</sub> and *x*<sub class="lower-index">*r*ββ+ββ1</sub>ββ>ββ*y*<sub class="lower-index">*r*ββ+ββ1</sub>.
We use notation |*a*| to denote length of sequence *a*. | [
{
"input": "5\n1\n2\n-3\n-4\n3",
"output": "second"
},
{
"input": "3\n-1\n-2\n3",
"output": "first"
},
{
"input": "2\n4\n-4",
"output": "second"
},
{
"input": "7\n1\n2\n-3\n4\n5\n-6\n7",
"output": "first"
},
{
"input": "14\n1\n2\n3\n4\n5\n6\n7\n-8\n-9\n-10\n-11\n-... | 390 | 6,144,000 | 0 | 3,326 | |
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<=β€<=*n*,<=*k*<=β€<=100; 1<=β€<=*d*<=β€<=*k*). | Print a single integer β 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... | 31 | 0 | 0 | 3,330 | |
913 | Power Substring | [
"math",
"number theory"
] | null | null | You are given *n* positive integers *a*1,<=*a*2,<=...,<=*a**n*.
For every *a**i* you need to find a positive integer *k**i* such that the decimal notation of 2*k**i* contains the decimal notation of *a**i* as a substring among its last *min*(100,<=*length*(2*k**i*)) digits. Here *length*(*m*) is the length of the decimal notation of *m*.
Note that you don't have to minimize *k**i*. The decimal notations in this problem do not contain leading zeros. | The first line contains a single integer *n* (1<=β€<=*n*<=β€<=2<=000)Β β the number of integers *a**i*.
Each of the next *n* lines contains a positive integer *a**i* (1<=β€<=*a**i*<=<<=1011). | Print *n* lines. The *i*-th of them should contain a positive integer *k**i* such that the last *min*(100,<=*length*(2*k**i*)) digits of 2*k**i* contain the decimal notation of *a**i* as a substring. Integers *k**i* must satisfy 1<=β€<=*k**i*<=β€<=1050.
It can be shown that the answer always exists under the given constraints. If there are multiple answers, print any of them. | [
"2\n8\n2\n",
"2\n3\n4857\n"
] | [
"3\n1\n",
"5\n20\n"
] | none | [
{
"input": "2\n8\n2",
"output": "3\n1"
},
{
"input": "2\n3\n4857",
"output": "5\n20"
},
{
"input": "7\n1\n7\n9\n5\n6\n10\n4",
"output": "9\n17\n13\n21\n4\n42\n2"
},
{
"input": "10\n384\n179\n982\n466\n646\n226\n759\n798\n291\n852",
"output": "14\n493\n230\n150\n66\n2050\n... | 140 | 7,168,000 | 3 | 3,335 | |
485 | Valuable Resources | [
"brute force",
"greedy"
] | null | null | Many computer strategy games require building cities, recruiting army, conquering tribes, collecting resources. Sometimes it leads to interesting problems.
Let's suppose that your task is to build a square city. The world map uses the Cartesian coordinates. The sides of the city should be parallel to coordinate axes. The map contains mines with valuable resources, located at some points with integer coordinates. The sizes of mines are relatively small, i.e. they can be treated as points. The city should be built in such a way that all the mines are inside or on the border of the city square.
Building a city takes large amount of money depending on the size of the city, so you have to build the city with the minimum area. Given the positions of the mines find the minimum possible area of the city. | The first line of the input contains number *n*Β β the number of mines on the map (2<=β€<=*n*<=β€<=1000). Each of the next *n* lines contains a pair of integers *x**i* and *y**i*Β β the coordinates of the corresponding mine (<=-<=109<=β€<=*x**i*,<=*y**i*<=β€<=109). All points are pairwise distinct. | Print the minimum area of the city that can cover all the mines with valuable resources. | [
"2\n0 0\n2 2\n",
"2\n0 0\n0 3\n"
] | [
"4\n",
"9\n"
] | none | [
{
"input": "2\n0 0\n2 2",
"output": "4"
},
{
"input": "2\n0 0\n0 3",
"output": "9"
},
{
"input": "2\n0 1\n1 0",
"output": "1"
},
{
"input": "3\n2 2\n1 1\n3 3",
"output": "4"
},
{
"input": "3\n3 1\n1 3\n2 2",
"output": "4"
},
{
"input": "3\n0 1\n1 0\n2 ... | 46 | 0 | 0 | 3,344 | |
548 | Mike and Fun | [
"brute force",
"dp",
"greedy",
"implementation"
] | null | null | Mike and some bears are playing a game just for fun. Mike is the judge. All bears except Mike are standing in an *n*<=Γ<=*m* grid, there's exactly one bear in each cell. We denote the bear standing in column number *j* of row number *i* by (*i*,<=*j*). Mike's hands are on his ears (since he's the judge) and each bear standing in the grid has hands either on his mouth or his eyes.
They play for *q* rounds. In each round, Mike chooses a bear (*i*,<=*j*) and tells him to change his state i. e. if his hands are on his mouth, then he'll put his hands on his eyes or he'll put his hands on his mouth otherwise. After that, Mike wants to know the score of the bears.
Score of the bears is the maximum over all rows of number of consecutive bears with hands on their eyes in that row.
Since bears are lazy, Mike asked you for help. For each round, tell him the score of these bears after changing the state of a bear selected in that round. | The first line of input contains three integers *n*, *m* and *q* (1<=β€<=*n*,<=*m*<=β€<=500 and 1<=β€<=*q*<=β€<=5000).
The next *n* lines contain the grid description. There are *m* integers separated by spaces in each line. Each of these numbers is either 0 (for mouth) or 1 (for eyes).
The next *q* lines contain the information about the rounds. Each of them contains two integers *i* and *j* (1<=β€<=*i*<=β€<=*n* and 1<=β€<=*j*<=β€<=*m*), the row number and the column number of the bear changing his state. | After each round, print the current score of the bears. | [
"5 4 5\n0 1 1 0\n1 0 0 1\n0 1 1 0\n1 0 0 1\n0 0 0 0\n1 1\n1 4\n1 1\n4 2\n4 3\n"
] | [
"3\n4\n3\n3\n4\n"
] | none | [
{
"input": "5 4 5\n0 1 1 0\n1 0 0 1\n0 1 1 0\n1 0 0 1\n0 0 0 0\n1 1\n1 4\n1 1\n4 2\n4 3",
"output": "3\n4\n3\n3\n4"
},
{
"input": "2 2 10\n1 1\n0 1\n1 1\n2 1\n1 1\n2 2\n1 1\n2 1\n2 2\n2 2\n1 1\n1 1",
"output": "1\n2\n2\n2\n1\n1\n1\n1\n2\n1"
},
{
"input": "2 2 10\n1 1\n0 1\n2 2\n2 2\n1 1\... | 686 | 15,155,200 | 3 | 3,347 |
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