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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
540 | Ice Cave | [
"dfs and similar"
] | null | null | You play a computer game. Your character stands on some level of a multilevel ice cave. In order to move on forward, you need to descend one level lower and the only way to do this is to fall through the ice.
The level of the cave where you are is a rectangular square grid of *n* rows and *m* columns. Each cell consists either from intact or from cracked ice. From each cell you can move to cells that are side-adjacent with yours (due to some limitations of the game engine you cannot make jumps on the same place, i.e. jump from a cell to itself). If you move to the cell with cracked ice, then your character falls down through it and if you move to the cell with intact ice, then the ice on this cell becomes cracked.
Let's number the rows with integers from 1 to *n* from top to bottom and the columns with integers from 1 to *m* from left to right. Let's denote a cell on the intersection of the *r*-th row and the *c*-th column as (*r*,<=*c*).
You are staying in the cell (*r*1,<=*c*1) and this cell is cracked because you've just fallen here from a higher level. You need to fall down through the cell (*r*2,<=*c*2) since the exit to the next level is there. Can you do this? | The first line contains two integers, *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=500) — the number of rows and columns in the cave description.
Each of the next *n* lines describes the initial state of the level of the cave, each line consists of *m* characters "." (that is, intact ice) and "X" (cracked ice).
The next line contains two integers, *r*1 and *c*1 (1<=≤<=*r*1<=≤<=*n*,<=1<=≤<=*c*1<=≤<=*m*) — your initial coordinates. It is guaranteed that the description of the cave contains character 'X' in cell (*r*1,<=*c*1), that is, the ice on the starting cell is initially cracked.
The next line contains two integers *r*2 and *c*2 (1<=≤<=*r*2<=≤<=*n*,<=1<=≤<=*c*2<=≤<=*m*) — the coordinates of the cell through which you need to fall. The final cell may coincide with the starting one. | If you can reach the destination, print 'YES', otherwise print 'NO'. | [
"4 6\nX...XX\n...XX.\n.X..X.\n......\n1 6\n2 2\n",
"5 4\n.X..\n...X\nX.X.\n....\n.XX.\n5 3\n1 1\n",
"4 7\n..X.XX.\n.XX..X.\nX...X..\nX......\n2 2\n1 6\n"
] | [
"YES\n",
"NO\n",
"YES\n"
] | In the first sample test one possible path is:
<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/c61f56de718beea14935ccdc85ae2c4ad45c1454.png" style="max-width: 100.0%;max-height: 100.0%;"/>
After the first visit of cell (2, 2) the ice on it cracks and when you step there for the second time, your character falls through the ice as intended. | [
{
"input": "4 6\nX...XX\n...XX.\n.X..X.\n......\n1 6\n2 2",
"output": "YES"
},
{
"input": "5 4\n.X..\n...X\nX.X.\n....\n.XX.\n5 3\n1 1",
"output": "NO"
},
{
"input": "4 7\n..X.XX.\n.XX..X.\nX...X..\nX......\n2 2\n1 6",
"output": "YES"
},
{
"input": "5 3\n.XX\n...\n.X.\n.X.\n.... | 46 | 2,150,400 | -1 | 1,384 | |
814 | An abandoned sentiment from past | [
"constructive algorithms",
"greedy",
"implementation",
"sortings"
] | null | null | A few years ago, Hitagi encountered a giant crab, who stole the whole of her body weight. Ever since, she tried to avoid contact with others, for fear that this secret might be noticed.
To get rid of the oddity and recover her weight, a special integer sequence is needed. Hitagi's sequence has been broken for a long time, but now Kaiki provides an opportunity.
Hitagi's sequence *a* has a length of *n*. Lost elements in it are denoted by zeros. Kaiki provides another sequence *b*, whose length *k* equals the number of lost elements in *a* (i.e. the number of zeros). Hitagi is to replace each zero in *a* with an element from *b* so that each element in *b* should be used exactly once. Hitagi knows, however, that, apart from 0, no integer occurs in *a* and *b* more than once in total.
If the resulting sequence is not an increasing sequence, then it has the power to recover Hitagi from the oddity. You are to determine whether this is possible, or Kaiki's sequence is just another fake. In other words, you should detect whether it is possible to replace each zero in *a* with an integer from *b* so that each integer from *b* is used exactly once, and the resulting sequence is not increasing. | The first line of input contains two space-separated positive integers *n* (2<=≤<=*n*<=≤<=100) and *k* (1<=≤<=*k*<=≤<=*n*) — the lengths of sequence *a* and *b* respectively.
The second line contains *n* space-separated integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=200) — Hitagi's broken sequence with exactly *k* zero elements.
The third line contains *k* space-separated integers *b*1,<=*b*2,<=...,<=*b**k* (1<=≤<=*b**i*<=≤<=200) — the elements to fill into Hitagi's sequence.
Input guarantees that apart from 0, no integer occurs in *a* and *b* more than once in total. | Output "Yes" if it's possible to replace zeros in *a* with elements in *b* and make the resulting sequence not increasing, and "No" otherwise. | [
"4 2\n11 0 0 14\n5 4\n",
"6 1\n2 3 0 8 9 10\n5\n",
"4 1\n8 94 0 4\n89\n",
"7 7\n0 0 0 0 0 0 0\n1 2 3 4 5 6 7\n"
] | [
"Yes\n",
"No\n",
"Yes\n",
"Yes\n"
] | In the first sample:
- Sequence *a* is 11, 0, 0, 14. - Two of the elements are lost, and the candidates in *b* are 5 and 4. - There are two possible resulting sequences: 11, 5, 4, 14 and 11, 4, 5, 14, both of which fulfill the requirements. Thus the answer is "Yes".
In the second sample, the only possible resulting sequence is 2, 3, 5, 8, 9, 10, which is an increasing sequence and therefore invalid. | [
{
"input": "4 2\n11 0 0 14\n5 4",
"output": "Yes"
},
{
"input": "6 1\n2 3 0 8 9 10\n5",
"output": "No"
},
{
"input": "4 1\n8 94 0 4\n89",
"output": "Yes"
},
{
"input": "7 7\n0 0 0 0 0 0 0\n1 2 3 4 5 6 7",
"output": "Yes"
},
{
"input": "40 1\n23 26 27 28 31 35 38 4... | 61 | 0 | 3 | 1,387 | |
778 | String Game | [
"binary search",
"greedy",
"strings"
] | null | null | Little Nastya has a hobby, she likes to remove some letters from word, to obtain another word. But it turns out to be pretty hard for her, because she is too young. Therefore, her brother Sergey always helps her.
Sergey gives Nastya the word *t* and wants to get the word *p* out of it. Nastya removes letters in a certain order (one after another, in this order strictly), which is specified by permutation of letters' indices of the word *t*: *a*1... *a*|*t*|. We denote the length of word *x* as |*x*|. Note that after removing one letter, the indices of other letters don't change. For example, if *t*<==<="nastya" and *a*<==<=[4,<=1,<=5,<=3,<=2,<=6] then removals make the following sequence of words "nastya" "nastya" "nastya" "nastya" "nastya" "nastya" "nastya".
Sergey knows this permutation. His goal is to stop his sister at some point and continue removing by himself to get the word *p*. Since Nastya likes this activity, Sergey wants to stop her as late as possible. Your task is to determine, how many letters Nastya can remove before she will be stopped by Sergey.
It is guaranteed that the word *p* can be obtained by removing the letters from word *t*. | The first and second lines of the input contain the words *t* and *p*, respectively. Words are composed of lowercase letters of the Latin alphabet (1<=≤<=|*p*|<=<<=|*t*|<=≤<=200<=000). It is guaranteed that the word *p* can be obtained by removing the letters from word *t*.
Next line contains a permutation *a*1,<=*a*2,<=...,<=*a*|*t*| of letter indices that specifies the order in which Nastya removes letters of *t* (1<=≤<=*a**i*<=≤<=|*t*|, all *a**i* are distinct). | Print a single integer number, the maximum number of letters that Nastya can remove. | [
"ababcba\nabb\n5 3 4 1 7 6 2\n",
"bbbabb\nbb\n1 6 3 4 2 5\n"
] | [
"3",
"4"
] | In the first sample test sequence of removing made by Nastya looks like this:
"ababcba" <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> "ababcba" <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> "ababcba" <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> "ababcba"
Nastya can not continue, because it is impossible to get word "abb" from word "ababcba".
So, Nastya will remove only three letters. | [
{
"input": "ababcba\nabb\n5 3 4 1 7 6 2",
"output": "3"
},
{
"input": "bbbabb\nbb\n1 6 3 4 2 5",
"output": "4"
},
{
"input": "cacaccccccacccc\ncacc\n10 9 14 5 1 7 15 3 6 12 4 8 11 13 2",
"output": "9"
},
{
"input": "aaaabaaabaabaaaaaaaa\naaaa\n18 5 4 6 13 9 1 3 7 8 16 10 12 1... | 140 | 307,200 | 0 | 1,390 | |
160 | Edges in MST | [
"dfs and similar",
"dsu",
"graphs",
"sortings"
] | null | null | You are given a connected weighted undirected graph without any loops and multiple edges.
Let us remind you that a graph's spanning tree is defined as an acyclic connected subgraph of the given graph that includes all of the graph's vertexes. The weight of a tree is defined as the sum of weights of the edges that the given tree contains. The minimum spanning tree (MST) of a graph is defined as the graph's spanning tree having the minimum possible weight. For any connected graph obviously exists the minimum spanning tree, but in the general case, a graph's minimum spanning tree is not unique.
Your task is to determine the following for each edge of the given graph: whether it is either included in any MST, or included at least in one MST, or not included in any MST. | The first line contains two integers *n* and *m* (2<=≤<=*n*<=≤<=105, ) — the number of the graph's vertexes and edges, correspondingly. Then follow *m* lines, each of them contains three integers — the description of the graph's edges as "*a**i* *b**i* *w**i*" (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*,<=1<=≤<=*w**i*<=≤<=106,<=*a**i*<=≠<=*b**i*), where *a**i* and *b**i* are the numbers of vertexes connected by the *i*-th edge, *w**i* is the edge's weight. It is guaranteed that the graph is connected and doesn't contain loops or multiple edges. | Print *m* lines — the answers for all edges. If the *i*-th edge is included in any MST, print "any"; if the *i*-th edge is included at least in one MST, print "at least one"; if the *i*-th edge isn't included in any MST, print "none". Print the answers for the edges in the order in which the edges are specified in the input. | [
"4 5\n1 2 101\n1 3 100\n2 3 2\n2 4 2\n3 4 1\n",
"3 3\n1 2 1\n2 3 1\n1 3 2\n",
"3 3\n1 2 1\n2 3 1\n1 3 1\n"
] | [
"none\nany\nat least one\nat least one\nany\n",
"any\nany\nnone\n",
"at least one\nat least one\nat least one\n"
] | In the second sample the MST is unique for the given graph: it contains two first edges.
In the third sample any two edges form the MST for the given graph. That means that each edge is included at least in one MST. | [] | 109 | 16,896,000 | 0 | 1,394 | |
416 | Art Union | [
"brute force",
"dp",
"implementation"
] | null | null | A well-known art union called "Kalevich is Alive!" manufactures objects d'art (pictures). The union consists of *n* painters who decided to organize their work as follows.
Each painter uses only the color that was assigned to him. The colors are distinct for all painters. Let's assume that the first painter uses color 1, the second one uses color 2, and so on. Each picture will contain all these *n* colors. Adding the *j*-th color to the *i*-th picture takes the *j*-th painter *t**ij* units of time.
Order is important everywhere, so the painters' work is ordered by the following rules:
- Each picture is first painted by the first painter, then by the second one, and so on. That is, after the *j*-th painter finishes working on the picture, it must go to the (*j*<=+<=1)-th painter (if *j*<=<<=*n*); - each painter works on the pictures in some order: first, he paints the first picture, then he paints the second picture and so on; - each painter can simultaneously work on at most one picture. However, the painters don't need any time to have a rest; - as soon as the *j*-th painter finishes his part of working on the picture, the picture immediately becomes available to the next painter.
Given that the painters start working at time 0, find for each picture the time when it is ready for sale. | The first line of the input contains integers *m*,<=*n* (1<=≤<=*m*<=≤<=50000,<=1<=≤<=*n*<=≤<=5), where *m* is the number of pictures and *n* is the number of painters. Then follow the descriptions of the pictures, one per line. Each line contains *n* integers *t**i*1,<=*t**i*2,<=...,<=*t**in* (1<=≤<=*t**ij*<=≤<=1000), where *t**ij* is the time the *j*-th painter needs to work on the *i*-th picture. | Print the sequence of *m* integers *r*1,<=*r*2,<=...,<=*r**m*, where *r**i* is the moment when the *n*-th painter stopped working on the *i*-th picture. | [
"5 1\n1\n2\n3\n4\n5\n",
"4 2\n2 5\n3 1\n5 3\n10 1\n"
] | [
"1 3 6 10 15 ",
"7 8 13 21 "
] | none | [
{
"input": "5 1\n1\n2\n3\n4\n5",
"output": "1 3 6 10 15 "
},
{
"input": "4 2\n2 5\n3 1\n5 3\n10 1",
"output": "7 8 13 21 "
},
{
"input": "1 1\n66",
"output": "66 "
},
{
"input": "2 2\n1 1\n1 1",
"output": "2 3 "
},
{
"input": "2 2\n10 1\n10 1",
"output": "11 2... | 374 | 16,896,000 | 3 | 1,395 | |
190 | Vasya and the Bus | [
"greedy",
"math"
] | null | null | One day Vasya heard a story: "In the city of High Bertown a bus number 62 left from the bus station. It had *n* grown-ups and *m* kids..."
The latter events happen to be of no importance to us. Vasya is an accountant and he loves counting money. So he wondered what maximum and minimum sum of money these passengers could have paid for the ride.
The bus fare equals one berland ruble in High Bertown. However, not everything is that easy — no more than one child can ride for free with each grown-up passenger. That means that a grown-up passenger who rides with his *k* (*k*<=><=0) children, pays overall *k* rubles: a ticket for himself and (*k*<=-<=1) tickets for his children. Also, a grown-up can ride without children, in this case he only pays one ruble.
We know that in High Bertown children can't ride in a bus unaccompanied by grown-ups.
Help Vasya count the minimum and the maximum sum in Berland rubles, that all passengers of this bus could have paid in total. | The input file consists of a single line containing two space-separated numbers *n* and *m* (0<=≤<=*n*,<=*m*<=≤<=105) — the number of the grown-ups and the number of the children in the bus, correspondingly. | If *n* grown-ups and *m* children could have ridden in the bus, then print on a single line two space-separated integers — the minimum and the maximum possible total bus fare, correspondingly.
Otherwise, print "Impossible" (without the quotes). | [
"1 2\n",
"0 5\n",
"2 2\n"
] | [
"2 2",
"Impossible",
"2 3"
] | In the first sample a grown-up rides with two children and pays two rubles.
In the second sample there are only children in the bus, so the situation is impossible.
In the third sample there are two cases: - Each of the two grown-ups rides with one children and pays one ruble for the tickets. In this case the passengers pay two rubles in total. - One of the grown-ups ride with two children's and pays two rubles, the another one rides alone and pays one ruble for himself. So, they pay three rubles in total. | [
{
"input": "1 2",
"output": "2 2"
},
{
"input": "0 5",
"output": "Impossible"
},
{
"input": "2 2",
"output": "2 3"
},
{
"input": "2 7",
"output": "7 8"
},
{
"input": "4 10",
"output": "10 13"
},
{
"input": "6 0",
"output": "6 6"
},
{
"input... | 0 | 0 | -1 | 1,403 | |
817 | Treasure Hunt | [
"implementation",
"math",
"number theory"
] | null | null | Captain Bill the Hummingbird and his crew recieved an interesting challenge offer. Some stranger gave them a map, potion of teleportation and said that only this potion might help them to reach the treasure.
Bottle with potion has two values *x* and *y* written on it. These values define four moves which can be performed using the potion:
- - - -
Map shows that the position of Captain Bill the Hummingbird is (*x*1,<=*y*1) and the position of the treasure is (*x*2,<=*y*2).
You task is to tell Captain Bill the Hummingbird whether he should accept this challenge or decline. If it is possible for Captain to reach the treasure using the potion then output "YES", otherwise "NO" (without quotes).
The potion can be used infinite amount of times. | The first line contains four integer numbers *x*1,<=*y*1,<=*x*2,<=*y*2 (<=-<=105<=≤<=*x*1,<=*y*1,<=*x*2,<=*y*2<=≤<=105) — positions of Captain Bill the Hummingbird and treasure respectively.
The second line contains two integer numbers *x*,<=*y* (1<=≤<=*x*,<=*y*<=≤<=105) — values on the potion bottle. | Print "YES" if it is possible for Captain to reach the treasure using the potion, otherwise print "NO" (without quotes). | [
"0 0 0 6\n2 3\n",
"1 1 3 6\n1 5\n"
] | [
"YES\n",
"NO\n"
] | In the first example there exists such sequence of moves:
1. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7c939890fb4ed35688177327dac981bfa9216c00.png" style="max-width: 100.0%;max-height: 100.0%;"/> — the first type of move 1. <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/afbfa42fbac4e0641e7466e3aac74cbbb08ed597.png" style="max-width: 100.0%;max-height: 100.0%;"/> — the third type of move | [
{
"input": "0 0 0 6\n2 3",
"output": "YES"
},
{
"input": "1 1 3 6\n1 5",
"output": "NO"
},
{
"input": "5 4 6 -10\n1 1",
"output": "NO"
},
{
"input": "6 -3 -7 -7\n1 2",
"output": "NO"
},
{
"input": "2 -5 -8 8\n2 1",
"output": "YES"
},
{
"input": "70 -81... | 62 | 0 | 3 | 1,408 | |
195 | After Training | [
"data structures",
"implementation",
"math"
] | null | null | After a team finished their training session on Euro football championship, Valeric was commissioned to gather the balls and sort them into baskets. Overall the stadium has *n* balls and *m* baskets. The baskets are positioned in a row from left to right and they are numbered with numbers from 1 to *m*, correspondingly. The balls are numbered with numbers from 1 to *n*.
Valeric decided to sort the balls in the order of increasing of their numbers by the following scheme. He will put each new ball in the basket with the least number of balls. And if he's got several variants, he chooses the basket which stands closer to the middle. That means that he chooses the basket for which is minimum, where *i* is the number of the basket. If in this case Valeric still has multiple variants, he chooses the basket with the minimum number.
For every ball print the number of the basket where it will go according to Valeric's scheme.
Note that the balls are sorted into baskets in the order of increasing numbers, that is, the first ball goes first, then goes the second ball and so on. | The first line contains two space-separated integers *n*, *m* (1<=≤<=*n*,<=*m*<=≤<=105) — the number of balls and baskets, correspondingly. | Print *n* numbers, one per line. The *i*-th line must contain the number of the basket for the *i*-th ball. | [
"4 3\n",
"3 1\n"
] | [
"2\n1\n3\n2\n",
"1\n1\n1\n"
] | none | [
{
"input": "4 3",
"output": "2\n1\n3\n2"
},
{
"input": "3 1",
"output": "1\n1\n1"
},
{
"input": "10 3",
"output": "2\n1\n3\n2\n1\n3\n2\n1\n3\n2"
},
{
"input": "6 5",
"output": "3\n2\n4\n1\n5\n3"
},
{
"input": "2 6",
"output": "3\n4"
},
{
"input": "5 2"... | 186 | 6,963,200 | 0 | 1,413 | |
913 | Party Lemonade | [
"bitmasks",
"dp",
"greedy"
] | null | null | A New Year party is not a New Year party without lemonade! As usual, you are expecting a lot of guests, and buying lemonade has already become a pleasant necessity.
Your favorite store sells lemonade in bottles of *n* different volumes at different costs. A single bottle of type *i* has volume 2*i*<=-<=1 liters and costs *c**i* roubles. The number of bottles of each type in the store can be considered infinite.
You want to buy at least *L* liters of lemonade. How many roubles do you have to spend? | The first line contains two integers *n* and *L* (1<=≤<=*n*<=≤<=30; 1<=≤<=*L*<=≤<=109) — the number of types of bottles in the store and the required amount of lemonade in liters, respectively.
The second line contains *n* integers *c*1,<=*c*2,<=...,<=*c**n* (1<=≤<=*c**i*<=≤<=109) — the costs of bottles of different types. | Output a single integer — the smallest number of roubles you have to pay in order to buy at least *L* liters of lemonade. | [
"4 12\n20 30 70 90\n",
"4 3\n10000 1000 100 10\n",
"4 3\n10 100 1000 10000\n",
"5 787787787\n123456789 234567890 345678901 456789012 987654321\n"
] | [
"150\n",
"10\n",
"30\n",
"44981600785557577\n"
] | In the first example you should buy one 8-liter bottle for 90 roubles and two 2-liter bottles for 30 roubles each. In total you'll get 12 liters of lemonade for just 150 roubles.
In the second example, even though you need only 3 liters, it's cheaper to buy a single 8-liter bottle for 10 roubles.
In the third example it's best to buy three 1-liter bottles for 10 roubles each, getting three liters for 30 roubles. | [
{
"input": "4 12\n20 30 70 90",
"output": "150"
},
{
"input": "4 3\n10000 1000 100 10",
"output": "10"
},
{
"input": "4 3\n10 100 1000 10000",
"output": "30"
},
{
"input": "5 787787787\n123456789 234567890 345678901 456789012 987654321",
"output": "44981600785557577"
},... | 140 | 20,172,800 | 0 | 1,415 | |
697 | Barnicle | [
"brute force",
"implementation",
"math",
"strings"
] | null | null | Barney is standing in a bar and starring at a pretty girl. He wants to shoot her with his heart arrow but he needs to know the distance between him and the girl to make his shot accurate.
Barney asked the bar tender Carl about this distance value, but Carl was so busy talking to the customers so he wrote the distance value (it's a real number) on a napkin. The problem is that he wrote it in scientific notation. The scientific notation of some real number *x* is the notation of form *AeB*, where *A* is a real number and *B* is an integer and *x*<==<=*A*<=×<=10*B* is true. In our case *A* is between 0 and 9 and *B* is non-negative.
Barney doesn't know anything about scientific notation (as well as anything scientific at all). So he asked you to tell him the distance value in usual decimal representation with minimal number of digits after the decimal point (and no decimal point if it is an integer). See the output format for better understanding. | The first and only line of input contains a single string of form *a*.*deb* where *a*, *d* and *b* are integers and *e* is usual character 'e' (0<=≤<=*a*<=≤<=9,<=0<=≤<=*d*<=<<=10100,<=0<=≤<=*b*<=≤<=100) — the scientific notation of the desired distance value.
*a* and *b* contain no leading zeros and *d* contains no trailing zeros (but may be equal to 0). Also, *b* can not be non-zero if *a* is zero. | Print the only real number *x* (the desired distance value) in the only line in its decimal notation.
Thus if *x* is an integer, print it's integer value without decimal part and decimal point and without leading zeroes.
Otherwise print *x* in a form of *p*.*q* such that *p* is an integer that have no leading zeroes (but may be equal to zero), and *q* is an integer that have no trailing zeroes (and may not be equal to zero). | [
"8.549e2\n",
"8.549e3\n",
"0.33e0\n"
] | [
"854.9\n",
"8549\n",
"0.33\n"
] | none | [
{
"input": "8.549e2",
"output": "854.9"
},
{
"input": "8.549e3",
"output": "8549"
},
{
"input": "0.33e0",
"output": "0.33"
},
{
"input": "1.31e1",
"output": "13.1"
},
{
"input": "1.038e0",
"output": "1.038"
},
{
"input": "8.25983e5",
"output": "825... | 140 | 7,270,400 | 3 | 1,419 | |
387 | George and Sleep | [
"implementation"
] | null | null | George woke up and saw the current time *s* on the digital clock. Besides, George knows that he has slept for time *t*.
Help George! Write a program that will, given time *s* and *t*, determine the time *p* when George went to bed. Note that George could have gone to bed yesterday relatively to the current time (see the second test sample). | The first line contains current time *s* as a string in the format "hh:mm". The second line contains time *t* in the format "hh:mm" — the duration of George's sleep. It is guaranteed that the input contains the correct time in the 24-hour format, that is, 00<=≤<=*hh*<=≤<=23, 00<=≤<=*mm*<=≤<=59. | In the single line print time *p* — the time George went to bed in the format similar to the format of the time in the input. | [
"05:50\n05:44\n",
"00:00\n01:00\n",
"00:01\n00:00\n"
] | [
"00:06\n",
"23:00\n",
"00:01\n"
] | In the first sample George went to bed at "00:06". Note that you should print the time only in the format "00:06". That's why answers "0:06", "00:6" and others will be considered incorrect.
In the second sample, George went to bed yesterday.
In the third sample, George didn't do to bed at all. | [
{
"input": "05:50\n05:44",
"output": "00:06"
},
{
"input": "00:00\n01:00",
"output": "23:00"
},
{
"input": "00:01\n00:00",
"output": "00:01"
},
{
"input": "23:59\n23:59",
"output": "00:00"
},
{
"input": "23:44\n23:55",
"output": "23:49"
},
{
"input": "... | 109 | 6,656,000 | 3 | 1,422 | |
347 | Fixed Points | [
"brute force",
"implementation",
"math"
] | null | null | A permutation of length *n* is an integer sequence such that each integer from 0 to (*n*<=-<=1) appears exactly once in it. For example, sequence [0,<=2,<=1] is a permutation of length 3 while both [0,<=2,<=2] and [1,<=2,<=3] are not.
A fixed point of a function is a point that is mapped to itself by the function. A permutation can be regarded as a bijective function. We'll get a definition of a fixed point in a permutation. An integer *i* is a fixed point of permutation *a*0,<=*a*1,<=...,<=*a**n*<=-<=1 if and only if *a**i*<==<=*i*. For example, permutation [0,<=2,<=1] has 1 fixed point and permutation [0,<=1,<=2] has 3 fixed points.
You are given permutation *a*. You are allowed to swap two elements of the permutation at most once. Your task is to maximize the number of fixed points in the resulting permutation. Note that you are allowed to make at most one swap operation. | The first line contains a single integer *n* (1<=≤<=*n*<=≤<=105). The second line contains *n* integers *a*0,<=*a*1,<=...,<=*a**n*<=-<=1 — the given permutation. | Print a single integer — the maximum possible number of fixed points in the permutation after at most one swap operation. | [
"5\n0 1 3 4 2\n"
] | [
"3\n"
] | none | [
{
"input": "5\n0 1 3 4 2",
"output": "3"
},
{
"input": "10\n6 9 4 7 8 2 3 5 0 1",
"output": "2"
},
{
"input": "100\n99 5 40 32 4 31 38 57 94 47 26 16 89 72 9 80 55 86 78 90 42 41 46 74 56 97 21 48 66 27 93 85 88 59 64 95 10 45 12 22 84 60 8 98 62 51 14 65 39 30 11 71 92 19 76 43 87 54 15... | 342 | 33,382,400 | 0 | 1,426 | |
803 | Magazine Ad | [
"binary search",
"greedy"
] | null | null | The main city magazine offers its readers an opportunity to publish their ads. The format of the ad should be like this:
There are space-separated non-empty words of lowercase and uppercase Latin letters.
There are hyphen characters '-' in some words, their positions set word wrapping points. Word can include more than one hyphen.
It is guaranteed that there are no adjacent spaces and no adjacent hyphens. No hyphen is adjacent to space. There are no spaces and no hyphens before the first word and after the last word.
When the word is wrapped, the part of the word before hyphen and the hyphen itself stay on current line and the next part of the word is put on the next line. You can also put line break between two words, in that case the space stays on current line. Check notes for better understanding.
The ad can occupy no more that *k* lines and should have minimal width. The width of the ad is the maximal length of string (letters, spaces and hyphens are counted) in it.
You should write a program that will find minimal width of the ad. | The first line contains number *k* (1<=≤<=*k*<=≤<=105).
The second line contains the text of the ad — non-empty space-separated words of lowercase and uppercase Latin letters and hyphens. Total length of the ad don't exceed 106 characters. | Output minimal width of the ad. | [
"4\ngarage for sa-le\n",
"4\nEdu-ca-tion-al Ro-unds are so fun\n"
] | [
"7\n",
"10\n"
] | Here all spaces are replaced with dots.
In the first example one of possible results after all word wraps looks like this:
The second example: | [
{
"input": "4\ngarage for sa-le",
"output": "7"
},
{
"input": "4\nEdu-ca-tion-al Ro-unds are so fun",
"output": "10"
},
{
"input": "1\nj",
"output": "1"
},
{
"input": "10\nb",
"output": "1"
},
{
"input": "1\nQGVsfZevMD",
"output": "10"
},
{
"input": "1... | 1,000 | 13,619,200 | 0 | 1,427 | |
639 | Bear and Forgotten Tree 3 | [
"constructive algorithms",
"graphs",
"trees"
] | null | null | A tree is a connected undirected graph consisting of *n* vertices and *n*<=<=-<=<=1 edges. Vertices are numbered 1 through *n*.
Limak is a little polar bear and Radewoosh is his evil enemy. Limak once had a tree but Radewoosh stolen it. Bear is very sad now because he doesn't remember much about the tree — he can tell you only three values *n*, *d* and *h*:
- The tree had exactly *n* vertices. - The tree had diameter *d*. In other words, *d* was the biggest distance between two vertices. - Limak also remembers that he once rooted the tree in vertex 1 and after that its height was *h*. In other words, *h* was the biggest distance between vertex 1 and some other vertex.
The distance between two vertices of the tree is the number of edges on the simple path between them.
Help Limak to restore his tree. Check whether there exists a tree satisfying the given conditions. Find any such tree and print its edges in any order. It's also possible that Limak made a mistake and there is no suitable tree – in this case print "-1". | The first line contains three integers *n*, *d* and *h* (2<=≤<=*n*<=≤<=100<=000,<=1<=≤<=*h*<=≤<=*d*<=≤<=*n*<=-<=1) — the number of vertices, diameter, and height after rooting in vertex 1, respectively. | If there is no tree matching what Limak remembers, print the only line with "-1" (without the quotes).
Otherwise, describe any tree matching Limak's description. Print *n*<=-<=1 lines, each with two space-separated integers – indices of vertices connected by an edge. If there are many valid trees, print any of them. You can print edges in any order. | [
"5 3 2\n",
"8 5 2\n",
"8 4 2\n"
] | [
"1 2\n1 3\n3 4\n3 5",
"-1\n",
"4 8\n5 7\n2 3\n8 1\n2 1\n5 6\n1 5\n"
] | Below you can see trees printed to the output in the first sample and the third sample. | [
{
"input": "5 3 2",
"output": "1 2\n2 3\n1 4\n5 1"
},
{
"input": "8 5 2",
"output": "-1"
},
{
"input": "8 4 2",
"output": "4 8\n5 7\n2 3\n8 1\n2 1\n5 6\n1 5"
},
{
"input": "2 1 1",
"output": "1 2"
},
{
"input": "10 3 3",
"output": "1 2\n2 3\n3 4\n5 2\n6 2\n7 2... | 46 | 4,608,000 | 0 | 1,429 | |
883 | Field of Wonders | [
"implementation",
"strings"
] | null | null | Polycarpus takes part in the "Field of Wonders" TV show. The participants of the show have to guess a hidden word as fast as possible. Initially all the letters of the word are hidden.
The game consists of several turns. At each turn the participant tells a letter and the TV show host responds if there is such letter in the word or not. If there is such letter then the host reveals all such letters. For example, if the hidden word is "abacaba" and the player tells the letter "a", the host will reveal letters at all positions, occupied by "a": 1, 3, 5 and 7 (positions are numbered from left to right starting from 1).
Polycarpus knows *m* words of exactly the same length as the hidden word. The hidden word is also known to him and appears as one of these *m* words.
At current moment a number of turns have already been made and some letters (possibly zero) of the hidden word are already revealed. Previously Polycarp has told exactly the letters which are currently revealed.
It is Polycarpus' turn. He wants to tell a letter in such a way, that the TV show host will assuredly reveal at least one more letter. Polycarpus cannot tell the letters, which are already revealed.
Your task is to help Polycarpus and find out the number of letters he can tell so that the show host will assuredly reveal at least one of the remaining letters. | The first line contains one integer *n* (1<=≤<=*n*<=≤<=50) — the length of the hidden word.
The following line describes already revealed letters. It contains the string of length *n*, which consists of lowercase Latin letters and symbols "*". If there is a letter at some position, then this letter was already revealed. If the position contains symbol "*", then the letter at this position has not been revealed yet. It is guaranteed, that at least one letter is still closed.
The third line contains an integer *m* (1<=≤<=*m*<=≤<=1000) — the number of words of length *n*, which Polycarpus knows. The following *m* lines contain the words themselves — *n*-letter strings of lowercase Latin letters. All words are distinct.
It is guaranteed that the hidden word appears as one of the given *m* words. Before the current move Polycarp has told exactly the letters which are currently revealed. | Output the single integer — the number of letters Polycarpus can tell so that the TV show host definitely reveals at least one more letter. It is possible that this number is zero. | [
"4\na**d\n2\nabcd\nacbd\n",
"5\nlo*er\n2\nlover\nloser\n",
"3\na*a\n2\naaa\naba\n"
] | [
"2\n",
"0\n",
"1\n"
] | In the first example Polycarpus can tell letters "b" and "c", which assuredly will be revealed.
The second example contains no letters which can be told as it is not clear, which of the letters "v" or "s" is located at the third position of the hidden word.
In the third example Polycarpus exactly knows that the hidden word is "aba", because in case it was "aaa", then the second letter "a" would have already been revealed in one of previous turns. | [
{
"input": "4\na**d\n2\nabcd\nacbd",
"output": "2"
},
{
"input": "5\nlo*er\n2\nlover\nloser",
"output": "0"
},
{
"input": "3\na*a\n2\naaa\naba",
"output": "1"
},
{
"input": "1\n*\n1\na",
"output": "1"
},
{
"input": "1\n*\n1\nz",
"output": "1"
},
{
"inp... | 62 | 6,041,600 | 3 | 1,434 | |
353 | Find Maximum | [
"implementation",
"math",
"number theory"
] | null | null | Valera has array *a*, consisting of *n* integers *a*0,<=*a*1,<=...,<=*a**n*<=-<=1, and function *f*(*x*), taking an integer from 0 to 2*n*<=-<=1 as its single argument. Value *f*(*x*) is calculated by formula , where value *bit*(*i*) equals one if the binary representation of number *x* contains a 1 on the *i*-th position, and zero otherwise.
For example, if *n*<==<=4 and *x*<==<=11 (11<==<=20<=+<=21<=+<=23), then *f*(*x*)<==<=*a*0<=+<=*a*1<=+<=*a*3.
Help Valera find the maximum of function *f*(*x*) among all *x*, for which an inequality holds: 0<=≤<=*x*<=≤<=*m*. | The first line contains integer *n* (1<=≤<=*n*<=≤<=105) — the number of array elements. The next line contains *n* space-separated integers *a*0,<=*a*1,<=...,<=*a**n*<=-<=1 (0<=≤<=*a**i*<=≤<=104) — elements of array *a*.
The third line contains a sequence of digits zero and one without spaces *s*0*s*1... *s**n*<=-<=1 — the binary representation of number *m*. Number *m* equals . | Print a single integer — the maximum value of function *f*(*x*) for all . | [
"2\n3 8\n10\n",
"5\n17 0 10 2 1\n11010\n"
] | [
"3\n",
"27\n"
] | In the first test case *m* = 2<sup class="upper-index">0</sup> = 1, *f*(0) = 0, *f*(1) = *a*<sub class="lower-index">0</sub> = 3.
In the second sample *m* = 2<sup class="upper-index">0</sup> + 2<sup class="upper-index">1</sup> + 2<sup class="upper-index">3</sup> = 11, the maximum value of function equals *f*(5) = *a*<sub class="lower-index">0</sub> + *a*<sub class="lower-index">2</sub> = 17 + 10 = 27. | [
{
"input": "2\n3 8\n10",
"output": "3"
},
{
"input": "5\n17 0 10 2 1\n11010",
"output": "27"
},
{
"input": "18\n4382 3975 9055 7554 8395 204 5313 5739 1555 2306 5423 828 8108 9736 2683 7940 1249 5495\n110001100101110111",
"output": "88691"
},
{
"input": "43\n475 2165 8771 714... | 186 | 1,126,400 | 0 | 1,439 | |
169 | Replacing Digits | [
"greedy"
] | null | null | You are given an integer *a* that consists of *n* digits. You are also given a sequence of digits *s* of length *m*. The digit in position *j* (1<=≤<=*j*<=≤<=*m*) of sequence *s* means that you can choose an arbitrary position *i* (1<=≤<=*i*<=≤<=*n*) in *a* and replace the digit in the chosen position *i* with *s**j*. Each element in the sequence *s* can participate in no more than one replacing operation.
Your task is to perform such sequence of replacements, that the given number *a* gets maximum value. You are allowed to use not all elements from *s*. | The first line contains positive integer *a*. Its length *n* is positive and doesn't exceed 105. The second line contains sequence of digits *s*. Its length *m* is positive and doesn't exceed 105. The digits in the sequence *s* are written consecutively without any separators.
The given number *a* doesn't contain leading zeroes. | Print the maximum value that can be obtained from *a* after a series of replacements. You are allowed to use not all elements from *s*. The printed number shouldn't contain any leading zeroes. | [
"1024\n010\n",
"987\n1234567\n"
] | [
"1124\n",
"987\n"
] | none | [
{
"input": "1024\n010",
"output": "1124"
},
{
"input": "987\n1234567",
"output": "987"
},
{
"input": "10\n1",
"output": "11"
},
{
"input": "11\n1",
"output": "11"
},
{
"input": "12\n2",
"output": "22"
},
{
"input": "1\n0",
"output": "1"
},
{
... | 248 | 0 | 0 | 1,441 | |
727 | T-shirts Distribution | [
"constructive algorithms",
"flows",
"greedy"
] | null | null | The organizers of a programming contest have decided to present t-shirts to participants. There are six different t-shirts sizes in this problem: S, M, L, XL, XXL, XXXL (sizes are listed in increasing order). The t-shirts are already prepared. For each size from S to XXXL you are given the number of t-shirts of this size.
During the registration, the organizers asked each of the *n* participants about the t-shirt size he wants. If a participant hesitated between two sizes, he could specify two neighboring sizes — this means that any of these two sizes suits him.
Write a program that will determine whether it is possible to present a t-shirt to each participant of the competition, or not. Of course, each participant should get a t-shirt of proper size:
- the size he wanted, if he specified one size; - any of the two neibouring sizes, if he specified two sizes.
If it is possible, the program should find any valid distribution of the t-shirts. | The first line of the input contains six non-negative integers — the number of t-shirts of each size. The numbers are given for the sizes S, M, L, XL, XXL, XXXL, respectively. The total number of t-shirts doesn't exceed 100<=000.
The second line contains positive integer *n* (1<=≤<=*n*<=≤<=100<=000) — the number of participants.
The following *n* lines contain the sizes specified by the participants, one line per participant. The *i*-th line contains information provided by the *i*-th participant: single size or two sizes separated by comma (without any spaces). If there are two sizes, the sizes are written in increasing order. It is guaranteed that two sizes separated by comma are neighboring. | If it is not possible to present a t-shirt to each participant, print «NO» (without quotes).
Otherwise, print *n*<=+<=1 lines. In the first line print «YES» (without quotes). In the following *n* lines print the t-shirt sizes the orginizers should give to participants, one per line. The order of the participants should be the same as in the input.
If there are multiple solutions, print any of them. | [
"0 1 0 1 1 0\n3\nXL\nS,M\nXL,XXL\n",
"1 1 2 0 1 1\n5\nS\nM\nS,M\nXXL,XXXL\nXL,XXL\n"
] | [
"YES\nXL\nM\nXXL\n",
"NO\n"
] | none | [
{
"input": "0 1 0 1 1 0\n3\nXL\nS,M\nXL,XXL",
"output": "YES\nXL\nM\nXXL"
},
{
"input": "1 1 2 0 1 1\n5\nS\nM\nS,M\nXXL,XXXL\nXL,XXL",
"output": "NO"
},
{
"input": "1 2 4 4 1 1\n10\nXL\nXL\nS,M\nL\nM,L\nL\nS,M\nM\nXL,XXL\nXL",
"output": "YES\nXL\nXL\nS\nL\nL\nL\nM\nM\nXL\nXL"
},
... | 358 | 4,403,200 | 0 | 1,443 | |
120 | Elevator | [
"brute force",
"implementation",
"math"
] | null | null | A sky scraper with 1000 floors has been built in the city of N. It has modern superfast elevators to help to travel from one floor to another. Each elevator has two doors, the front one and the back one. If one goes in through the front door, he goes out through the back one and vice versa. The elevator has two rails numbered with numbers 1 and 2. Rail 1 is located to the left of the entrance to the front door (or correspondingly, to the right of the entrance to the back door). Rail 2 is located opposite it, to the right of the entrance to the front door and to the left of the entrance to the back door. We know that each person in the city of N holds at a rail with the strongest hand.
One day a VIP person visited the city and of course, he took a look at the skyscraper and took a ride in the elevator. We know the door through which he entered and the rail he was holding at. Now we need to determine as soon as possible whether he is left-handed or right-handed. | The first line indicates the door through which the very important person entered the elevator. It contains "front" if the person enters the elevator through the front door and "back" if he entered the elevator through the back door. The second line contains integer *a* (1<=≤<=*a*<=≤<=2) which denotes the number of the rail at which the person was holding. | Print character "R" if the VIP is right-handed or "L" if he is left-handed. | [
"front\n1\n"
] | [
"L\n"
] | none | [
{
"input": "front\n1",
"output": "L"
},
{
"input": "back\n1",
"output": "R"
},
{
"input": "front\n2",
"output": "R"
},
{
"input": "back\n2",
"output": "L"
}
] | 60 | 0 | 0 | 1,444 | |
276 | Little Girl and Maximum Sum | [
"data structures",
"greedy",
"implementation",
"sortings"
] | null | null | The little girl loves the problems on array queries very much.
One day she came across a rather well-known problem: you've got an array of $n$ elements (the elements of the array are indexed starting from 1); also, there are $q$ queries, each one is defined by a pair of integers $l_i$, $r_i$ $(1 \le l_i \le r_i \le n)$. You need to find for each query the sum of elements of the array with indexes from $l_i$ to $r_i$, inclusive.
The little girl found the problem rather boring. She decided to reorder the array elements before replying to the queries in a way that makes the sum of query replies maximum possible. Your task is to find the value of this maximum sum. | The first line contains two space-separated integers $n$ ($1 \le n \le 2\cdot10^5$) and $q$ ($1 \le q \le 2\cdot10^5$) — the number of elements in the array and the number of queries, correspondingly.
The next line contains $n$ space-separated integers $a_i$ ($1 \le a_i \le 2\cdot10^5$) — the array elements.
Each of the following $q$ lines contains two space-separated integers $l_i$ and $r_i$ ($1 \le l_i \le r_i \le n$) — the $i$-th query. | In a single line print, a single integer — the maximum sum of query replies after the array elements are reordered.
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier. | [
"3 3\n5 3 2\n1 2\n2 3\n1 3\n",
"5 3\n5 2 4 1 3\n1 5\n2 3\n2 3\n"
] | [
"25\n",
"33\n"
] | none | [
{
"input": "3 3\n5 3 2\n1 2\n2 3\n1 3",
"output": "25"
},
{
"input": "5 3\n5 2 4 1 3\n1 5\n2 3\n2 3",
"output": "33"
},
{
"input": "34 21\n23 38 16 49 44 50 48 34 33 19 18 31 11 15 20 47 44 30 39 33 45 46 1 13 27 16 31 36 17 23 38 5 30 16\n8 16\n14 27\n8 26\n1 8\n5 6\n23 28\n4 33\n13 30\... | 499 | 26,316,800 | 3 | 1,445 | |
425 | Sereja and Squares | [
"binary search",
"data structures",
"hashing"
] | null | null | Sereja has painted *n* distinct points on the plane. The coordinates of each point are integers. Now he is wondering: how many squares are there with sides parallel to the coordinate axes and with points painted in all its four vertexes? Help him, calculate this number. | The first line contains integer *n* (1<=≤<=*n*<=≤<=105). Each of the next *n* lines contains two integers *x**i*,<=*y**i* (0<=≤<=*x**i*,<=*y**i*<=≤<=105), the integers represent the coordinates of the *i*-th point. It is guaranteed that all the given points are distinct. | In a single line print the required number of squares. | [
"5\n0 0\n0 2\n2 0\n2 2\n1 1\n",
"9\n0 0\n1 1\n2 2\n0 1\n1 0\n0 2\n2 0\n1 2\n2 1\n"
] | [
"1\n",
"5\n"
] | none | [
{
"input": "5\n0 0\n0 2\n2 0\n2 2\n1 1",
"output": "1"
},
{
"input": "9\n0 0\n1 1\n2 2\n0 1\n1 0\n0 2\n2 0\n1 2\n2 1",
"output": "5"
},
{
"input": "54\n0 8\n3 2\n9 3\n7 2\n8 2\n2 8\n10 10\n7 6\n1 1\n9 7\n4 0\n6 10\n10 1\n10 8\n5 1\n0 4\n7 10\n3 6\n0 5\n4 3\n3 0\n5 10\n6 9\n5 4\n6 6\n8 5\... | 62 | 2,867,200 | -1 | 1,452 | |
846 | Curriculum Vitae | [
"brute force",
"implementation"
] | null | null | Hideo Kojima has just quit his job at Konami. Now he is going to find a new place to work. Despite being such a well-known person, he still needs a CV to apply for a job.
During all his career Hideo has produced *n* games. Some of them were successful, some were not. Hideo wants to remove several of them (possibly zero) from his CV to make a better impression on employers. As a result there should be no unsuccessful game which comes right after successful one in his CV.
More formally, you are given an array *s*1,<=*s*2,<=...,<=*s**n* of zeros and ones. Zero corresponds to an unsuccessful game, one — to a successful one. Games are given in order they were produced, and Hideo can't swap these values. He should remove some elements from this array in such a way that no zero comes right after one.
Besides that, Hideo still wants to mention as much games in his CV as possible. Help this genius of a man determine the maximum number of games he can leave in his CV. | The first line contains one integer number *n* (1<=≤<=*n*<=≤<=100).
The second line contains *n* space-separated integer numbers *s*1,<=*s*2,<=...,<=*s**n* (0<=≤<=*s**i*<=≤<=1). 0 corresponds to an unsuccessful game, 1 — to a successful one. | Print one integer — the maximum number of games Hideo can leave in his CV so that no unsuccessful game comes after a successful one. | [
"4\n1 1 0 1\n",
"6\n0 1 0 0 1 0\n",
"1\n0\n"
] | [
"3\n",
"4\n",
"1\n"
] | none | [
{
"input": "4\n1 1 0 1",
"output": "3"
},
{
"input": "6\n0 1 0 0 1 0",
"output": "4"
},
{
"input": "1\n0",
"output": "1"
},
{
"input": "100\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0... | 61 | 0 | 3 | 1,454 | |
599 | Patrick and Shopping | [
"implementation"
] | null | null | Today Patrick waits for a visit from his friend Spongebob. To prepare for the visit, Patrick needs to buy some goodies in two stores located near his house. There is a *d*1 meter long road between his house and the first shop and a *d*2 meter long road between his house and the second shop. Also, there is a road of length *d*3 directly connecting these two shops to each other. Help Patrick calculate the minimum distance that he needs to walk in order to go to both shops and return to his house.
Patrick always starts at his house. He should visit both shops moving only along the three existing roads and return back to his house. He doesn't mind visiting the same shop or passing the same road multiple times. The only goal is to minimize the total distance traveled. | The first line of the input contains three integers *d*1, *d*2, *d*3 (1<=≤<=*d*1,<=*d*2,<=*d*3<=≤<=108) — the lengths of the paths.
- *d*1 is the length of the path connecting Patrick's house and the first shop; - *d*2 is the length of the path connecting Patrick's house and the second shop; - *d*3 is the length of the path connecting both shops. | Print the minimum distance that Patrick will have to walk in order to visit both shops and return to his house. | [
"10 20 30\n",
"1 1 5\n"
] | [
"60\n",
"4\n"
] | The first sample is shown on the picture in the problem statement. One of the optimal routes is: house <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> first shop <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> second shop <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> house.
In the second sample one of the optimal routes is: house <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> first shop <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> house <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> second shop <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/70a0795f45d32287dba0eb83fc4a3f470c6e5537.png" style="max-width: 100.0%;max-height: 100.0%;"/> house. | [
{
"input": "10 20 30",
"output": "60"
},
{
"input": "1 1 5",
"output": "4"
},
{
"input": "100 33 34",
"output": "134"
},
{
"input": "777 777 777",
"output": "2331"
},
{
"input": "2 2 8",
"output": "8"
},
{
"input": "12 34 56",
"output": "92"
},
... | 93 | 0 | 0 | 1,455 | |
608 | Hamming Distance Sum | [
"combinatorics",
"strings"
] | null | null | Genos needs your help. He was asked to solve the following programming problem by Saitama:
The length of some string *s* is denoted |*s*|. The Hamming distance between two strings *s* and *t* of equal length is defined as , where *s**i* is the *i*-th character of *s* and *t**i* is the *i*-th character of *t*. For example, the Hamming distance between string "0011" and string "0110" is |0<=-<=0|<=+<=|0<=-<=1|<=+<=|1<=-<=1|<=+<=|1<=-<=0|<==<=0<=+<=1<=+<=0<=+<=1<==<=2.
Given two binary strings *a* and *b*, find the sum of the Hamming distances between *a* and all contiguous substrings of *b* of length |*a*|. | The first line of the input contains binary string *a* (1<=≤<=|*a*|<=≤<=200<=000).
The second line of the input contains binary string *b* (|*a*|<=≤<=|*b*|<=≤<=200<=000).
Both strings are guaranteed to consist of characters '0' and '1' only. | Print a single integer — the sum of Hamming distances between *a* and all contiguous substrings of *b* of length |*a*|. | [
"01\n00111\n",
"0011\n0110\n"
] | [
"3\n",
"2\n"
] | For the first sample case, there are four contiguous substrings of *b* of length |*a*|: "00", "01", "11", and "11". The distance between "01" and "00" is |0 - 0| + |1 - 0| = 1. The distance between "01" and "01" is |0 - 0| + |1 - 1| = 0. The distance between "01" and "11" is |0 - 1| + |1 - 1| = 1. Last distance counts twice, as there are two occurrences of string "11". The sum of these edit distances is 1 + 0 + 1 + 1 = 3.
The second sample case is described in the statement. | [
{
"input": "01\n00111",
"output": "3"
},
{
"input": "0011\n0110",
"output": "2"
},
{
"input": "0\n0",
"output": "0"
},
{
"input": "1\n0",
"output": "1"
},
{
"input": "0\n1",
"output": "1"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "1... | 2,000 | 8,908,800 | 0 | 1,458 | |
892 | Wrath | [
"greedy",
"implementation",
"two pointers"
] | null | null | Hands that shed innocent blood!
There are *n* guilty people in a line, the *i*-th of them holds a claw with length *L**i*. The bell rings and every person kills some of people in front of him. All people kill others at the same time. Namely, the *i*-th person kills the *j*-th person if and only if *j*<=<<=*i* and *j*<=≥<=*i*<=-<=*L**i*.
You are given lengths of the claws. You need to find the total number of alive people after the bell rings. | The first line contains one integer *n* (1<=≤<=*n*<=≤<=106) — the number of guilty people.
Second line contains *n* space-separated integers *L*1,<=*L*2,<=...,<=*L**n* (0<=≤<=*L**i*<=≤<=109), where *L**i* is the length of the *i*-th person's claw. | Print one integer — the total number of alive people after the bell rings. | [
"4\n0 1 0 10\n",
"2\n0 0\n",
"10\n1 1 3 0 0 0 2 1 0 3\n"
] | [
"1\n",
"2\n",
"3\n"
] | In first sample the last person kills everyone in front of him. | [
{
"input": "4\n0 1 0 10",
"output": "1"
},
{
"input": "2\n0 0",
"output": "2"
},
{
"input": "10\n1 1 3 0 0 0 2 1 0 3",
"output": "3"
},
{
"input": "10\n0 0 2 0 0 3 3 2 2 0",
"output": "2"
},
{
"input": "1\n0",
"output": "1"
},
{
"input": "5\n0 0 0 1 0"... | 31 | 4,198,400 | 0 | 1,459 | |
411 | Password Check | [
"*special",
"implementation"
] | null | null | You have probably registered on Internet sites many times. And each time you should enter your invented password. Usually the registration form automatically checks the password's crypt resistance. If the user's password isn't complex enough, a message is displayed. Today your task is to implement such an automatic check.
Web-developers of the company Q assume that a password is complex enough, if it meets all of the following conditions:
- the password length is at least 5 characters; - the password contains at least one large English letter; - the password contains at least one small English letter; - the password contains at least one digit.
You are given a password. Please implement the automatic check of its complexity for company Q. | The first line contains a non-empty sequence of characters (at most 100 characters). Each character is either a large English letter, or a small English letter, or a digit, or one of characters: "!", "?", ".", ",", "_". | If the password is complex enough, print message "Correct" (without the quotes), otherwise print message "Too weak" (without the quotes). | [
"abacaba\n",
"X12345\n",
"CONTEST_is_STARTED!!11\n"
] | [
"Too weak\n",
"Too weak\n",
"Correct\n"
] | none | [
{
"input": "abacaba",
"output": "Too weak"
},
{
"input": "X12345",
"output": "Too weak"
},
{
"input": "CONTEST_is_STARTED!!11",
"output": "Correct"
},
{
"input": "1zA__",
"output": "Correct"
},
{
"input": "1zA_",
"output": "Too weak"
},
{
"input": "zA_... | 46 | 0 | 3 | 1,460 | |
1,006 | Polycarp's Practice | [
"greedy",
"implementation",
"sortings"
] | null | null | Polycarp is practicing his problem solving skill. He has a list of $n$ problems with difficulties $a_1, a_2, \dots, a_n$, respectively. His plan is to practice for exactly $k$ days. Each day he has to solve at least one problem from his list. Polycarp solves the problems in the order they are given in his list, he cannot skip any problem from his list. He has to solve all $n$ problems in exactly $k$ days.
Thus, each day Polycarp solves a contiguous sequence of (consecutive) problems from the start of the list. He can't skip problems or solve them multiple times. As a result, in $k$ days he will solve all the $n$ problems.
The profit of the $j$-th day of Polycarp's practice is the maximum among all the difficulties of problems Polycarp solves during the $j$-th day (i.e. if he solves problems with indices from $l$ to $r$ during a day, then the profit of the day is $\max\limits_{l \le i \le r}a_i$). The total profit of his practice is the sum of the profits over all $k$ days of his practice.
You want to help Polycarp to get the maximum possible total profit over all valid ways to solve problems. Your task is to distribute all $n$ problems between $k$ days satisfying the conditions above in such a way, that the total profit is maximum.
For example, if $n = 8, k = 3$ and $a = [5, 4, 2, 6, 5, 1, 9, 2]$, one of the possible distributions with maximum total profit is: $[5, 4, 2], [6, 5], [1, 9, 2]$. Here the total profit equals $5 + 6 + 9 = 20$. | The first line of the input contains two integers $n$ and $k$ ($1 \le k \le n \le 2000$) — the number of problems and the number of days, respectively.
The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 2000$) — difficulties of problems in Polycarp's list, in the order they are placed in the list (i.e. in the order Polycarp will solve them). | In the first line of the output print the maximum possible total profit.
In the second line print exactly $k$ positive integers $t_1, t_2, \dots, t_k$ ($t_1 + t_2 + \dots + t_k$ must equal $n$), where $t_j$ means the number of problems Polycarp will solve during the $j$-th day in order to achieve the maximum possible total profit of his practice.
If there are many possible answers, you may print any of them. | [
"8 3\n5 4 2 6 5 1 9 2\n",
"5 1\n1 1 1 1 1\n",
"4 2\n1 2000 2000 2\n"
] | [
"20\n3 2 3",
"1\n5\n",
"4000\n2 2\n"
] | The first example is described in the problem statement.
In the second example there is only one possible distribution.
In the third example the best answer is to distribute problems in the following way: $[1, 2000], [2000, 2]$. The total profit of this distribution is $2000 + 2000 = 4000$. | [
{
"input": "8 3\n5 4 2 6 5 1 9 2",
"output": "20\n4 1 3"
},
{
"input": "5 1\n1 1 1 1 1",
"output": "1\n5"
},
{
"input": "4 2\n1 2000 2000 2",
"output": "4000\n2 2"
},
{
"input": "1 1\n2000",
"output": "2000\n1"
},
{
"input": "1 1\n1234",
"output": "1234\n1"
... | 108 | 6,963,200 | 3 | 1,462 | |
845 | Two TVs | [
"data structures",
"greedy",
"sortings"
] | null | null | Polycarp is a great fan of television.
He wrote down all the TV programs he is interested in for today. His list contains *n* shows, *i*-th of them starts at moment *l**i* and ends at moment *r**i*.
Polycarp owns two TVs. He can watch two different shows simultaneously with two TVs but he can only watch one show at any given moment on a single TV. If one show ends at the same moment some other show starts then you can't watch them on a single TV.
Polycarp wants to check out all *n* shows. Are two TVs enough to do so? | The first line contains one integer *n* (1<=≤<=*n*<=≤<=2·105) — the number of shows.
Each of the next *n* lines contains two integers *l**i* and *r**i* (0<=≤<=*l**i*<=<<=*r**i*<=≤<=109) — starting and ending time of *i*-th show. | If Polycarp is able to check out all the shows using only two TVs then print "YES" (without quotes). Otherwise, print "NO" (without quotes). | [
"3\n1 2\n2 3\n4 5\n",
"4\n1 2\n2 3\n2 3\n1 2\n"
] | [
"YES\n",
"NO\n"
] | none | [
{
"input": "3\n1 2\n2 3\n4 5",
"output": "YES"
},
{
"input": "4\n1 2\n2 3\n2 3\n1 2",
"output": "NO"
},
{
"input": "4\n0 1\n1 2\n2 3\n3 4",
"output": "YES"
},
{
"input": "3\n1 2\n2 3\n2 4",
"output": "NO"
},
{
"input": "3\n0 100\n0 100\n0 100",
"output": "NO"
... | 2,000 | 21,504,000 | 0 | 1,466 | |
560 | Currency System in Geraldion | [
"implementation",
"sortings"
] | null | null | A magic island Geraldion, where Gerald lives, has its own currency system. It uses banknotes of several values. But the problem is, the system is not perfect and sometimes it happens that Geraldionians cannot express a certain sum of money with any set of banknotes. Of course, they can use any number of banknotes of each value. Such sum is called unfortunate. Gerald wondered: what is the minimum unfortunate sum? | The first line contains number *n* (1<=≤<=*n*<=≤<=1000) — the number of values of the banknotes that used in Geraldion.
The second line contains *n* distinct space-separated numbers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=106) — the values of the banknotes. | Print a single line — the minimum unfortunate sum. If there are no unfortunate sums, print <=-<=1. | [
"5\n1 2 3 4 5\n"
] | [
"-1\n"
] | none | [
{
"input": "5\n1 2 3 4 5",
"output": "-1"
},
{
"input": "1\n2",
"output": "1"
},
{
"input": "10\n371054 506438 397130 1 766759 208409 769264 549213 641270 771837",
"output": "-1"
},
{
"input": "10\n635370 154890 909382 220996 276501 716105 538714 140162 171960 271264",
"o... | 46 | 6,758,400 | -1 | 1,471 | |
372 | Counting Kangaroos is Fun | [
"binary search",
"greedy",
"sortings",
"two pointers"
] | null | null | There are *n* kangaroos with pockets. Each kangaroo has a size (integer number). A kangaroo can go into another kangaroo's pocket if and only if the size of kangaroo who hold the kangaroo is at least twice as large as the size of kangaroo who is held.
Each kangaroo can hold at most one kangaroo, and the kangaroo who is held by another kangaroo cannot hold any kangaroos.
The kangaroo who is held by another kangaroo cannot be visible from outside. Please, find a plan of holding kangaroos with the minimal number of kangaroos who is visible. | The first line contains a single integer — *n* (1<=≤<=*n*<=≤<=5·105). Each of the next *n* lines contains an integer *s**i* — the size of the *i*-th kangaroo (1<=≤<=*s**i*<=≤<=105). | Output a single integer — the optimal number of visible kangaroos. | [
"8\n2\n5\n7\n6\n9\n8\n4\n2\n",
"8\n9\n1\n6\n2\n6\n5\n8\n3\n"
] | [
"5\n",
"5\n"
] | none | [
{
"input": "8\n2\n5\n7\n6\n9\n8\n4\n2",
"output": "5"
},
{
"input": "8\n9\n1\n6\n2\n6\n5\n8\n3",
"output": "5"
},
{
"input": "12\n3\n99\n24\n46\n75\n63\n57\n55\n10\n62\n34\n52",
"output": "7"
},
{
"input": "12\n55\n75\n1\n98\n63\n64\n9\n39\n82\n18\n47\n9",
"output": "6"
... | 561 | 33,075,200 | 3 | 1,475 | |
14 | Four Segments | [
"brute force",
"constructive algorithms",
"geometry",
"implementation",
"math"
] | C. Four Segments | 2 | 64 | Several months later Alex finally got his brother Bob's creation by post. And now, in his turn, Alex wants to boast about something to his brother. He thought for a while, and came to the conclusion that he has no ready creations, and decided to write a program for rectangles detection. According to his plan, the program detects if the four given segments form a rectangle of a positive area and with sides parallel to coordinate axes. As Alex does badly at school and can't write this program by himself, he asks you to help him. | The input data contain four lines. Each of these lines contains four integers *x*1, *y*1, *x*2, *y*2 (<=-<=109<=≤<=*x*1,<=*y*1,<=*x*2,<=*y*2<=≤<=109) — coordinates of segment's beginning and end positions. The given segments can degenerate into points. | Output the word «YES», if the given four segments form the required rectangle, otherwise output «NO». | [
"1 1 6 1\n1 0 6 0\n6 0 6 1\n1 1 1 0\n",
"0 0 0 3\n2 0 0 0\n2 2 2 0\n0 2 2 2\n"
] | [
"YES\n",
"NO\n"
] | none | [
{
"input": "1 1 6 1\n1 0 6 0\n6 0 6 1\n1 1 1 0",
"output": "YES"
},
{
"input": "0 0 0 3\n2 0 0 0\n2 2 2 0\n0 2 2 2",
"output": "NO"
},
{
"input": "0 0 0 2\n2 0 0 0\n2 2 2 0\n0 2 2 2",
"output": "YES"
},
{
"input": "0 0 10 0\n0 0 10 0\n0 0 0 5\n0 0 0 -5",
"output": "NO"
... | 92 | 0 | 3.977 | 1,476 |
459 | Pashmak and Parmida's problem | [
"data structures",
"divide and conquer",
"sortings"
] | null | null | Parmida is a clever girl and she wants to participate in Olympiads this year. Of course she wants her partner to be clever too (although he's not)! Parmida has prepared the following test problem for Pashmak.
There is a sequence *a* that consists of *n* integers *a*1,<=*a*2,<=...,<=*a**n*. Let's denote *f*(*l*,<=*r*,<=*x*) the number of indices *k* such that: *l*<=≤<=*k*<=≤<=*r* and *a**k*<==<=*x*. His task is to calculate the number of pairs of indicies *i*,<=*j* (1<=≤<=*i*<=<<=*j*<=≤<=*n*) such that *f*(1,<=*i*,<=*a**i*)<=><=*f*(*j*,<=*n*,<=*a**j*).
Help Pashmak with the test. | The first line of the input contains an integer *n* (1<=≤<=*n*<=≤<=106). The second line contains *n* space-separated integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=109). | Print a single integer — the answer to the problem. | [
"7\n1 2 1 1 2 2 1\n",
"3\n1 1 1\n",
"5\n1 2 3 4 5\n"
] | [
"8\n",
"1\n",
"0\n"
] | none | [
{
"input": "7\n1 2 1 1 2 2 1",
"output": "8"
},
{
"input": "3\n1 1 1",
"output": "1"
},
{
"input": "5\n1 2 3 4 5",
"output": "0"
},
{
"input": "24\n1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4",
"output": "114"
},
{
"input": "1\n1",
"output": "0"
},
{
... | 3,000 | 121,241,600 | 0 | 1,481 | |
20 | Dijkstra? | [
"graphs",
"shortest paths"
] | C. Dijkstra? | 1 | 64 | You are given a weighted undirected graph. The vertices are enumerated from 1 to *n*. Your task is to find the shortest path between the vertex 1 and the vertex *n*. | The first line contains two integers *n* and *m* (2<=≤<=*n*<=≤<=105,<=0<=≤<=*m*<=≤<=105), where *n* is the number of vertices and *m* is the number of edges. Following *m* lines contain one edge each in form *a**i*, *b**i* and *w**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*,<=1<=≤<=*w**i*<=≤<=106), where *a**i*,<=*b**i* are edge endpoints and *w**i* is the length of the edge.
It is possible that the graph has loops and multiple edges between pair of vertices. | Write the only integer -1 in case of no path. Write the shortest path in opposite case. If there are many solutions, print any of them. | [
"5 6\n1 2 2\n2 5 5\n2 3 4\n1 4 1\n4 3 3\n3 5 1\n",
"5 6\n1 2 2\n2 5 5\n2 3 4\n1 4 1\n4 3 3\n3 5 1\n"
] | [
"1 4 3 5 ",
"1 4 3 5 "
] | none | [
{
"input": "5 6\n1 2 2\n2 5 5\n2 3 4\n1 4 1\n4 3 3\n3 5 1",
"output": "1 4 3 5 "
},
{
"input": "5 6\n1 2 2\n2 5 5\n2 3 4\n1 4 1\n4 3 3\n3 5 1",
"output": "1 4 3 5 "
},
{
"input": "2 1\n1 2 1",
"output": "1 2 "
},
{
"input": "3 1\n1 2 1",
"output": "-1"
},
{
"input... | 108 | 9,830,400 | 0 | 1,482 |
1,003 | Binary String Constructing | [
"constructive algorithms"
] | null | null | You are given three integers $a$, $b$ and $x$. Your task is to construct a binary string $s$ of length $n = a + b$ such that there are exactly $a$ zeroes, exactly $b$ ones and exactly $x$ indices $i$ (where $1 \le i < n$) such that $s_i \ne s_{i + 1}$. It is guaranteed that the answer always exists.
For example, for the string "01010" there are four indices $i$ such that $1 \le i < n$ and $s_i \ne s_{i + 1}$ ($i = 1, 2, 3, 4$). For the string "111001" there are two such indices $i$ ($i = 3, 5$).
Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1. | The first line of the input contains three integers $a$, $b$ and $x$ ($1 \le a, b \le 100, 1 \le x < a + b)$. | Print only one string $s$, where $s$ is any binary string satisfying conditions described above. It is guaranteed that the answer always exists. | [
"2 2 1\n",
"3 3 3\n",
"5 3 6\n"
] | [
"1100\n",
"101100\n",
"01010100\n"
] | All possible answers for the first example:
- 1100; - 0011.
All possible answers for the second example:
- 110100; - 101100; - 110010; - 100110; - 011001; - 001101; - 010011; - 001011. | [
{
"input": "2 2 1",
"output": "1100"
},
{
"input": "3 3 3",
"output": "101100"
},
{
"input": "5 3 6",
"output": "01010100"
},
{
"input": "100 1 2",
"output": "01000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
},
{
... | 140 | 0 | 3 | 1,484 | |
544 | Set of Strings | [
"implementation",
"strings"
] | null | null | You are given a string *q*. A sequence of *k* strings *s*1,<=*s*2,<=...,<=*s**k* is called beautiful, if the concatenation of these strings is string *q* (formally, *s*1<=+<=*s*2<=+<=...<=+<=*s**k*<==<=*q*) and the first characters of these strings are distinct.
Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist. | The first line contains a positive integer *k* (1<=≤<=*k*<=≤<=26) — the number of strings that should be in a beautiful sequence.
The second line contains string *q*, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive. | If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next *k* lines print the beautiful sequence of strings *s*1,<=*s*2,<=...,<=*s**k*.
If there are multiple possible answers, print any of them. | [
"1\nabca\n",
"2\naaacas\n",
"4\nabc\n"
] | [
"YES\nabca\n",
"YES\naaa\ncas\n",
"NO\n"
] | In the second sample there are two possible answers: {"*aaaca*", "*s*"} and {"*aaa*", "*cas*"}. | [
{
"input": "1\nabca",
"output": "YES\nabca"
},
{
"input": "2\naaacas",
"output": "YES\naaa\ncas"
},
{
"input": "4\nabc",
"output": "NO"
},
{
"input": "3\nnddkhkhkdndknndkhrnhddkrdhrnrrnkkdnnndndrdhnknknhnrnnkrrdhrkhkrkhnkhkhhrhdnrndnknrrhdrdrkhdrkkhkrnkk",
"output": "YES\... | 62 | 0 | 3 | 1,487 | |
402 | Searching for Graph | [
"brute force",
"constructive algorithms",
"graphs"
] | null | null | Let's call an undirected graph of *n* vertices *p*-interesting, if the following conditions fulfill:
- the graph contains exactly 2*n*<=+<=*p* edges; - the graph doesn't contain self-loops and multiple edges; - for any integer *k* (1<=≤<=*k*<=≤<=*n*), any subgraph consisting of *k* vertices contains at most 2*k*<=+<=*p* edges.
A subgraph of a graph is some set of the graph vertices and some set of the graph edges. At that, the set of edges must meet the condition: both ends of each edge from the set must belong to the chosen set of vertices.
Your task is to find a *p*-interesting graph consisting of *n* vertices. | The first line contains a single integer *t* (1<=≤<=*t*<=≤<=5) — the number of tests in the input. Next *t* lines each contains two space-separated integers: *n*, *p* (5<=≤<=*n*<=≤<=24; *p*<=≥<=0; ) — the number of vertices in the graph and the interest value for the appropriate test.
It is guaranteed that the required graph exists. | For each of the *t* tests print 2*n*<=+<=*p* lines containing the description of the edges of a *p*-interesting graph: the *i*-th line must contain two space-separated integers *a**i*,<=*b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*; *a**i*<=≠<=*b**i*) — two vertices, connected by an edge in the resulting graph. Consider the graph vertices numbered with integers from 1 to *n*.
Print the answers to the tests in the order the tests occur in the input. If there are multiple solutions, you can print any of them. | [
"1\n6 0\n"
] | [
"1 2\n1 3\n1 4\n1 5\n1 6\n2 3\n2 4\n2 5\n2 6\n3 4\n3 5\n3 6\n"
] | none | [
{
"input": "1\n6 0",
"output": "1 2\n1 3\n1 4\n1 5\n1 6\n2 3\n2 4\n2 5\n2 6\n3 4\n3 5\n3 6"
},
{
"input": "1\n5 0",
"output": "1 2\n1 3\n1 4\n1 5\n2 3\n2 4\n2 5\n3 4\n3 5\n4 5"
},
{
"input": "5\n6 0\n5 0\n7 0\n8 0\n9 0",
"output": "1 2\n1 3\n1 4\n1 5\n1 6\n2 3\n2 4\n2 5\n2 6\n3 4\n3 ... | 124 | 4,915,200 | 3 | 1,489 | |
93 | Frames | [
"implementation"
] | A. Frames | 2 | 256 | Throughout Igor K.'s life he has had many situations worthy of attention. We remember the story with the virus, the story of his mathematical career and of course, his famous programming achievements. However, one does not always adopt new hobbies, one can quit something as well.
This time Igor K. got disappointed in one of his hobbies: editing and voicing videos. Moreover, he got disappointed in it so much, that he decided to destroy his secret archive for good.
Igor K. use Pindows XR operation system which represents files and folders by small icons. At that, *m* icons can fit in a horizontal row in any window.
Igor K.'s computer contains *n* folders in the D: disk's root catalog. The folders are numbered from 1 to *n* in the order from the left to the right and from top to bottom (see the images). At that the folders with secret videos have numbers from *a* to *b* inclusive. Igor K. wants to delete them forever, at that making as few frame selections as possible, and then pressing Shift+Delete exactly once. What is the minimum number of times Igor K. will have to select the folder in order to select folders from *a* to *b* and only them? Let us note that if some selected folder is selected repeatedly, then it is deselected. Each selection possesses the shape of some rectangle with sides parallel to the screen's borders. | The only line contains four integers *n*, *m*, *a*, *b* (1<=≤<=*n*,<=*m*<=≤<=109, 1<=≤<=*a*<=≤<=*b*<=≤<=*n*). They are the number of folders in Igor K.'s computer, the width of a window and the numbers of the first and the last folders that need to be deleted. | Print a single number: the least possible number of times Igor K. will have to select the folders using frames to select only the folders with numbers from *a* to *b*. | [
"11 4 3 9\n",
"20 5 2 20\n"
] | [
"3\n",
"2\n"
] | The images below illustrate statement tests.
The first test:
<img class="tex-graphics" src="https://espresso.codeforces.com/a0e4ba690dd16e3c68210a28afd82020b23fb605.png" style="max-width: 100.0%;max-height: 100.0%;"/>
In this test we can select folders 3 and 4 with out first selection, folders 5, 6, 7, 8 with our second selection and folder 9 with our third, last selection.
The second test:
<img class="tex-graphics" src="https://espresso.codeforces.com/289e2666a3d8b3dfe5b22ff3d88976df711640f7.png" style="max-width: 100.0%;max-height: 100.0%;"/>
In this test we can first select all folders in the first row (2, 3, 4, 5), then — all other ones. | [
{
"input": "11 4 3 9",
"output": "3"
},
{
"input": "20 5 2 20",
"output": "2"
},
{
"input": "1 1 1 1",
"output": "1"
},
{
"input": "26 5 2 18",
"output": "3"
},
{
"input": "21 5 1 15",
"output": "1"
},
{
"input": "21 5 1 21",
"output": "1"
},
{... | 124 | 0 | 3.969 | 1,494 |
807 | Is it rated? | [
"implementation",
"sortings"
] | null | null | Is it rated?
Here it is. The Ultimate Question of Competitive Programming, Codeforces, and Everything. And you are here to answer it.
Another Codeforces round has been conducted. No two participants have the same number of points. For each participant, from the top to the bottom of the standings, their rating before and after the round is known.
It's known that if at least one participant's rating has changed, then the round was rated for sure.
It's also known that if the round was rated and a participant with lower rating took a better place in the standings than a participant with higher rating, then at least one round participant's rating has changed.
In this problem, you should not make any other assumptions about the rating system.
Determine if the current round is rated, unrated, or it's impossible to determine whether it is rated of not. | The first line contains a single integer *n* (2<=≤<=*n*<=≤<=1000) — the number of round participants.
Each of the next *n* lines contains two integers *a**i* and *b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=4126) — the rating of the *i*-th participant before and after the round, respectively. The participants are listed in order from the top to the bottom of the standings. | If the round is rated for sure, print "rated". If the round is unrated for sure, print "unrated". If it's impossible to determine whether the round is rated or not, print "maybe". | [
"6\n3060 3060\n2194 2194\n2876 2903\n2624 2624\n3007 2991\n2884 2884\n",
"4\n1500 1500\n1300 1300\n1200 1200\n1400 1400\n",
"5\n3123 3123\n2777 2777\n2246 2246\n2246 2246\n1699 1699\n"
] | [
"rated\n",
"unrated\n",
"maybe\n"
] | In the first example, the ratings of the participants in the third and fifth places have changed, therefore, the round was rated.
In the second example, no one's rating has changed, but the participant in the second place has lower rating than the participant in the fourth place. Therefore, if the round was rated, someone's rating would've changed for sure.
In the third example, no one's rating has changed, and the participants took places in non-increasing order of their rating. Therefore, it's impossible to determine whether the round is rated or not. | [
{
"input": "6\n3060 3060\n2194 2194\n2876 2903\n2624 2624\n3007 2991\n2884 2884",
"output": "rated"
},
{
"input": "4\n1500 1500\n1300 1300\n1200 1200\n1400 1400",
"output": "unrated"
},
{
"input": "5\n3123 3123\n2777 2777\n2246 2246\n2246 2246\n1699 1699",
"output": "maybe"
},
{
... | 46 | 0 | 3 | 1,495 | |
382 | Number Busters | [
"binary search",
"math"
] | null | null | Arthur and Alexander are number busters. Today they've got a competition.
Arthur took a group of four integers *a*,<=*b*,<=*w*,<=*x* (0<=≤<=*b*<=<<=*w*,<=0<=<<=*x*<=<<=*w*) and Alexander took integer *с*. Arthur and Alexander use distinct approaches to number bustings. Alexander is just a regular guy. Each second, he subtracts one from his number. In other words, he performs the assignment: *c*<==<=*c*<=-<=1. Arthur is a sophisticated guy. Each second Arthur performs a complex operation, described as follows: if *b*<=≥<=*x*, perform the assignment *b*<==<=*b*<=-<=*x*, if *b*<=<<=*x*, then perform two consecutive assignments *a*<==<=*a*<=-<=1; *b*<==<=*w*<=-<=(*x*<=-<=*b*).
You've got numbers *a*,<=*b*,<=*w*,<=*x*,<=*c*. Determine when Alexander gets ahead of Arthur if both guys start performing the operations at the same time. Assume that Alexander got ahead of Arthur if *c*<=≤<=*a*. | The first line contains integers *a*,<=*b*,<=*w*,<=*x*,<=*c* (1<=≤<=*a*<=≤<=2·109,<=1<=≤<=*w*<=≤<=1000,<=0<=≤<=*b*<=<<=*w*,<=0<=<<=*x*<=<<=*w*,<=1<=≤<=*c*<=≤<=2·109). | Print a single integer — the minimum time in seconds Alexander needs to get ahead of Arthur. You can prove that the described situation always occurs within the problem's limits. | [
"4 2 3 1 6\n",
"4 2 3 1 7\n",
"1 2 3 2 6\n",
"1 1 2 1 1\n"
] | [
"2\n",
"4\n",
"13\n",
"0\n"
] | none | [
{
"input": "4 2 3 1 6",
"output": "2"
},
{
"input": "4 2 3 1 7",
"output": "4"
},
{
"input": "1 2 3 2 6",
"output": "13"
},
{
"input": "1 1 2 1 1",
"output": "0"
},
{
"input": "1 0 1000 999 2000000000",
"output": "1999999999000"
},
{
"input": "10 1 6 4... | 46 | 0 | 0 | 1,500 | |
489 | Given Length and Sum of Digits... | [
"dp",
"greedy",
"implementation"
] | null | null | You have a positive integer *m* and a non-negative integer *s*. Your task is to find the smallest and the largest of the numbers that have length *m* and sum of digits *s*. The required numbers should be non-negative integers written in the decimal base without leading zeroes. | The single line of the input contains a pair of integers *m*, *s* (1<=≤<=*m*<=≤<=100,<=0<=≤<=*s*<=≤<=900) — the length and the sum of the digits of the required numbers. | In the output print the pair of the required non-negative integer numbers — first the minimum possible number, then — the maximum possible number. If no numbers satisfying conditions required exist, print the pair of numbers "-1 -1" (without the quotes). | [
"2 15\n",
"3 0\n"
] | [
"69 96\n",
"-1 -1\n"
] | none | [
{
"input": "2 15",
"output": "69 96"
},
{
"input": "3 0",
"output": "-1 -1"
},
{
"input": "2 1",
"output": "10 10"
},
{
"input": "3 10",
"output": "109 910"
},
{
"input": "100 100",
"output": "1000000000000000000000000000000000000000000000000000000000000000000... | 1,000 | 0 | 0 | 1,505 | |
768 | Oath of the Night's Watch | [
"constructive algorithms",
"sortings"
] | null | null | "Night gathers, and now my watch begins. It shall not end until my death. I shall take no wife, hold no lands, father no children. I shall wear no crowns and win no glory. I shall live and die at my post. I am the sword in the darkness. I am the watcher on the walls. I am the shield that guards the realms of men. I pledge my life and honor to the Night's Watch, for this night and all the nights to come." — The Night's Watch oath.
With that begins the watch of Jon Snow. He is assigned the task to support the stewards.
This time he has *n* stewards with him whom he has to provide support. Each steward has his own strength. Jon Snow likes to support a steward only if there exists at least one steward who has strength strictly less than him and at least one steward who has strength strictly greater than him.
Can you find how many stewards will Jon support? | First line consists of a single integer *n* (1<=≤<=*n*<=≤<=105) — the number of stewards with Jon Snow.
Second line consists of *n* space separated integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=109) representing the values assigned to the stewards. | Output a single integer representing the number of stewards which Jon will feed. | [
"2\n1 5\n",
"3\n1 2 5\n"
] | [
"0",
"1"
] | In the first sample, Jon Snow cannot support steward with strength 1 because there is no steward with strength less than 1 and he cannot support steward with strength 5 because there is no steward with strength greater than 5.
In the second sample, Jon Snow can support steward with strength 2 because there are stewards with strength less than 2 and greater than 2. | [
{
"input": "2\n1 5",
"output": "0"
},
{
"input": "3\n1 2 5",
"output": "1"
},
{
"input": "4\n1 2 3 4",
"output": "2"
},
{
"input": "8\n7 8 9 4 5 6 1 2",
"output": "6"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "1\n100",
"output": "0"
},
... | 15 | 0 | 0 | 1,506 | |
0 | none | [
"none"
] | null | null | Alice likes snow a lot! Unfortunately, this year's winter is already over, and she can't expect to have any more of it. Bob has thus bought her a gift — a large snow maker. He plans to make some amount of snow every day. On day *i* he will make a pile of snow of volume *V**i* and put it in her garden.
Each day, every pile will shrink a little due to melting. More precisely, when the temperature on a given day is *T**i*, each pile will reduce its volume by *T**i*. If this would reduce the volume of a pile to or below zero, it disappears forever. All snow piles are independent of each other.
Note that the pile made on day *i* already loses part of its volume on the same day. In an extreme case, this may mean that there are no piles left at the end of a particular day.
You are given the initial pile sizes and the temperature on each day. Determine the total volume of snow melted on each day. | The first line contains a single integer *N* (1<=≤<=*N*<=≤<=105) — the number of days.
The second line contains *N* integers *V*1,<=*V*2,<=...,<=*V**N* (0<=≤<=*V**i*<=≤<=109), where *V**i* is the initial size of a snow pile made on the day *i*.
The third line contains *N* integers *T*1,<=*T*2,<=...,<=*T**N* (0<=≤<=*T**i*<=≤<=109), where *T**i* is the temperature on the day *i*. | Output a single line with *N* integers, where the *i*-th integer represents the total volume of snow melted on day *i*. | [
"3\n10 10 5\n5 7 2\n",
"5\n30 25 20 15 10\n9 10 12 4 13\n"
] | [
"5 12 4\n",
"9 20 35 11 25\n"
] | In the first sample, Bob first makes a snow pile of volume 10, which melts to the size of 5 on the same day. On the second day, he makes another pile of size 10. Since it is a bit warmer than the day before, the first pile disappears completely while the second pile shrinks to 3. At the end of the second day, he has only a single pile of size 3. On the third day he makes a smaller pile than usual, but as the temperature dropped too, both piles survive till the end of the day. | [
{
"input": "3\n10 10 5\n5 7 2",
"output": "5 12 4"
},
{
"input": "5\n30 25 20 15 10\n9 10 12 4 13",
"output": "9 20 35 11 25"
},
{
"input": "4\n0 0 0 0\n1 2 3 4",
"output": "0 0 0 0"
},
{
"input": "10\n11 39 16 34 25 3 12 11 31 16\n10 0 4 9 8 9 7 8 9 2",
"output": "10 0 9... | 1,000 | 15,360,000 | 0 | 1,512 | |
625 | Guest From the Past | [
"implementation",
"math"
] | null | null | Kolya Gerasimov loves kefir very much. He lives in year 1984 and knows all the details of buying this delicious drink. One day, as you probably know, he found himself in year 2084, and buying kefir there is much more complicated.
Kolya is hungry, so he went to the nearest milk shop. In 2084 you may buy kefir in a plastic liter bottle, that costs *a* rubles, or in glass liter bottle, that costs *b* rubles. Also, you may return empty glass bottle and get *c* (*c*<=<<=*b*) rubles back, but you cannot return plastic bottles.
Kolya has *n* rubles and he is really hungry, so he wants to drink as much kefir as possible. There were no plastic bottles in his 1984, so Kolya doesn't know how to act optimally and asks for your help. | First line of the input contains a single integer *n* (1<=≤<=*n*<=≤<=1018) — the number of rubles Kolya has at the beginning.
Then follow three lines containing integers *a*, *b* and *c* (1<=≤<=*a*<=≤<=1018, 1<=≤<=*c*<=<<=*b*<=≤<=1018) — the cost of one plastic liter bottle, the cost of one glass liter bottle and the money one can get back by returning an empty glass bottle, respectively. | Print the only integer — maximum number of liters of kefir, that Kolya can drink. | [
"10\n11\n9\n8\n",
"10\n5\n6\n1\n"
] | [
"2\n",
"2\n"
] | In the first sample, Kolya can buy one glass bottle, then return it and buy one more glass bottle. Thus he will drink 2 liters of kefir.
In the second sample, Kolya can buy two plastic bottle and get two liters of kefir, or he can buy one liter glass bottle, then return it and buy one plastic bottle. In both cases he will drink two liters of kefir. | [
{
"input": "10\n11\n9\n8",
"output": "2"
},
{
"input": "10\n5\n6\n1",
"output": "2"
},
{
"input": "2\n2\n2\n1",
"output": "1"
},
{
"input": "10\n3\n3\n1",
"output": "4"
},
{
"input": "10\n1\n2\n1",
"output": "10"
},
{
"input": "10\n2\n3\n1",
"outpu... | 62 | 0 | 0 | 1,513 | |
199 | Hexadecimal's theorem | [
"brute force",
"constructive algorithms",
"implementation",
"number theory"
] | null | null | Recently, a chaotic virus Hexadecimal advanced a new theorem which will shake the Universe. She thinks that each Fibonacci number can be represented as sum of three not necessary different Fibonacci numbers.
Let's remember how Fibonacci numbers can be calculated. *F*0<==<=0, *F*1<==<=1, and all the next numbers are *F**i*<==<=*F**i*<=-<=2<=+<=*F**i*<=-<=1.
So, Fibonacci numbers make a sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, ...
If you haven't run away from the PC in fear, you have to help the virus. Your task is to divide given Fibonacci number *n* by three not necessary different Fibonacci numbers or say that it is impossible. | The input contains of a single integer *n* (0<=≤<=*n*<=<<=109) — the number that should be represented by the rules described above. It is guaranteed that *n* is a Fibonacci number. | Output three required numbers: *a*, *b* and *c*. If there is no answer for the test you have to print "I'm too stupid to solve this problem" without the quotes.
If there are multiple answers, print any of them. | [
"3\n",
"13\n"
] | [
"1 1 1\n",
"2 3 8\n"
] | none | [
{
"input": "3",
"output": "1 1 1"
},
{
"input": "13",
"output": "2 3 8"
},
{
"input": "0",
"output": "0 0 0"
},
{
"input": "1",
"output": "1 0 0"
},
{
"input": "2",
"output": "1 1 0"
},
{
"input": "1597",
"output": "233 377 987"
},
{
"input... | 92 | 0 | 3 | 1,517 | |
570 | Replacement | [
"constructive algorithms",
"data structures",
"implementation"
] | null | null | Daniel has a string *s*, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string *s*, of all occurrences of the substring let's choose the first one, and replace this substring with string ".". In other words, during the replacement operation, the first two consecutive periods are replaced by one. If string *s* contains no two consecutive periods, then nothing happens.
Let's define *f*(*s*) as the minimum number of operations of replacement to perform, so that the string does not have any two consecutive periods left.
You need to process *m* queries, the *i*-th results in that the character at position *x**i* (1<=≤<=*x**i*<=≤<=*n*) of string *s* is assigned value *c**i*. After each operation you have to calculate and output the value of *f*(*s*).
Help Daniel to process all queries. | The first line contains two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=300<=000) the length of the string and the number of queries.
The second line contains string *s*, consisting of *n* lowercase English letters and period signs.
The following *m* lines contain the descriptions of queries. The *i*-th line contains integer *x**i* and *c**i* (1<=≤<=*x**i*<=≤<=*n*, *c**i* — a lowercas English letter or a period sign), describing the query of assigning symbol *c**i* to position *x**i*. | Print *m* numbers, one per line, the *i*-th of these numbers must be equal to the value of *f*(*s*) after performing the *i*-th assignment. | [
"10 3\n.b..bz....\n1 h\n3 c\n9 f\n",
"4 4\n.cc.\n2 .\n3 .\n2 a\n1 a\n"
] | [
"4\n3\n1\n",
"1\n3\n1\n1\n"
] | Note to the first sample test (replaced periods are enclosed in square brackets).
The original string is ".b..bz....".
- after the first query *f*(hb..bz....) = 4 ("hb[..]bz...." → "hb.bz[..].." → "hb.bz[..]." → "hb.bz[..]" → "hb.bz.")- after the second query *f*(hbс.bz....) = 3 ("hbс.bz[..].." → "hbс.bz[..]." → "hbс.bz[..]" → "hbс.bz.")- after the third query *f*(hbс.bz..f.) = 1 ("hbс.bz[..]f." → "hbс.bz.f.")
Note to the second sample test.
The original string is ".cc.".
- after the first query: *f*(..c.) = 1 ("[..]c." → ".c.")- after the second query: *f*(....) = 3 ("[..].." → "[..]." → "[..]" → ".")- after the third query: *f*(.a..) = 1 (".a[..]" → ".a.")- after the fourth query: *f*(aa..) = 1 ("aa[..]" → "aa.") | [
{
"input": "10 3\n.b..bz....\n1 h\n3 c\n9 f",
"output": "4\n3\n1"
},
{
"input": "4 4\n.cc.\n2 .\n3 .\n2 a\n1 a",
"output": "1\n3\n1\n1"
},
{
"input": "3 3\n...\n1 .\n2 a\n3 b",
"output": "2\n0\n0"
},
{
"input": "5 1\n.....\n5 z",
"output": "3"
},
{
"input": "1 5\n... | 2,000 | 54,681,600 | 0 | 1,518 | |
862 | Mahmoud and Ehab and the bipartiteness | [
"dfs and similar",
"graphs",
"trees"
] | null | null | Mahmoud and Ehab continue their adventures! As everybody in the evil land knows, Dr. Evil likes bipartite graphs, especially trees.
A tree is a connected acyclic graph. A bipartite graph is a graph, whose vertices can be partitioned into 2 sets in such a way, that for each edge (*u*,<=*v*) that belongs to the graph, *u* and *v* belong to different sets. You can find more formal definitions of a tree and a bipartite graph in the notes section below.
Dr. Evil gave Mahmoud and Ehab a tree consisting of *n* nodes and asked them to add edges to it in such a way, that the graph is still bipartite. Besides, after adding these edges the graph should be simple (doesn't contain loops or multiple edges). What is the maximum number of edges they can add?
A loop is an edge, which connects a node with itself. Graph doesn't contain multiple edges when for each pair of nodes there is no more than one edge between them. A cycle and a loop aren't the same . | The first line of input contains an integer *n* — the number of nodes in the tree (1<=≤<=*n*<=≤<=105).
The next *n*<=-<=1 lines contain integers *u* and *v* (1<=≤<=*u*,<=*v*<=≤<=*n*, *u*<=≠<=*v*) — the description of the edges of the tree.
It's guaranteed that the given graph is a tree. | Output one integer — the maximum number of edges that Mahmoud and Ehab can add to the tree while fulfilling the conditions. | [
"3\n1 2\n1 3\n",
"5\n1 2\n2 3\n3 4\n4 5\n"
] | [
"0\n",
"2\n"
] | Tree definition: [https://en.wikipedia.org/wiki/Tree_(graph_theory)](https://en.wikipedia.org/wiki/Tree_(graph_theory))
Bipartite graph definition: [https://en.wikipedia.org/wiki/Bipartite_graph](https://en.wikipedia.org/wiki/Bipartite_graph)
In the first test case the only edge that can be added in such a way, that graph won't contain loops or multiple edges is (2, 3), but adding this edge will make the graph non-bipartite so the answer is 0.
In the second test case Mahmoud and Ehab can add edges (1, 4) and (2, 5). | [
{
"input": "3\n1 2\n1 3",
"output": "0"
},
{
"input": "5\n1 2\n2 3\n3 4\n4 5",
"output": "2"
},
{
"input": "10\n3 8\n6 2\n9 7\n10 1\n3 5\n1 3\n6 7\n5 4\n3 6",
"output": "16"
},
{
"input": "10\n7 6\n2 7\n4 1\n8 5\n9 4\n5 3\n8 7\n10 8\n10 4",
"output": "16"
},
{
"in... | 61 | 6,963,200 | 0 | 1,519 | |
99 | Help Chef Gerasim | [
"implementation",
"sortings"
] | B. Help Chef Gerasim | 0 | 256 | In a far away kingdom young pages help to set the table for the King. As they are terribly mischievous, one needs to keep an eye on the control whether they have set everything correctly. This time the royal chef Gerasim had the impression that the pages have played a prank again: they had poured the juice from one cup to another. Now Gerasim wants to check his hypothesis. The good thing is that chef Gerasim always pour the same number of milliliters of juice to all cups in the royal kitchen. Having thoroughly measured the juice in each cup, Gerasim asked you to write a program that will determine from which cup juice was poured to which one; otherwise, the program should determine that this time the pages set the table diligently.
To simplify your task we shall consider the cups to be bottomless so that the juice never overfills a cup and pours out, however much it can be. Besides, by some strange reason in a far away kingdom one can only pour to a cup or from one cup to another an integer number of milliliters of juice. | The first line contains integer *n* — the number of cups on the royal table (1<=≤<=*n*<=≤<=1000). Next *n* lines contain volumes of juice in each cup — non-negative integers, not exceeding 104. | If the pages didn't pour the juice, print "Exemplary pages." (without the quotes). If you can determine the volume of juice poured during exactly one juice pouring, print "*v* ml. from cup #*a* to cup #*b*." (without the quotes), where *v* represents the volume of poured juice, *a* represents the number of the cup from which the juice was poured (the cups are numbered with consecutive positive integers starting from one in the order in which the cups are described in the input data), *b* represents the number of the cup into which the juice was poured. Finally, if the given juice's volumes cannot be obtained using no more than one pouring (for example, the pages poured the juice from one cup to another more than once or the royal kitchen maids poured the juice into the cups incorrectly), print "Unrecoverable configuration." (without the quotes). | [
"5\n270\n250\n250\n230\n250\n",
"5\n250\n250\n250\n250\n250\n",
"5\n270\n250\n249\n230\n250\n"
] | [
"20 ml. from cup #4 to cup #1.\n",
"Exemplary pages.\n",
"Unrecoverable configuration.\n"
] | none | [
{
"input": "5\n270\n250\n250\n230\n250",
"output": "20 ml. from cup #4 to cup #1."
},
{
"input": "5\n250\n250\n250\n250\n250",
"output": "Exemplary pages."
},
{
"input": "5\n270\n250\n249\n230\n250",
"output": "Unrecoverable configuration."
},
{
"input": "4\n200\n190\n210\n20... | 31 | 0 | 0 | 1,521 |
18 | Stripe | [
"data structures",
"implementation"
] | C. Stripe | 2 | 64 | Once Bob took a paper stripe of *n* squares (the height of the stripe is 1 square). In each square he wrote an integer number, possibly negative. He became interested in how many ways exist to cut this stripe into two pieces so that the sum of numbers from one piece is equal to the sum of numbers from the other piece, and each piece contains positive integer amount of squares. Would you help Bob solve this problem? | The first input line contains integer *n* (1<=≤<=*n*<=≤<=105) — amount of squares in the stripe. The second line contains *n* space-separated numbers — they are the numbers written in the squares of the stripe. These numbers are integer and do not exceed 10000 in absolute value. | Output the amount of ways to cut the stripe into two non-empty pieces so that the sum of numbers from one piece is equal to the sum of numbers from the other piece. Don't forget that it's allowed to cut the stripe along the squares' borders only. | [
"9\n1 5 -6 7 9 -16 0 -2 2\n",
"3\n1 1 1\n",
"2\n0 0\n"
] | [
"3\n",
"0\n",
"1\n"
] | none | [
{
"input": "9\n1 5 -6 7 9 -16 0 -2 2",
"output": "3"
},
{
"input": "3\n1 1 1",
"output": "0"
},
{
"input": "2\n0 0",
"output": "1"
},
{
"input": "4\n100 1 10 111",
"output": "1"
},
{
"input": "10\n0 4 -3 0 -2 2 -3 -3 2 5",
"output": "3"
},
{
"input": "... | 466 | 8,499,200 | 3.820176 | 1,523 |
38 | The Great Marathon | [
"dp"
] | H. The Great Marathon | 4 | 256 | On the Berland Dependence Day it was decided to organize a great marathon. Berland consists of *n* cities, some of which are linked by two-way roads. Each road has a certain length. The cities are numbered from 1 to *n*. It is known that one can get from any city to any other one by the roads.
*n* runners take part in the competition, one from each city. But Berland runners are talkative by nature and that's why the juries took measures to avoid large crowds of marathon participants. The jury decided that every runner should start the marathon from their hometown. Before the start every sportsman will get a piece of paper containing the name of the city where the sportsman's finishing line is. The finish is chosen randomly for every sportsman but it can't coincide with the sportsman's starting point. Several sportsmen are allowed to finish in one and the same city. All the sportsmen start simultaneously and everyone runs the shortest route from the starting point to the finishing one. All the sportsmen run at one speed which equals to 1.
After the competition a follow-up table of the results will be composed where the sportsmen will be sorted according to the nondecrease of time they spent to cover the distance. The first *g* sportsmen in the table will get golden medals, the next *s* sportsmen will get silver medals and the rest will get bronze medals. Besides, if two or more sportsmen spend the same amount of time to cover the distance, they are sorted according to the number of the city where a sportsman started to run in the ascending order. That means no two sportsmen share one and the same place.
According to the rules of the competition the number of gold medals *g* must satisfy the inequation *g*1<=≤<=*g*<=≤<=*g*2, where *g*1 and *g*2 are values formed historically. In a similar way, the number of silver medals *s* must satisfy the inequation *s*1<=≤<=*s*<=≤<=*s*2, where *s*1 and *s*2 are also values formed historically.
At present, before the start of the competition, the destination points of every sportsman are unknown. However, the press demands details and that's why you are given the task of counting the number of the ways to distribute the medals. Two ways to distribute the medals are considered different if at least one sportsman could have received during those distributions different kinds of medals. | The first input line contains given integers *n* and *m* (3<=≤<=*n*<=≤<=50, *n*<=-<=1<=≤<=*m*<=≤<=1000), where *n* is the number of Berland towns and *m* is the number of roads.
Next in *m* lines road descriptions are given as groups of three integers *v*, *u*, *c*, which are the numbers of linked towns and its length (1<=≤<=*v*,<=*u*<=≤<=*n*, *v*<=≠<=*u*, 1<=≤<=*c*<=≤<=1000). Every pair of cities have no more than one road between them.
The last line contains integers *g*1, *g*2, *s*1, *s*2 (1<=≤<=*g*1<=≤<=*g*2, 1<=≤<=*s*1<=≤<=*s*2, *g*2<=+<=*s*2<=<<=*n*). The input data numbers, located on one line, are space-separated. | Print the single number — the number of ways to distribute the medals. It is guaranteed that the number fits in the standard 64-bit signed data type. | [
"3 2\n1 2 1\n2 3 1\n1 1 1 1\n",
"4 5\n1 2 2\n2 3 1\n3 4 2\n4 1 2\n1 3 3\n1 2 1 1\n",
"3 3\n1 2 2\n2 3 1\n3 1 2\n1 1 1 1\n"
] | [
"3\n",
"19\n",
"4\n"
] | none | [] | 62 | 0 | 0 | 1,530 |
784 | Numbers Joke | [
"*special"
] | null | null | The input contains a single integer *a* (1<=≤<=*a*<=≤<=30).
Output a single integer. | The input contains a single integer *a* (1<=≤<=*a*<=≤<=30). | Output a single integer. | [
"3\n"
] | [
"27\n"
] | none | [
{
"input": "3",
"output": "27"
},
{
"input": "1",
"output": "4"
},
{
"input": "2",
"output": "22"
},
{
"input": "4",
"output": "58"
},
{
"input": "5",
"output": "85"
},
{
"input": "6",
"output": "94"
},
{
"input": "7",
"output": "121"
... | 109 | 0 | 0 | 1,531 | |
223 | Partial Sums | [
"combinatorics",
"math",
"number theory"
] | null | null | You've got an array *a*, consisting of *n* integers. The array elements are indexed from 1 to *n*. Let's determine a two step operation like that:
1. First we build by the array *a* an array *s* of partial sums, consisting of *n* elements. Element number *i* (1<=≤<=*i*<=≤<=*n*) of array *s* equals . The operation *x* *mod* *y* means that we take the remainder of the division of number *x* by number *y*. 1. Then we write the contents of the array *s* to the array *a*. Element number *i* (1<=≤<=*i*<=≤<=*n*) of the array *s* becomes the *i*-th element of the array *a* (*a**i*<==<=*s**i*).
You task is to find array *a* after exactly *k* described operations are applied. | The first line contains two space-separated integers *n* and *k* (1<=≤<=*n*<=≤<=2000, 0<=≤<=*k*<=≤<=109). The next line contains *n* space-separated integers *a*1,<=*a*2,<=...,<=*a**n* — elements of the array *a* (0<=≤<=*a**i*<=≤<=109). | Print *n* integers — elements of the array *a* after the operations are applied to it. Print the elements in the order of increasing of their indexes in the array *a*. Separate the printed numbers by spaces. | [
"3 1\n1 2 3\n",
"5 0\n3 14 15 92 6\n"
] | [
"1 3 6\n",
"3 14 15 92 6\n"
] | none | [
{
"input": "3 1\n1 2 3",
"output": "1 3 6"
},
{
"input": "5 0\n3 14 15 92 6",
"output": "3 14 15 92 6"
},
{
"input": "1 1\n3",
"output": "3"
},
{
"input": "1 0\n0",
"output": "0"
},
{
"input": "1 0\n123",
"output": "123"
},
{
"input": "1 1\n0",
"ou... | 92 | 0 | 0 | 1,532 | |
922 | Cloning Toys | [
"implementation"
] | null | null | Imp likes his plush toy a lot.
Recently, he found a machine that can clone plush toys. Imp knows that if he applies the machine to an original toy, he additionally gets one more original toy and one copy, and if he applies the machine to a copied toy, he gets two additional copies.
Initially, Imp has only one original toy. He wants to know if it is possible to use machine to get exactly *x* copied toys and *y* original toys? He can't throw toys away, and he can't apply the machine to a copy if he doesn't currently have any copies. | The only line contains two integers *x* and *y* (0<=≤<=*x*,<=*y*<=≤<=109) — the number of copies and the number of original toys Imp wants to get (including the initial one). | Print "Yes", if the desired configuration is possible, and "No" otherwise.
You can print each letter in arbitrary case (upper or lower). | [
"6 3\n",
"4 2\n",
"1000 1001\n"
] | [
"Yes\n",
"No\n",
"Yes\n"
] | In the first example, Imp has to apply the machine twice to original toys and then twice to copies. | [
{
"input": "6 3",
"output": "Yes"
},
{
"input": "4 2",
"output": "No"
},
{
"input": "1000 1001",
"output": "Yes"
},
{
"input": "1000000000 999999999",
"output": "Yes"
},
{
"input": "81452244 81452247",
"output": "No"
},
{
"input": "188032448 86524683",... | 30 | 0 | 0 | 1,538 | |
366 | Dima and Guards | [
"implementation"
] | null | null | Nothing has changed since the last round. Dima and Inna still love each other and want to be together. They've made a deal with Seryozha and now they need to make a deal with the dorm guards...
There are four guardposts in Dima's dorm. Each post contains two guards (in Russia they are usually elderly women). You can bribe a guard by a chocolate bar or a box of juice. For each guard you know the minimum price of the chocolate bar she can accept as a gift and the minimum price of the box of juice she can accept as a gift. If a chocolate bar for some guard costs less than the minimum chocolate bar price for this guard is, or if a box of juice for some guard costs less than the minimum box of juice price for this guard is, then the guard doesn't accept such a gift.
In order to pass through a guardpost, one needs to bribe both guards.
The shop has an unlimited amount of juice and chocolate of any price starting with 1. Dima wants to choose some guardpost, buy one gift for each guard from the guardpost and spend exactly *n* rubles on it.
Help him choose a post through which he can safely sneak Inna or otherwise say that this is impossible. Mind you, Inna would be very sorry to hear that! | The first line of the input contains integer *n* (1<=≤<=*n*<=≤<=105) — the money Dima wants to spend. Then follow four lines describing the guardposts. Each line contains four integers *a*,<=*b*,<=*c*,<=*d* (1<=≤<=*a*,<=*b*,<=*c*,<=*d*<=≤<=105) — the minimum price of the chocolate and the minimum price of the juice for the first guard and the minimum price of the chocolate and the minimum price of the juice for the second guard, correspondingly. | In a single line of the output print three space-separated integers: the number of the guardpost, the cost of the first present and the cost of the second present. If there is no guardpost Dima can sneak Inna through at such conditions, print -1 in a single line.
The guardposts are numbered from 1 to 4 according to the order given in the input.
If there are multiple solutions, you can print any of them. | [
"10\n5 6 5 6\n6 6 7 7\n5 8 6 6\n9 9 9 9\n",
"10\n6 6 6 6\n7 7 7 7\n4 4 4 4\n8 8 8 8\n",
"5\n3 3 3 3\n3 3 3 3\n3 3 3 3\n3 3 3 3\n"
] | [
"1 5 5\n",
"3 4 6\n",
"-1\n"
] | Explanation of the first example.
The only way to spend 10 rubles to buy the gifts that won't be less than the minimum prices is to buy two 5 ruble chocolates to both guards from the first guardpost.
Explanation of the second example.
Dima needs 12 rubles for the first guardpost, 14 for the second one, 16 for the fourth one. So the only guardpost we can sneak through is the third one. So, Dima can buy 4 ruble chocolate for the first guard and 6 ruble juice of the second guard. | [
{
"input": "10\n5 6 5 6\n6 6 7 7\n5 8 6 6\n9 9 9 9",
"output": "1 5 5"
},
{
"input": "10\n6 6 6 6\n7 7 7 7\n4 4 4 4\n8 8 8 8",
"output": "3 4 6"
},
{
"input": "5\n3 3 3 3\n3 3 3 3\n3 3 3 3\n3 3 3 3",
"output": "-1"
},
{
"input": "100000\n100000 100000 100000 100000\n100000 10... | 124 | 307,200 | 3 | 1,544 | |
877 | Alex and broken contest | [
"implementation",
"strings"
] | null | null | One day Alex was creating a contest about his friends, but accidentally deleted it. Fortunately, all the problems were saved, but now he needs to find them among other problems.
But there are too many problems, to do it manually. Alex asks you to write a program, which will determine if a problem is from this contest by its name.
It is known, that problem is from this contest if and only if its name contains one of Alex's friends' name exactly once. His friends' names are "Danil", "Olya", "Slava", "Ann" and "Nikita".
Names are case sensitive. | The only line contains string from lowercase and uppercase letters and "_" symbols of length, not more than 100 — the name of the problem. | Print "YES", if problem is from this contest, and "NO" otherwise. | [
"Alex_and_broken_contest\n",
"NikitaAndString\n",
"Danil_and_Olya\n"
] | [
"NO",
"YES",
"NO"
] | none | [
{
"input": "Alex_and_broken_contest",
"output": "NO"
},
{
"input": "NikitaAndString",
"output": "YES"
},
{
"input": "Danil_and_Olya",
"output": "NO"
},
{
"input": "Slava____and_the_game",
"output": "YES"
},
{
"input": "Olya_and_energy_drinks",
"output": "YES"
... | 46 | 0 | 0 | 1,545 | |
893 | Rumor | [
"dfs and similar",
"graphs",
"greedy"
] | null | null | Vova promised himself that he would never play computer games... But recently Firestorm — a well-known game developing company — published their newest game, World of Farcraft, and it became really popular. Of course, Vova started playing it.
Now he tries to solve a quest. The task is to come to a settlement named Overcity and spread a rumor in it.
Vova knows that there are *n* characters in Overcity. Some characters are friends to each other, and they share information they got. Also Vova knows that he can bribe each character so he or she starts spreading the rumor; *i*-th character wants *c**i* gold in exchange for spreading the rumor. When a character hears the rumor, he tells it to all his friends, and they start spreading the rumor to their friends (for free), and so on.
The quest is finished when all *n* characters know the rumor. What is the minimum amount of gold Vova needs to spend in order to finish the quest?
Take a look at the notes if you think you haven't understood the problem completely. | The first line contains two integer numbers *n* and *m* (1<=≤<=*n*<=≤<=105,<=0<=≤<=*m*<=≤<=105) — the number of characters in Overcity and the number of pairs of friends.
The second line contains *n* integer numbers *c**i* (0<=≤<=*c**i*<=≤<=109) — the amount of gold *i*-th character asks to start spreading the rumor.
Then *m* lines follow, each containing a pair of numbers (*x**i*,<=*y**i*) which represent that characters *x**i* and *y**i* are friends (1<=≤<=*x**i*,<=*y**i*<=≤<=*n*, *x**i*<=≠<=*y**i*). It is guaranteed that each pair is listed at most once. | Print one number — the minimum amount of gold Vova has to spend in order to finish the quest. | [
"5 2\n2 5 3 4 8\n1 4\n4 5\n",
"10 0\n1 2 3 4 5 6 7 8 9 10\n",
"10 5\n1 6 2 7 3 8 4 9 5 10\n1 2\n3 4\n5 6\n7 8\n9 10\n"
] | [
"10\n",
"55\n",
"15\n"
] | In the first example the best decision is to bribe the first character (he will spread the rumor to fourth character, and the fourth one will spread it to fifth). Also Vova has to bribe the second and the third characters, so they know the rumor.
In the second example Vova has to bribe everyone.
In the third example the optimal decision is to bribe the first, the third, the fifth, the seventh and the ninth characters. | [
{
"input": "5 2\n2 5 3 4 8\n1 4\n4 5",
"output": "10"
},
{
"input": "10 0\n1 2 3 4 5 6 7 8 9 10",
"output": "55"
},
{
"input": "10 5\n1 6 2 7 3 8 4 9 5 10\n1 2\n3 4\n5 6\n7 8\n9 10",
"output": "15"
},
{
"input": "1 0\n0",
"output": "0"
},
{
"input": "1 0\n10000000... | 1,747 | 11,366,400 | 0 | 1,547 | |
793 | Presents in Bankopolis | [
"dp",
"graphs",
"shortest paths"
] | null | null | Bankopolis is an incredible city in which all the *n* crossroads are located on a straight line and numbered from 1 to *n* along it. On each crossroad there is a bank office.
The crossroads are connected with *m* oriented bicycle lanes (the *i*-th lane goes from crossroad *u**i* to crossroad *v**i*), the difficulty of each of the lanes is known.
Oleg the bank client wants to gift happiness and joy to the bank employees. He wants to visit exactly *k* offices, in each of them he wants to gift presents to the employees.
The problem is that Oleg don't want to see the reaction on his gifts, so he can't use a bicycle lane which passes near the office in which he has already presented his gifts (formally, the *i*-th lane passes near the office on the *x*-th crossroad if and only if *min*(*u**i*,<=*v**i*)<=<<=*x*<=<<=*max*(*u**i*,<=*v**i*))). Of course, in each of the offices Oleg can present gifts exactly once. Oleg is going to use exactly *k*<=-<=1 bicycle lane to move between offices. Oleg can start his path from any office and finish it in any office.
Oleg wants to choose such a path among possible ones that the total difficulty of the lanes he will use is minimum possible. Find this minimum possible total difficulty. | The first line contains two integers *n* and *k* (1<=≤<=*n*,<=*k*<=≤<=80) — the number of crossroads (and offices) and the number of offices Oleg wants to visit.
The second line contains single integer *m* (0<=≤<=*m*<=≤<=2000) — the number of bicycle lanes in Bankopolis.
The next *m* lines contain information about the lanes.
The *i*-th of these lines contains three integers *u**i*, *v**i* and *c**i* (1<=≤<=*u**i*,<=*v**i*<=≤<=*n*, 1<=≤<=*c**i*<=≤<=1000), denoting the crossroads connected by the *i*-th road and its difficulty. | In the only line print the minimum possible total difficulty of the lanes in a valid path, or -1 if there are no valid paths. | [
"7 4\n4\n1 6 2\n6 2 2\n2 4 2\n2 7 1\n",
"4 3\n4\n2 1 2\n1 3 2\n3 4 2\n4 1 1\n"
] | [
"6\n",
"3\n"
] | In the first example Oleg visiting banks by path 1 → 6 → 2 → 4.
Path 1 → 6 → 2 → 7 with smaller difficulity is incorrect because crossroad 2 → 7 passes near already visited office on the crossroad 6.
In the second example Oleg can visit banks by path 4 → 1 → 3. | [
{
"input": "7 4\n4\n1 6 2\n6 2 2\n2 4 2\n2 7 1",
"output": "6"
},
{
"input": "4 3\n4\n2 1 2\n1 3 2\n3 4 2\n4 1 1",
"output": "3"
},
{
"input": "3 2\n10\n2 3 290\n3 1 859\n3 1 852\n1 2 232\n1 2 358\n2 1 123\n1 3 909\n2 1 296\n1 3 119\n1 2 584",
"output": "119"
},
{
"input": "3... | 124 | 409,600 | 0 | 1,548 | |
831 | Unimodal Array | [
"implementation"
] | null | null | Array of integers is unimodal, if:
- it is strictly increasing in the beginning; - after that it is constant; - after that it is strictly decreasing.
The first block (increasing) and the last block (decreasing) may be absent. It is allowed that both of this blocks are absent.
For example, the following three arrays are unimodal: [5,<=7,<=11,<=11,<=2,<=1], [4,<=4,<=2], [7], but the following three are not unimodal: [5,<=5,<=6,<=6,<=1], [1,<=2,<=1,<=2], [4,<=5,<=5,<=6].
Write a program that checks if an array is unimodal. | The first line contains integer *n* (1<=≤<=*n*<=≤<=100) — the number of elements in the array.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=1<=000) — the elements of the array. | Print "YES" if the given array is unimodal. Otherwise, print "NO".
You can output each letter in any case (upper or lower). | [
"6\n1 5 5 5 4 2\n",
"5\n10 20 30 20 10\n",
"4\n1 2 1 2\n",
"7\n3 3 3 3 3 3 3\n"
] | [
"YES\n",
"YES\n",
"NO\n",
"YES\n"
] | In the first example the array is unimodal, because it is strictly increasing in the beginning (from position 1 to position 2, inclusively), that it is constant (from position 2 to position 4, inclusively) and then it is strictly decreasing (from position 4 to position 6, inclusively). | [
{
"input": "6\n1 5 5 5 4 2",
"output": "YES"
},
{
"input": "5\n10 20 30 20 10",
"output": "YES"
},
{
"input": "4\n1 2 1 2",
"output": "NO"
},
{
"input": "7\n3 3 3 3 3 3 3",
"output": "YES"
},
{
"input": "6\n5 7 11 11 2 1",
"output": "YES"
},
{
"input":... | 46 | 0 | 3 | 1,549 | |
12 | Fruits | [
"greedy",
"implementation",
"sortings"
] | C. Fruits | 1 | 256 | The spring is coming and it means that a lot of fruits appear on the counters. One sunny day little boy Valera decided to go shopping. He made a list of *m* fruits he wanted to buy. If Valera want to buy more than one fruit of some kind, he includes it into the list several times.
When he came to the fruit stall of Ashot, he saw that the seller hadn't distributed price tags to the goods, but put all price tags on the counter. Later Ashot will attach every price tag to some kind of fruits, and Valera will be able to count the total price of all fruits from his list. But Valera wants to know now what can be the smallest total price (in case of the most «lucky» for him distribution of price tags) and the largest total price (in case of the most «unlucky» for him distribution of price tags). | The first line of the input contains two integer number *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=100) — the number of price tags (which is equal to the number of different kinds of fruits that Ashot sells) and the number of items in Valera's list. The second line contains *n* space-separated positive integer numbers. Each of them doesn't exceed 100 and stands for the price of one fruit of some kind. The following *m* lines contain names of the fruits from the list. Each name is a non-empty string of small Latin letters which length doesn't exceed 32. It is guaranteed that the number of distinct fruits from the list is less of equal to *n*. Also it is known that the seller has in stock all fruits that Valera wants to buy. | Print two numbers *a* and *b* (*a*<=≤<=*b*) — the minimum and the maximum possible sum which Valera may need to buy all fruits from his list. | [
"5 3\n4 2 1 10 5\napple\norange\nmango\n",
"6 5\n3 5 1 6 8 1\npeach\ngrapefruit\nbanana\norange\norange\n"
] | [
"7 19\n",
"11 30\n"
] | none | [
{
"input": "5 3\n4 2 1 10 5\napple\norange\nmango",
"output": "7 19"
},
{
"input": "6 5\n3 5 1 6 8 1\npeach\ngrapefruit\nbanana\norange\norange",
"output": "11 30"
},
{
"input": "2 2\n91 82\neiiofpfpmemlakcystpun\nmcnzeiiofpfpmemlakcystpunfl",
"output": "173 173"
},
{
"input"... | 46 | 102,400 | 3.976809 | 1,553 |
182 | Vasya's Calendar | [
"implementation"
] | null | null | Vasya lives in a strange world. The year has *n* months and the *i*-th month has *a**i* days. Vasya got a New Year present — the clock that shows not only the time, but also the date.
The clock's face can display any number from 1 to *d*. It is guaranteed that *a**i*<=≤<=*d* for all *i* from 1 to *n*. The clock does not keep information about the current month, so when a new day comes, it simply increases the current day number by one. The clock cannot display number *d*<=+<=1, so after day number *d* it shows day 1 (the current day counter resets). The mechanism of the clock allows you to increase the day number by one manually. When you execute this operation, day *d* is also followed by day 1.
Vasya begins each day checking the day number on the clock. If the day number on the clock does not match the actual day number in the current month, then Vasya manually increases it by one. Vasya is persistent and repeats this operation until the day number on the clock matches the actual number of the current day in the current month.
A year passed and Vasya wonders how many times he manually increased the day number by one, from the first day of the first month to the last day of the *n*-th month inclusive, considering that on the first day of the first month the clock display showed day 1. | The first line contains the single number *d* — the maximum number of the day that Vasya's clock can show (1<=≤<=*d*<=≤<=106).
The second line contains a single integer *n* — the number of months in the year (1<=≤<=*n*<=≤<=2000).
The third line contains *n* space-separated integers: *a**i* (1<=≤<=*a**i*<=≤<=*d*) — the number of days in each month in the order in which they follow, starting from the first one. | Print a single number — the number of times Vasya manually increased the day number by one throughout the last year. | [
"4\n2\n2 2\n",
"5\n3\n3 4 3\n",
"31\n12\n31 28 31 30 31 30 31 31 30 31 30 31\n"
] | [
"2\n",
"3\n",
"7\n"
] | In the first sample the situation is like this:
- Day 1. Month 1. The clock shows 1. Vasya changes nothing. - Day 2. Month 1. The clock shows 2. Vasya changes nothing. - Day 1. Month 2. The clock shows 3. Vasya manually increases the day number by 1. After that the clock shows 4. Vasya increases the day number by 1 manually. After that the clock shows 1. - Day 2. Month 2. The clock shows 2. Vasya changes nothing. | [
{
"input": "4\n2\n2 2",
"output": "2"
},
{
"input": "5\n3\n3 4 3",
"output": "3"
},
{
"input": "31\n12\n31 28 31 30 31 30 31 31 30 31 30 31",
"output": "7"
},
{
"input": "1\n1\n1",
"output": "0"
},
{
"input": "1\n2\n1 1",
"output": "0"
},
{
"input": "2... | 1,000 | 6,963,200 | 0 | 1,554 | |
598 | Igor In the Museum | [
"dfs and similar",
"graphs",
"shortest paths"
] | null | null | Igor is in the museum and he wants to see as many pictures as possible.
Museum can be represented as a rectangular field of *n*<=×<=*m* cells. Each cell is either empty or impassable. Empty cells are marked with '.', impassable cells are marked with '*'. Every two adjacent cells of different types (one empty and one impassable) are divided by a wall containing one picture.
At the beginning Igor is in some empty cell. At every moment he can move to any empty cell that share a side with the current one.
For several starting positions you should calculate the maximum number of pictures that Igor can see. Igor is able to see the picture only if he is in the cell adjacent to the wall with this picture. Igor have a lot of time, so he will examine every picture he can see. | First line of the input contains three integers *n*, *m* and *k* (3<=≤<=*n*,<=*m*<=≤<=1000,<=1<=≤<=*k*<=≤<=*min*(*n*·*m*,<=100<=000)) — the museum dimensions and the number of starting positions to process.
Each of the next *n* lines contains *m* symbols '.', '*' — the description of the museum. It is guaranteed that all border cells are impassable, so Igor can't go out from the museum.
Each of the last *k* lines contains two integers *x* and *y* (1<=≤<=*x*<=≤<=*n*,<=1<=≤<=*y*<=≤<=*m*) — the row and the column of one of Igor's starting positions respectively. Rows are numbered from top to bottom, columns — from left to right. It is guaranteed that all starting positions are empty cells. | Print *k* integers — the maximum number of pictures, that Igor can see if he starts in corresponding position. | [
"5 6 3\n******\n*..*.*\n******\n*....*\n******\n2 2\n2 5\n4 3\n",
"4 4 1\n****\n*..*\n*.**\n****\n3 2\n"
] | [
"6\n4\n10\n",
"8\n"
] | none | [
{
"input": "5 6 3\n******\n*..*.*\n******\n*....*\n******\n2 2\n2 5\n4 3",
"output": "6\n4\n10"
},
{
"input": "4 4 1\n****\n*..*\n*.**\n****\n3 2",
"output": "8"
},
{
"input": "3 3 1\n***\n*.*\n***\n2 2",
"output": "4"
},
{
"input": "5 5 10\n*****\n*...*\n*..**\n*.***\n*****\... | 1,000 | 87,552,000 | 0 | 1,555 | |
922 | Magic Forest | [
"brute force"
] | null | null | Imp is in a magic forest, where xorangles grow (wut?)
A xorangle of order *n* is such a non-degenerate triangle, that lengths of its sides are integers not exceeding *n*, and the xor-sum of the lengths is equal to zero. Imp has to count the number of distinct xorangles of order *n* to get out of the forest.
Formally, for a given integer *n* you have to find the number of such triples (*a*,<=*b*,<=*c*), that:
- 1<=≤<=*a*<=≤<=*b*<=≤<=*c*<=≤<=*n*; - , where denotes the [bitwise xor](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of integers *x* and *y*. - (*a*,<=*b*,<=*c*) form a non-degenerate (with strictly positive area) triangle. | The only line contains a single integer *n* (1<=≤<=*n*<=≤<=2500). | Print the number of xorangles of order *n*. | [
"6\n",
"10\n"
] | [
"1\n",
"2\n"
] | The only xorangle in the first sample is (3, 5, 6). | [
{
"input": "6",
"output": "1"
},
{
"input": "10",
"output": "2"
},
{
"input": "3",
"output": "0"
},
{
"input": "4",
"output": "0"
},
{
"input": "5",
"output": "0"
},
{
"input": "2500",
"output": "700393"
},
{
"input": "952",
"output": "... | 171 | 1,638,400 | 3 | 1,557 | |
525 | Arthur and Walls | [
"constructive algorithms",
"data structures",
"graphs",
"greedy",
"shortest paths"
] | null | null | Finally it is a day when Arthur has enough money for buying an apartment. He found a great option close to the center of the city with a nice price.
Plan of the apartment found by Arthur looks like a rectangle *n*<=×<=*m* consisting of squares of size 1<=×<=1. Each of those squares contains either a wall (such square is denoted by a symbol "*" on the plan) or a free space (such square is denoted on the plan by a symbol ".").
Room in an apartment is a maximal connected area consisting of free squares. Squares are considered adjacent if they share a common side.
The old Arthur dream is to live in an apartment where all rooms are rectangles. He asks you to calculate minimum number of walls you need to remove in order to achieve this goal. After removing a wall from a square it becomes a free square. While removing the walls it is possible that some rooms unite into a single one. | The first line of the input contains two integers *n*,<=*m* (1<=≤<=*n*,<=*m*<=≤<=2000) denoting the size of the Arthur apartments.
Following *n* lines each contain *m* symbols — the plan of the apartment.
If the cell is denoted by a symbol "*" then it contains a wall.
If the cell is denoted by a symbol "." then it this cell is free from walls and also this cell is contained in some of the rooms. | Output *n* rows each consisting of *m* symbols that show how the Arthur apartment plan should look like after deleting the minimum number of walls in order to make each room (maximum connected area free from walls) be a rectangle.
If there are several possible answers, output any of them. | [
"5 5\n.*.*.\n*****\n.*.*.\n*****\n.*.*.\n",
"6 7\n***.*.*\n..*.*.*\n*.*.*.*\n*.*.*.*\n..*...*\n*******\n",
"4 5\n.....\n.....\n..***\n..*..\n"
] | [
".*.*.\n*****\n.*.*.\n*****\n.*.*.\n",
"***...*\n..*...*\n..*...*\n..*...*\n..*...*\n*******\n",
".....\n.....\n.....\n.....\n"
] | none | [
{
"input": "5 5\n.*.*.\n*****\n.*.*.\n*****\n.*.*.",
"output": ".*.*.\n*****\n.*.*.\n*****\n.*.*."
},
{
"input": "6 7\n***.*.*\n..*.*.*\n*.*.*.*\n*.*.*.*\n..*...*\n*******",
"output": "***...*\n..*...*\n..*...*\n..*...*\n..*...*\n*******"
},
{
"input": "4 5\n.....\n.....\n..***\n..*..",
... | 2,000 | 49,356,800 | 0 | 1,558 | |
952 | A Map of the Cat | [
"brute force",
"interactive"
] | null | null | If you have ever interacted with a cat, you have probably noticed that they are quite particular about how to pet them. Here is an approximate map of a normal cat.
However, some cats won't tolerate this nonsense from the humans. Here is a map of a grumpy cat.
You have met a cat. Can you figure out whether it's normal or grumpy? | none | none | [] | [] | Please make sure to use the stream flushing operation after each query in order not to leave part of your output in some buffer. | [
{
"input": "5 0 1 2 5 3 5 4 5 5",
"output": "Correct answer 'normal'"
},
{
"input": "5 5 5 6 6 7 8 9 10 11",
"output": "Correct answer 'grumpy'"
},
{
"input": "10 6 5 7 5 6 11 5 8 9",
"output": "Correct answer 'grumpy'"
},
{
"input": "7 10 8 9 6 5 5 11 5 6",
"output": "Co... | 109 | 0 | 0 | 1,559 | |
213 | Game | [
"dfs and similar",
"greedy"
] | null | null | Furik and Rubik love playing computer games. Furik has recently found a new game that greatly interested Rubik. The game consists of *n* parts and to complete each part a player may probably need to complete some other ones. We know that the game can be fully completed, that is, its parts do not form cyclic dependencies.
Rubik has 3 computers, on which he can play this game. All computers are located in different houses. Besides, it has turned out that each part of the game can be completed only on one of these computers. Let's number the computers with integers from 1 to 3. Rubik can perform the following actions:
- Complete some part of the game on some computer. Rubik spends exactly 1 hour on completing any part on any computer. - Move from the 1-st computer to the 2-nd one. Rubik spends exactly 1 hour on that. - Move from the 1-st computer to the 3-rd one. Rubik spends exactly 2 hours on that. - Move from the 2-nd computer to the 1-st one. Rubik spends exactly 2 hours on that. - Move from the 2-nd computer to the 3-rd one. Rubik spends exactly 1 hour on that. - Move from the 3-rd computer to the 1-st one. Rubik spends exactly 1 hour on that. - Move from the 3-rd computer to the 2-nd one. Rubik spends exactly 2 hours on that.
Help Rubik to find the minimum number of hours he will need to complete all parts of the game. Initially Rubik can be located at the computer he considers necessary. | The first line contains integer *n* (1<=≤<=*n*<=≤<=200) — the number of game parts. The next line contains *n* integers, the *i*-th integer — *c**i* (1<=≤<=*c**i*<=≤<=3) represents the number of the computer, on which you can complete the game part number *i*.
Next *n* lines contain descriptions of game parts. The *i*-th line first contains integer *k**i* (0<=≤<=*k**i*<=≤<=*n*<=-<=1), then *k**i* distinct integers *a**i*,<=*j* (1<=≤<=*a**i*,<=*j*<=≤<=*n*; *a**i*,<=*j*<=≠<=*i*) — the numbers of parts to complete before part *i*.
Numbers on all lines are separated by single spaces. You can assume that the parts of the game are numbered from 1 to *n* in some way. It is guaranteed that there are no cyclic dependencies between the parts of the game. | On a single line print the answer to the problem. | [
"1\n1\n0\n",
"5\n2 2 1 1 3\n1 5\n2 5 1\n2 5 4\n1 5\n0\n"
] | [
"1\n",
"7\n"
] | Note to the second sample: before the beginning of the game the best strategy is to stand by the third computer. First we complete part 5. Then we go to the 1-st computer and complete parts 3 and 4. Then we go to the 2-nd computer and complete parts 1 and 2. In total we get 1+1+2+1+2, which equals 7 hours. | [
{
"input": "1\n1\n0",
"output": "1"
},
{
"input": "5\n2 2 1 1 3\n1 5\n2 5 1\n2 5 4\n1 5\n0",
"output": "7"
},
{
"input": "7\n1 3 3 1 2 1 1\n0\n1 1\n1 1\n2 1 6\n3 1 2 7\n1 1\n1 1",
"output": "11"
},
{
"input": "2\n2 1\n0\n1 1",
"output": "4"
},
{
"input": "3\n2 1 2... | 92 | 0 | 0 | 1,563 | |
617 | Elephant | [
"math"
] | null | null | An elephant decided to visit his friend. It turned out that the elephant's house is located at point 0 and his friend's house is located at point *x*(*x*<=><=0) of the coordinate line. In one step the elephant can move 1, 2, 3, 4 or 5 positions forward. Determine, what is the minimum number of steps he need to make in order to get to his friend's house. | The first line of the input contains an integer *x* (1<=≤<=*x*<=≤<=1<=000<=000) — The coordinate of the friend's house. | Print the minimum number of steps that elephant needs to make to get from point 0 to point *x*. | [
"5\n",
"12\n"
] | [
"1\n",
"3\n"
] | In the first sample the elephant needs to make one step of length 5 to reach the point *x*.
In the second sample the elephant can get to point *x* if he moves by 3, 5 and 4. There are other ways to get the optimal answer but the elephant cannot reach *x* in less than three moves. | [
{
"input": "5",
"output": "1"
},
{
"input": "12",
"output": "3"
},
{
"input": "999999",
"output": "200000"
},
{
"input": "41",
"output": "9"
},
{
"input": "1000000",
"output": "200000"
},
{
"input": "1",
"output": "1"
},
{
"input": "2",
... | 46 | 0 | 3 | 1,564 | |
28 | Bath Queue | [
"combinatorics",
"dp",
"probabilities"
] | C. Bath Queue | 2 | 256 | There are *n* students living in the campus. Every morning all students wake up at the same time and go to wash. There are *m* rooms with wash basins. The *i*-th of these rooms contains *a**i* wash basins. Every student independently select one the rooms with equal probability and goes to it. After all students selected their rooms, students in each room divide into queues by the number of wash basins so that the size of the largest queue is the least possible. Calculate the expected value of the size of the largest queue among all rooms. | The first line contains two positive integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=50) — the amount of students and the amount of rooms. The second line contains *m* integers *a*1,<=*a*2,<=... ,<=*a**m* (1<=≤<=*a**i*<=≤<=50). *a**i* means the amount of wash basins in the *i*-th room. | Output single number: the expected value of the size of the largest queue. Your answer must have an absolute or relative error less than 10<=-<=9. | [
"1 1\n2\n",
"2 2\n1 1\n",
"2 3\n1 1 1\n",
"7 5\n1 1 2 3 1\n"
] | [
"1.00000000000000000000\n",
"1.50000000000000000000\n",
"1.33333333333333350000\n",
"2.50216960000000070000\n"
] | none | [
{
"input": "1 1\n2",
"output": "1.00000000000000000000"
},
{
"input": "2 2\n1 1",
"output": "1.50000000000000000000"
},
{
"input": "2 3\n1 1 1",
"output": "1.33333333333333350000"
},
{
"input": "7 5\n1 1 2 3 1",
"output": "2.50216960000000070000"
},
{
"input": "10... | 0 | 0 | -1 | 1,565 |
515 | Drazil and Date | [
"math"
] | null | null | Someday, Drazil wanted to go on date with Varda. Drazil and Varda live on Cartesian plane. Drazil's home is located in point (0,<=0) and Varda's home is located in point (*a*,<=*b*). In each step, he can move in a unit distance in horizontal or vertical direction. In other words, from position (*x*,<=*y*) he can go to positions (*x*<=+<=1,<=*y*), (*x*<=-<=1,<=*y*), (*x*,<=*y*<=+<=1) or (*x*,<=*y*<=-<=1).
Unfortunately, Drazil doesn't have sense of direction. So he randomly chooses the direction he will go to in each step. He may accidentally return back to his house during his travel. Drazil may even not notice that he has arrived to (*a*,<=*b*) and continue travelling.
Luckily, Drazil arrived to the position (*a*,<=*b*) successfully. Drazil said to Varda: "It took me exactly *s* steps to travel from my house to yours". But Varda is confused about his words, she is not sure that it is possible to get from (0,<=0) to (*a*,<=*b*) in exactly *s* steps. Can you find out if it is possible for Varda? | You are given three integers *a*, *b*, and *s* (<=-<=109<=≤<=*a*,<=*b*<=≤<=109, 1<=≤<=*s*<=≤<=2·109) in a single line. | If you think Drazil made a mistake and it is impossible to take exactly *s* steps and get from his home to Varda's home, print "No" (without quotes).
Otherwise, print "Yes". | [
"5 5 11\n",
"10 15 25\n",
"0 5 1\n",
"0 0 2\n"
] | [
"No\n",
"Yes\n",
"No\n",
"Yes\n"
] | In fourth sample case one possible route is: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0d30660ddf6eb6c64ffd071055a4e8ddd016cde5.png" style="max-width: 100.0%;max-height: 100.0%;"/>. | [
{
"input": "5 5 11",
"output": "No"
},
{
"input": "10 15 25",
"output": "Yes"
},
{
"input": "0 5 1",
"output": "No"
},
{
"input": "0 0 2",
"output": "Yes"
},
{
"input": "999999999 999999999 2000000000",
"output": "Yes"
},
{
"input": "-606037695 9983201... | 46 | 0 | 3 | 1,570 | |
439 | Devu, the Dumb Guy | [
"implementation",
"sortings"
] | null | null | Devu is a dumb guy, his learning curve is very slow. You are supposed to teach him *n* subjects, the *i**th* subject has *c**i* chapters. When you teach him, you are supposed to teach all the chapters of a subject continuously.
Let us say that his initial per chapter learning power of a subject is *x* hours. In other words he can learn a chapter of a particular subject in *x* hours.
Well Devu is not complete dumb, there is a good thing about him too. If you teach him a subject, then time required to teach any chapter of the next subject will require exactly 1 hour less than previously required (see the examples to understand it more clearly). Note that his per chapter learning power can not be less than 1 hour.
You can teach him the *n* subjects in any possible order. Find out minimum amount of time (in hours) Devu will take to understand all the subjects and you will be free to do some enjoying task rather than teaching a dumb guy.
Please be careful that answer might not fit in 32 bit data type. | The first line will contain two space separated integers *n*, *x* (1<=≤<=*n*,<=*x*<=≤<=105). The next line will contain *n* space separated integers: *c*1,<=*c*2,<=...,<=*c**n* (1<=≤<=*c**i*<=≤<=105). | Output a single integer representing the answer to the problem. | [
"2 3\n4 1\n",
"4 2\n5 1 2 1\n",
"3 3\n1 1 1\n"
] | [
"11\n",
"10\n",
"6\n"
] | Look at the first example. Consider the order of subjects: 1, 2. When you teach Devu the first subject, it will take him 3 hours per chapter, so it will take 12 hours to teach first subject. After teaching first subject, his per chapter learning time will be 2 hours. Now teaching him second subject will take 2 × 1 = 2 hours. Hence you will need to spend 12 + 2 = 14 hours.
Consider the order of subjects: 2, 1. When you teach Devu the second subject, then it will take him 3 hours per chapter, so it will take 3 × 1 = 3 hours to teach the second subject. After teaching the second subject, his per chapter learning time will be 2 hours. Now teaching him the first subject will take 2 × 4 = 8 hours. Hence you will need to spend 11 hours.
So overall, minimum of both the cases is 11 hours.
Look at the third example. The order in this example doesn't matter. When you teach Devu the first subject, it will take him 3 hours per chapter. When you teach Devu the second subject, it will take him 2 hours per chapter. When you teach Devu the third subject, it will take him 1 hours per chapter. In total it takes 6 hours. | [
{
"input": "2 3\n4 1",
"output": "11"
},
{
"input": "4 2\n5 1 2 1",
"output": "10"
},
{
"input": "3 3\n1 1 1",
"output": "6"
},
{
"input": "20 4\n1 1 3 5 5 1 3 4 2 5 2 4 3 1 3 3 3 3 4 3",
"output": "65"
},
{
"input": "20 10\n6 6 1 2 6 4 5 3 6 5 4 5 6 5 4 6 6 2 3 3... | 218 | 7,680,000 | 3 | 1,572 | |
272 | Dima and Friends | [
"implementation",
"math"
] | null | null | Dima and his friends have been playing hide and seek at Dima's place all night. As a result, Dima's place got messy. In the morning they decided that they need to clean the place.
To decide who exactly would clean the apartment, the friends want to play a counting-out game. First, all the guys stand in a circle, and then each of them shows some number of fingers on one hand (one to five), and then the boys count in a circle, starting from Dima, the number of people, respective to the total number of fingers shown. The person on who the countdown stops will clean the apartment.
For example, if Dima and one of his friends played hide and seek, and 7 fingers were shown during the counting-out, then Dima would clean the place. If there were 2 or say, 8 fingers shown, then his friend would clean the place.
Dima knows how many fingers each of his friends will show during the counting-out. Now he is interested in the number of ways to show some number of fingers on one hand (one to five), so that he did not have to clean the place. Help Dima. | The first line contains integer *n* (1<=≤<=*n*<=≤<=100) — the number of Dima's friends. Dima himself isn't considered to be his own friend. The second line contains *n* positive integers, not exceeding 5, representing, how many fingers the Dima's friends will show.
The numbers in the lines are separated by a single space. | In a single line print the answer to the problem. | [
"1\n1\n",
"1\n2\n",
"2\n3 5\n"
] | [
"3\n",
"2\n",
"3\n"
] | In the first sample Dima can show 1, 3 or 5 fingers. If Dima shows 3 fingers, then the counting-out will go like that: Dima, his friend, Dima, his friend.
In the second sample Dima can show 2 or 4 fingers. | [
{
"input": "1\n1",
"output": "3"
},
{
"input": "1\n2",
"output": "2"
},
{
"input": "2\n3 5",
"output": "3"
},
{
"input": "2\n3 5",
"output": "3"
},
{
"input": "1\n5",
"output": "3"
},
{
"input": "5\n4 4 3 5 1",
"output": "4"
},
{
"input": "... | 310 | 0 | 3 | 1,574 | |
27 | Tournament | [
"bitmasks",
"brute force",
"dfs and similar",
"greedy"
] | B. Tournament | 2 | 256 | The tournament «Sleepyhead-2010» in the rapid falling asleep has just finished in Berland. *n* best participants from the country have participated in it. The tournament consists of games, each of them is a match between two participants. *n*·(*n*<=-<=1)<=/<=2 games were played during the tournament, and each participant had a match with each other participant.
The rules of the game are quite simple — the participant who falls asleep first wins. The secretary made a record of each game in the form «*x**i* *y**i*», where *x**i* and *y**i* are the numbers of participants. The first number in each pair is a winner (i.e. *x**i* is a winner and *y**i* is a loser). There is no draws.
Recently researches form the «Institute Of Sleep» have found that every person is characterized by a value *p**j* — the speed of falling asleep. The person who has lower speed wins. Every person has its own value *p**j*, constant during the life.
It is known that all participants of the tournament have distinct speeds of falling asleep. Also it was found that the secretary made records about all the games except one. You are to find the result of the missing game. | The first line contains one integer *n* (3<=≤<=*n*<=≤<=50) — the number of participants. The following *n*·(*n*<=-<=1)<=/<=2<=-<=1 lines contain the results of the games. Each game is described in a single line by two integers *x**i*,<=*y**i* (1<=≤<=*x**i*,<=*y**i*<=≤<=*n*,<=*x**i*<=≠<=*y**i*), where *x**i* и *y**i* are the numbers of the opponents in this game. It is known that during the tournament each of the *n* participants played *n*<=-<=1 games, one game with each other participant. | Output two integers *x* and *y* — the missing record. If there are several solutions, output any of them. | [
"4\n4 2\n4 1\n2 3\n2 1\n3 1\n"
] | [
"4 3\n"
] | none | [
{
"input": "3\n3 2\n1 2",
"output": "1 3"
},
{
"input": "4\n2 4\n3 4\n1 2\n1 4\n1 3",
"output": "2 3"
},
{
"input": "5\n3 5\n2 5\n1 5\n1 4\n4 3\n1 3\n2 3\n4 5\n4 2",
"output": "1 2"
},
{
"input": "6\n3 4\n3 5\n5 4\n1 2\n5 6\n2 6\n5 2\n3 6\n3 2\n4 6\n2 4\n1 3\n1 5\n1 4",
"... | 216 | 0 | 0 | 1,575 |
287 | Pipeline | [
"binary search",
"math"
] | null | null | Vova, the Ultimate Thule new shaman, wants to build a pipeline. As there are exactly *n* houses in Ultimate Thule, Vova wants the city to have exactly *n* pipes, each such pipe should be connected to the water supply. A pipe can be connected to the water supply if there's water flowing out of it. Initially Vova has only one pipe with flowing water. Besides, Vova has several splitters.
A splitter is a construction that consists of one input (it can be connected to a water pipe) and *x* output pipes. When a splitter is connected to a water pipe, water flows from each output pipe. You can assume that the output pipes are ordinary pipes. For example, you can connect water supply to such pipe if there's water flowing out from it. At most one splitter can be connected to any water pipe.
Vova has one splitter of each kind: with 2, 3, 4, ..., *k* outputs. Help Vova use the minimum number of splitters to build the required pipeline or otherwise state that it's impossible.
Vova needs the pipeline to have exactly *n* pipes with flowing out water. Note that some of those pipes can be the output pipes of the splitters. | The first line contains two space-separated integers *n* and *k* (1<=≤<=*n*<=≤<=1018, 2<=≤<=*k*<=≤<=109).
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier. | Print a single integer — the minimum number of splitters needed to build the pipeline. If it is impossible to build a pipeline with the given splitters, print -1. | [
"4 3\n",
"5 5\n",
"8 4\n"
] | [
"2\n",
"1\n",
"-1\n"
] | none | [
{
"input": "4 3",
"output": "2"
},
{
"input": "5 5",
"output": "1"
},
{
"input": "8 4",
"output": "-1"
},
{
"input": "1000000000000000000 1000000000",
"output": "-1"
},
{
"input": "499999998500000001 1000000000",
"output": "999955279"
},
{
"input": "49... | 62 | 307,200 | 0 | 1,577 | |
330 | Road Construction | [
"constructive algorithms",
"graphs"
] | null | null | A country has *n* cities. Initially, there is no road in the country. One day, the king decides to construct some roads connecting pairs of cities. Roads can be traversed either way. He wants those roads to be constructed in such a way that it is possible to go from each city to any other city by traversing at most two roads. You are also given *m* pairs of cities — roads cannot be constructed between these pairs of cities.
Your task is to construct the minimum number of roads that still satisfy the above conditions. The constraints will guarantee that this is always possible. | The first line consists of two integers *n* and *m* .
Then *m* lines follow, each consisting of two integers *a**i* and *b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*, *a**i*<=≠<=*b**i*), which means that it is not possible to construct a road connecting cities *a**i* and *b**i*. Consider the cities are numbered from 1 to *n*.
It is guaranteed that every pair of cities will appear at most once in the input. | You should print an integer *s*: the minimum number of roads that should be constructed, in the first line. Then *s* lines should follow, each consisting of two integers *a**i* and *b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*,<=*a**i*<=≠<=*b**i*), which means that a road should be constructed between cities *a**i* and *b**i*.
If there are several solutions, you may print any of them. | [
"4 1\n1 3\n"
] | [
"3\n1 2\n4 2\n2 3\n"
] | This is one possible solution of the example:
These are examples of wrong solutions: | [
{
"input": "4 1\n1 3",
"output": "3\n1 2\n4 2\n2 3"
},
{
"input": "1000 0",
"output": "999\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n1 9\n1 10\n1 11\n1 12\n1 13\n1 14\n1 15\n1 16\n1 17\n1 18\n1 19\n1 20\n1 21\n1 22\n1 23\n1 24\n1 25\n1 26\n1 27\n1 28\n1 29\n1 30\n1 31\n1 32\n1 33\n1 34\n1 35\n1 36\n1 ... | 342 | 3,072,000 | 3 | 1,578 | |
545 | Woodcutters | [
"dp",
"greedy"
] | null | null | Little Susie listens to fairy tales before bed every day. Today's fairy tale was about wood cutters and the little girl immediately started imagining the choppers cutting wood. She imagined the situation that is described below.
There are *n* trees located along the road at points with coordinates *x*1,<=*x*2,<=...,<=*x**n*. Each tree has its height *h**i*. Woodcutters can cut down a tree and fell it to the left or to the right. After that it occupies one of the segments [*x**i*<=-<=*h**i*,<=*x**i*] or [*x**i*;*x**i*<=+<=*h**i*]. The tree that is not cut down occupies a single point with coordinate *x**i*. Woodcutters can fell a tree if the segment to be occupied by the fallen tree doesn't contain any occupied point. The woodcutters want to process as many trees as possible, so Susie wonders, what is the maximum number of trees to fell. | The first line contains integer *n* (1<=≤<=*n*<=≤<=105) — the number of trees.
Next *n* lines contain pairs of integers *x**i*,<=*h**i* (1<=≤<=*x**i*,<=*h**i*<=≤<=109) — the coordinate and the height of the *і*-th tree.
The pairs are given in the order of ascending *x**i*. No two trees are located at the point with the same coordinate. | Print a single number — the maximum number of trees that you can cut down by the given rules. | [
"5\n1 2\n2 1\n5 10\n10 9\n19 1\n",
"5\n1 2\n2 1\n5 10\n10 9\n20 1\n"
] | [
"3\n",
"4\n"
] | In the first sample you can fell the trees like that:
- fell the 1-st tree to the left — now it occupies segment [ - 1;1] - fell the 2-nd tree to the right — now it occupies segment [2;3] - leave the 3-rd tree — it occupies point 5 - leave the 4-th tree — it occupies point 10 - fell the 5-th tree to the right — now it occupies segment [19;20]
In the second sample you can also fell 4-th tree to the right, after that it will occupy segment [10;19]. | [
{
"input": "5\n1 2\n2 1\n5 10\n10 9\n19 1",
"output": "3"
},
{
"input": "5\n1 2\n2 1\n5 10\n10 9\n20 1",
"output": "4"
},
{
"input": "4\n10 4\n15 1\n19 3\n20 1",
"output": "4"
},
{
"input": "35\n1 7\n3 11\n6 12\n7 6\n8 5\n9 11\n15 3\n16 10\n22 2\n23 3\n25 7\n27 3\n34 5\n35 10... | 343 | 8,089,600 | 0 | 1,580 | |
295 | Greg and Array | [
"data structures",
"implementation"
] | null | null | Greg has an array *a*<==<=*a*1,<=*a*2,<=...,<=*a**n* and *m* operations. Each operation looks as: *l**i*, *r**i*, *d**i*, (1<=≤<=*l**i*<=≤<=*r**i*<=≤<=*n*). To apply operation *i* to the array means to increase all array elements with numbers *l**i*,<=*l**i*<=+<=1,<=...,<=*r**i* by value *d**i*.
Greg wrote down *k* queries on a piece of paper. Each query has the following form: *x**i*, *y**i*, (1<=≤<=*x**i*<=≤<=*y**i*<=≤<=*m*). That means that one should apply operations with numbers *x**i*,<=*x**i*<=+<=1,<=...,<=*y**i* to the array.
Now Greg is wondering, what the array *a* will be after all the queries are executed. Help Greg. | The first line contains integers *n*, *m*, *k* (1<=≤<=*n*,<=*m*,<=*k*<=≤<=105). The second line contains *n* integers: *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=105) — the initial array.
Next *m* lines contain operations, the operation number *i* is written as three integers: *l**i*, *r**i*, *d**i*, (1<=≤<=*l**i*<=≤<=*r**i*<=≤<=*n*), (0<=≤<=*d**i*<=≤<=105).
Next *k* lines contain the queries, the query number *i* is written as two integers: *x**i*, *y**i*, (1<=≤<=*x**i*<=≤<=*y**i*<=≤<=*m*).
The numbers in the lines are separated by single spaces. | On a single line print *n* integers *a*1,<=*a*2,<=...,<=*a**n* — the array after executing all the queries. Separate the printed numbers by spaces.
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams of the %I64d specifier. | [
"3 3 3\n1 2 3\n1 2 1\n1 3 2\n2 3 4\n1 2\n1 3\n2 3\n",
"1 1 1\n1\n1 1 1\n1 1\n",
"4 3 6\n1 2 3 4\n1 2 1\n2 3 2\n3 4 4\n1 2\n1 3\n2 3\n1 2\n1 3\n2 3\n"
] | [
"9 18 17\n",
"2\n",
"5 18 31 20\n"
] | none | [
{
"input": "3 3 3\n1 2 3\n1 2 1\n1 3 2\n2 3 4\n1 2\n1 3\n2 3",
"output": "9 18 17"
},
{
"input": "1 1 1\n1\n1 1 1\n1 1",
"output": "2"
},
{
"input": "4 3 6\n1 2 3 4\n1 2 1\n2 3 2\n3 4 4\n1 2\n1 3\n2 3\n1 2\n1 3\n2 3",
"output": "5 18 31 20"
},
{
"input": "1 1 1\n0\n1 1 0\n1 1... | 920 | 22,016,000 | 3 | 1,581 | |
411 | Kicker | [
"implementation"
] | null | null | Kicker (table football) is a board game based on football, in which players control the footballers' figures mounted on rods by using bars to get the ball into the opponent's goal. When playing two on two, one player of each team controls the goalkeeper and the full-backs (plays defence), the other player controls the half-backs and forwards (plays attack).
Two teams of company Q decided to battle each other. Let's enumerate players from both teams by integers from 1 to 4. The first and second player play in the first team, the third and the fourth one play in the second team. For each of the four players we know their game skills in defence and attack. The defence skill of the *i*-th player is *a**i*, the attack skill is *b**i*.
Before the game, the teams determine how they will play. First the players of the first team decide who will play in the attack, and who will play in the defence. Then the second team players do the same, based on the choice of their opponents.
We will define a team's defence as the defence skill of player of the team who plays defence. Similarly, a team's attack is the attack skill of the player of the team who plays attack. We assume that one team is guaranteed to beat the other one, if its defence is strictly greater than the opponent's attack and its attack is strictly greater than the opponent's defence.
The teams of company Q know each other's strengths and therefore arrange their teams optimally. Identify the team that is guaranteed to win (if both teams act optimally) or tell that there is no such team. | The input contain the players' description in four lines. The *i*-th line contains two space-separated integers *a**i* and *b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=100) — the defence and the attack skill of the *i*-th player, correspondingly. | If the first team can win, print phrase "Team 1" (without the quotes), if the second team can win, print phrase "Team 2" (without the quotes). If no of the teams can definitely win, print "Draw" (without the quotes). | [
"1 100\n100 1\n99 99\n99 99\n",
"1 1\n2 2\n3 3\n2 2\n",
"3 3\n2 2\n1 1\n2 2\n"
] | [
"Team 1\n",
"Team 2\n",
"Draw\n"
] | Let consider the first test sample. The first team can definitely win if it will choose the following arrangement: the first player plays attack, the second player plays defence.
Consider the second sample. The order of the choosing roles for players makes sense in this sample. As the members of the first team choose first, the members of the second team can beat them (because they know the exact defence value and attack value of the first team). | [
{
"input": "1 100\n100 1\n99 99\n99 99",
"output": "Team 1"
},
{
"input": "1 1\n2 2\n3 3\n2 2",
"output": "Team 2"
},
{
"input": "3 3\n2 2\n1 1\n2 2",
"output": "Draw"
},
{
"input": "80 79\n79 30\n80 81\n40 80",
"output": "Team 2"
},
{
"input": "10 10\n4 9\n8 9\n7... | 62 | 0 | 0 | 1,585 | |
729 | Spotlights | [
"dp",
"implementation"
] | null | null | Theater stage is a rectangular field of size *n*<=×<=*m*. The director gave you the stage's plan which actors will follow. For each cell it is stated in the plan if there would be an actor in this cell or not.
You are to place a spotlight on the stage in some good position. The spotlight will project light in one of the four directions (if you look at the stage from above) — left, right, up or down. Thus, the spotlight's position is a cell it is placed to and a direction it shines.
A position is good if two conditions hold:
- there is no actor in the cell the spotlight is placed to; - there is at least one actor in the direction the spotlight projects.
Count the number of good positions for placing the spotlight. Two positions of spotlight are considered to be different if the location cells or projection direction differ. | The first line contains two positive integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=1000) — the number of rows and the number of columns in the plan.
The next *n* lines contain *m* integers, 0 or 1 each — the description of the plan. Integer 1, means there will be an actor in the corresponding cell, while 0 means the cell will remain empty. It is guaranteed that there is at least one actor in the plan. | Print one integer — the number of good positions for placing the spotlight. | [
"2 4\n0 1 0 0\n1 0 1 0\n",
"4 4\n0 0 0 0\n1 0 0 1\n0 1 1 0\n0 1 0 0\n"
] | [
"9\n",
"20\n"
] | In the first example the following positions are good:
1. the (1, 1) cell and right direction; 1. the (1, 1) cell and down direction; 1. the (1, 3) cell and left direction; 1. the (1, 3) cell and down direction; 1. the (1, 4) cell and left direction; 1. the (2, 2) cell and left direction; 1. the (2, 2) cell and up direction; 1. the (2, 2) and right direction; 1. the (2, 4) cell and left direction.
Therefore, there are 9 good positions in this example. | [
{
"input": "2 4\n0 1 0 0\n1 0 1 0",
"output": "9"
},
{
"input": "4 4\n0 0 0 0\n1 0 0 1\n0 1 1 0\n0 1 0 0",
"output": "20"
},
{
"input": "1 5\n1 1 0 0 0",
"output": "3"
},
{
"input": "2 10\n0 0 0 0 0 0 0 1 0 0\n1 0 0 0 0 0 0 0 0 0",
"output": "20"
},
{
"input": "3 ... | 233 | 11,366,400 | 3 | 1,594 | |
0 | none | [
"none"
] | null | null | You have *n* devices that you want to use simultaneously.
The *i*-th device uses *a**i* units of power per second. This usage is continuous. That is, in λ seconds, the device will use λ·*a**i* units of power. The *i*-th device currently has *b**i* units of power stored. All devices can store an arbitrary amount of power.
You have a single charger that can plug to any single device. The charger will add *p* units of power per second to a device. This charging is continuous. That is, if you plug in a device for λ seconds, it will gain λ·*p* units of power. You can switch which device is charging at any arbitrary unit of time (including real numbers), and the time it takes to switch is negligible.
You are wondering, what is the maximum amount of time you can use the devices until one of them hits 0 units of power.
If you can use the devices indefinitely, print -1. Otherwise, print the maximum amount of time before any one device hits 0 power. | The first line contains two integers, *n* and *p* (1<=≤<=*n*<=≤<=100<=000, 1<=≤<=*p*<=≤<=109) — the number of devices and the power of the charger.
This is followed by *n* lines which contain two integers each. Line *i* contains the integers *a**i* and *b**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=100<=000) — the power of the device and the amount of power stored in the device in the beginning. | If you can use the devices indefinitely, print -1. Otherwise, print the maximum amount of time before any one device hits 0 power.
Your answer will be considered correct if its absolute or relative error does not exceed 10<=-<=4.
Namely, let's assume that your answer is *a* and the answer of the jury is *b*. The checker program will consider your answer correct if . | [
"2 1\n2 2\n2 1000\n",
"1 100\n1 1\n",
"3 5\n4 3\n5 2\n6 1\n"
] | [
"2.0000000000",
"-1\n",
"0.5000000000"
] | In sample test 1, you can charge the first device for the entire time until it hits zero power. The second device has enough power to last this time without being charged.
In sample test 2, you can use the device indefinitely.
In sample test 3, we can charge the third device for 2 / 5 of a second, then switch to charge the second device for a 1 / 10 of a second. | [
{
"input": "2 1\n2 2\n2 1000",
"output": "2.0000000000"
},
{
"input": "1 100\n1 1",
"output": "-1"
},
{
"input": "3 5\n4 3\n5 2\n6 1",
"output": "0.5000000000"
},
{
"input": "1 1\n1 87",
"output": "-1"
},
{
"input": "1 1\n100 77",
"output": "0.7777777778"
},... | 46 | 4,812,800 | 0 | 1,595 | |
846 | Math Show | [
"brute force",
"greedy"
] | null | null | Polycarp takes part in a math show. He is given *n* tasks, each consists of *k* subtasks, numbered 1 through *k*. It takes him *t**j* minutes to solve the *j*-th subtask of any task. Thus, time required to solve a subtask depends only on its index, but not on the task itself. Polycarp can solve subtasks in any order.
By solving subtask of arbitrary problem he earns one point. Thus, the number of points for task is equal to the number of solved subtasks in it. Moreover, if Polycarp completely solves the task (solves all *k* of its subtasks), he recieves one extra point. Thus, total number of points he recieves for the complete solution of the task is *k*<=+<=1.
Polycarp has *M* minutes of time. What is the maximum number of points he can earn? | The first line contains three integer numbers *n*, *k* and *M* (1<=≤<=*n*<=≤<=45, 1<=≤<=*k*<=≤<=45, 0<=≤<=*M*<=≤<=2·109).
The second line contains *k* integer numbers, values *t**j* (1<=≤<=*t**j*<=≤<=1000000), where *t**j* is the time in minutes required to solve *j*-th subtask of any task. | Print the maximum amount of points Polycarp can earn in *M* minutes. | [
"3 4 11\n1 2 3 4\n",
"5 5 10\n1 2 4 8 16\n"
] | [
"6\n",
"7\n"
] | In the first example Polycarp can complete the first task and spend 1 + 2 + 3 + 4 = 10 minutes. He also has the time to solve one subtask of the second task in one minute.
In the second example Polycarp can solve the first subtask of all five tasks and spend 5·1 = 5 minutes. Also he can solve the second subtasks of two tasks and spend 2·2 = 4 minutes. Thus, he earns 5 + 2 = 7 points in total. | [
{
"input": "3 4 11\n1 2 3 4",
"output": "6"
},
{
"input": "5 5 10\n1 2 4 8 16",
"output": "7"
},
{
"input": "1 1 0\n2",
"output": "0"
},
{
"input": "1 1 1\n1",
"output": "2"
},
{
"input": "2 1 0\n2",
"output": "0"
},
{
"input": "2 2 2\n2 3",
"outpu... | 46 | 0 | 0 | 1,606 | |
4 | Registration System | [
"data structures",
"hashing",
"implementation"
] | C. Registration system | 5 | 64 | A new e-mail service "Berlandesk" is going to be opened in Berland in the near future. The site administration wants to launch their project as soon as possible, that's why they ask you to help. You're suggested to implement the prototype of site registration system. The system should work on the following principle.
Each time a new user wants to register, he sends to the system a request with his name. If such a name does not exist in the system database, it is inserted into the database, and the user gets the response OK, confirming the successful registration. If the name already exists in the system database, the system makes up a new user name, sends it to the user as a prompt and also inserts the prompt into the database. The new name is formed by the following rule. Numbers, starting with 1, are appended one after another to name (name1, name2, ...), among these numbers the least *i* is found so that name*i* does not yet exist in the database. | The first line contains number *n* (1<=≤<=*n*<=≤<=105). The following *n* lines contain the requests to the system. Each request is a non-empty line, and consists of not more than 32 characters, which are all lowercase Latin letters. | Print *n* lines, which are system responses to the requests: OK in case of successful registration, or a prompt with a new name, if the requested name is already taken. | [
"4\nabacaba\nacaba\nabacaba\nacab\n",
"6\nfirst\nfirst\nsecond\nsecond\nthird\nthird\n"
] | [
"OK\nOK\nabacaba1\nOK\n",
"OK\nfirst1\nOK\nsecond1\nOK\nthird1\n"
] | none | [
{
"input": "4\nabacaba\nacaba\nabacaba\nacab",
"output": "OK\nOK\nabacaba1\nOK"
},
{
"input": "6\nfirst\nfirst\nsecond\nsecond\nthird\nthird",
"output": "OK\nfirst1\nOK\nsecond1\nOK\nthird1"
},
{
"input": "1\nn",
"output": "OK"
},
{
"input": "2\nu\nu",
"output": "OK\nu1"
... | 92 | 0 | 0 | 1,607 |
620 | New Year Tree | [
"bitmasks",
"data structures",
"trees"
] | null | null | The New Year holidays are over, but Resha doesn't want to throw away the New Year tree. He invited his best friends Kerim and Gural to help him to redecorate the New Year tree.
The New Year tree is an undirected tree with *n* vertices and root in the vertex 1.
You should process the queries of the two types:
1. Change the colours of all vertices in the subtree of the vertex *v* to the colour *c*. 1. Find the number of different colours in the subtree of the vertex *v*. | The first line contains two integers *n*,<=*m* (1<=≤<=*n*,<=*m*<=≤<=4·105) — the number of vertices in the tree and the number of the queries.
The second line contains *n* integers *c**i* (1<=≤<=*c**i*<=≤<=60) — the colour of the *i*-th vertex.
Each of the next *n*<=-<=1 lines contains two integers *x**j*,<=*y**j* (1<=≤<=*x**j*,<=*y**j*<=≤<=*n*) — the vertices of the *j*-th edge. It is guaranteed that you are given correct undirected tree.
The last *m* lines contains the description of the queries. Each description starts with the integer *t**k* (1<=≤<=*t**k*<=≤<=2) — the type of the *k*-th query. For the queries of the first type then follows two integers *v**k*,<=*c**k* (1<=≤<=*v**k*<=≤<=*n*,<=1<=≤<=*c**k*<=≤<=60) — the number of the vertex whose subtree will be recoloured with the colour *c**k*. For the queries of the second type then follows integer *v**k* (1<=≤<=*v**k*<=≤<=*n*) — the number of the vertex for which subtree you should find the number of different colours. | For each query of the second type print the integer *a* — the number of different colours in the subtree of the vertex given in the query.
Each of the numbers should be printed on a separate line in order of query appearing in the input. | [
"7 10\n1 1 1 1 1 1 1\n1 2\n1 3\n1 4\n3 5\n3 6\n3 7\n1 3 2\n2 1\n1 4 3\n2 1\n1 2 5\n2 1\n1 6 4\n2 1\n2 2\n2 3\n",
"23 30\n1 2 2 6 5 3 2 1 1 1 2 4 5 3 4 4 3 3 3 3 3 4 6\n1 2\n1 3\n1 4\n2 5\n2 6\n3 7\n3 8\n4 9\n4 10\n4 11\n6 12\n6 13\n7 14\n7 15\n7 16\n8 17\n8 18\n10 19\n10 20\n10 21\n11 22\n11 23\n2 1\n2 5\n2 6\n2 ... | [
"2\n3\n4\n5\n1\n2\n",
"6\n1\n3\n3\n2\n1\n2\n3\n5\n5\n1\n2\n2\n1\n1\n1\n2\n3\n"
] | none | [
{
"input": "7 10\n1 1 1 1 1 1 1\n1 2\n1 3\n1 4\n3 5\n3 6\n3 7\n1 3 2\n2 1\n1 4 3\n2 1\n1 2 5\n2 1\n1 6 4\n2 1\n2 2\n2 3",
"output": "2\n3\n4\n5\n1\n2"
},
{
"input": "23 30\n1 2 2 6 5 3 2 1 1 1 2 4 5 3 4 4 3 3 3 3 3 4 6\n1 2\n1 3\n1 4\n2 5\n2 6\n3 7\n3 8\n4 9\n4 10\n4 11\n6 12\n6 13\n7 14\n7 15\n7 16... | 0 | 0 | -1 | 1,608 | |
299 | Ksusha and Array | [
"brute force",
"number theory",
"sortings"
] | null | null | Ksusha is a beginner coder. Today she starts studying arrays. She has array *a*1,<=*a*2,<=...,<=*a**n*, consisting of *n* positive integers.
Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number! | The first line contains integer *n* (1<=≤<=*n*<=≤<=105), showing how many numbers the array has. The next line contains integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=109) — the array elements. | Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1.
If there are multiple answers, you are allowed to print any of them. | [
"3\n2 2 4\n",
"5\n2 1 3 1 6\n",
"3\n2 3 5\n"
] | [
"2\n",
"1\n",
"-1\n"
] | none | [
{
"input": "3\n2 2 4",
"output": "2"
},
{
"input": "5\n2 1 3 1 6",
"output": "1"
},
{
"input": "3\n2 3 5",
"output": "-1"
},
{
"input": "1\n331358794",
"output": "331358794"
},
{
"input": "5\n506904227 214303304 136194869 838256937 183952885",
"output": "-1"
... | 372 | 8,192,000 | 3 | 1,612 | |
468 | Hack it! | [
"binary search",
"constructive algorithms",
"math"
] | null | null | Little X has met the following problem recently.
Let's define *f*(*x*) as the sum of digits in decimal representation of number *x* (for example, *f*(1234)<==<=1<=+<=2<=+<=3<=+<=4). You are to calculate
Of course Little X has solved this problem quickly, has locked it, and then has tried to hack others. He has seen the following C++ code: | The first line contains a single integer *a* (1<=≤<=*a*<=≤<=1018). | Print two integers: *l*,<=*r* (1<=≤<=*l*<=≤<=*r*<=<<=10200) — the required test data. Leading zeros aren't allowed. It's guaranteed that the solution exists. | [
"46\n",
"126444381000032\n"
] | [
"1 10\n",
"2333333 2333333333333\n"
] | none | [
{
"input": "46",
"output": "1 10"
},
{
"input": "126444381000032",
"output": "2333333 2333333333333"
},
{
"input": "69645082595",
"output": "613752823618441225798858488535 713259406474207764329704856394"
},
{
"input": "70602205995",
"output": "11 2492213340204320744986569... | 62 | 0 | 3 | 1,613 | |
688 | Lovely Palindromes | [
"constructive algorithms",
"math"
] | null | null | Pari has a friend who loves palindrome numbers. A palindrome number is a number that reads the same forward or backward. For example 12321, 100001 and 1 are palindrome numbers, while 112 and 1021 are not.
Pari is trying to love them too, but only very special and gifted people can understand the beauty behind palindrome numbers. Pari loves integers with even length (i.e. the numbers with even number of digits), so she tries to see a lot of big palindrome numbers with even length (like a 2-digit 11 or 6-digit 122221), so maybe she could see something in them.
Now Pari asks you to write a program that gets a huge integer *n* from the input and tells what is the *n*-th even-length positive palindrome number? | The only line of the input contains a single integer *n* (1<=≤<=*n*<=≤<=10100<=000). | Print the *n*-th even-length palindrome number. | [
"1\n",
"10\n"
] | [
"11\n",
"1001\n"
] | The first 10 even-length palindrome numbers are 11, 22, 33, ... , 88, 99 and 1001. | [
{
"input": "1",
"output": "11"
},
{
"input": "10",
"output": "1001"
},
{
"input": "11",
"output": "1111"
},
{
"input": "12",
"output": "1221"
},
{
"input": "100",
"output": "100001"
},
{
"input": "1321",
"output": "13211231"
},
{
"input": "... | 77 | 409,600 | 3 | 1,618 | |
870 | Maximum of Maximums of Minimums | [
"greedy"
] | null | null | You are given an array *a*1,<=*a*2,<=...,<=*a**n* consisting of *n* integers, and an integer *k*. You have to split the array into exactly *k* non-empty subsegments. You'll then compute the minimum integer on each subsegment, and take the maximum integer over the *k* obtained minimums. What is the maximum possible integer you can get?
Definitions of subsegment and array splitting are given in notes. | The first line contains two integers *n* and *k* (1<=≤<=*k*<=≤<=*n*<=≤<=<=105) — the size of the array *a* and the number of subsegments you have to split the array to.
The second line contains *n* integers *a*1,<=<=*a*2,<=<=...,<=<=*a**n* (<=-<=109<=<=≤<=<=*a**i*<=≤<=<=109). | Print single integer — the maximum possible integer you can get if you split the array into *k* non-empty subsegments and take maximum of minimums on the subsegments. | [
"5 2\n1 2 3 4 5\n",
"5 1\n-4 -5 -3 -2 -1\n"
] | [
"5\n",
"-5\n"
] | A subsegment [*l*, *r*] (*l* ≤ *r*) of array *a* is the sequence *a*<sub class="lower-index">*l*</sub>, *a*<sub class="lower-index">*l* + 1</sub>, ..., *a*<sub class="lower-index">*r*</sub>.
Splitting of array *a* of *n* elements into *k* subsegments [*l*<sub class="lower-index">1</sub>, *r*<sub class="lower-index">1</sub>], [*l*<sub class="lower-index">2</sub>, *r*<sub class="lower-index">2</sub>], ..., [*l*<sub class="lower-index">*k*</sub>, *r*<sub class="lower-index">*k*</sub>] (*l*<sub class="lower-index">1</sub> = 1, *r*<sub class="lower-index">*k*</sub> = *n*, *l*<sub class="lower-index">*i*</sub> = *r*<sub class="lower-index">*i* - 1</sub> + 1 for all *i* > 1) is *k* sequences (*a*<sub class="lower-index">*l*<sub class="lower-index">1</sub></sub>, ..., *a*<sub class="lower-index">*r*<sub class="lower-index">1</sub></sub>), ..., (*a*<sub class="lower-index">*l*<sub class="lower-index">*k*</sub></sub>, ..., *a*<sub class="lower-index">*r*<sub class="lower-index">*k*</sub></sub>).
In the first example you should split the array into subsegments [1, 4] and [5, 5] that results in sequences (1, 2, 3, 4) and (5). The minimums are *min*(1, 2, 3, 4) = 1 and *min*(5) = 5. The resulting maximum is *max*(1, 5) = 5. It is obvious that you can't reach greater result.
In the second example the only option you have is to split the array into one subsegment [1, 5], that results in one sequence ( - 4, - 5, - 3, - 2, - 1). The only minimum is *min*( - 4, - 5, - 3, - 2, - 1) = - 5. The resulting maximum is - 5. | [
{
"input": "5 2\n1 2 3 4 5",
"output": "5"
},
{
"input": "5 1\n-4 -5 -3 -2 -1",
"output": "-5"
},
{
"input": "10 2\n10 9 1 -9 -7 -9 3 8 -10 5",
"output": "10"
},
{
"input": "10 4\n-8 -1 2 -3 9 -8 4 -3 5 9",
"output": "9"
},
{
"input": "1 1\n504262064",
"output... | 108 | 0 | 0 | 1,619 | |
492 | Vanya and Lanterns | [
"binary search",
"implementation",
"math",
"sortings"
] | null | null | Vanya walks late at night along a straight street of length *l*, lit by *n* lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point *l*. Then the *i*-th lantern is at the point *a**i*. The lantern lights all points of the street that are at the distance of at most *d* from it, where *d* is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius *d* should the lanterns have to light the whole street? | The first line contains two integers *n*, *l* (1<=≤<=*n*<=≤<=1000, 1<=≤<=*l*<=≤<=109) — the number of lanterns and the length of the street respectively.
The next line contains *n* integers *a**i* (0<=≤<=*a**i*<=≤<=*l*). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street. | Print the minimum light radius *d*, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10<=-<=9. | [
"7 15\n15 5 3 7 9 14 0\n",
"2 5\n2 5\n"
] | [
"2.5000000000\n",
"2.0000000000\n"
] | Consider the second sample. At *d* = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit. | [
{
"input": "7 15\n15 5 3 7 9 14 0",
"output": "2.5000000000"
},
{
"input": "2 5\n2 5",
"output": "2.0000000000"
},
{
"input": "46 615683844\n431749087 271781274 274974690 324606253 480870261 401650581 13285442 478090364 266585394 425024433 588791449 492057200 391293435 563090494 317950 1... | 46 | 0 | 0 | 1,620 | |
510 | Fox And Snake | [
"implementation"
] | null | null | Fox Ciel starts to learn programming. The first task is drawing a fox! However, that turns out to be too hard for a beginner, so she decides to draw a snake instead.
A snake is a pattern on a *n* by *m* table. Denote *c*-th cell of *r*-th row as (*r*,<=*c*). The tail of the snake is located at (1,<=1), then it's body extends to (1,<=*m*), then goes down 2 rows to (3,<=*m*), then goes left to (3,<=1) and so on.
Your task is to draw this snake for Fox Ciel: the empty cells should be represented as dot characters ('.') and the snake cells should be filled with number signs ('#').
Consider sample tests in order to understand the snake pattern. | The only line contains two integers: *n* and *m* (3<=≤<=*n*,<=*m*<=≤<=50).
*n* is an odd number. | Output *n* lines. Each line should contain a string consisting of *m* characters. Do not output spaces. | [
"3 3\n",
"3 4\n",
"5 3\n",
"9 9\n"
] | [
"###\n..#\n###\n",
"####\n...#\n####\n",
"###\n..#\n###\n#..\n###\n",
"#########\n........#\n#########\n#........\n#########\n........#\n#########\n#........\n#########\n"
] | none | [
{
"input": "3 3",
"output": "###\n..#\n###"
},
{
"input": "3 4",
"output": "####\n...#\n####"
},
{
"input": "5 3",
"output": "###\n..#\n###\n#..\n###"
},
{
"input": "9 9",
"output": "#########\n........#\n#########\n#........\n#########\n........#\n#########\n#........\n#... | 46 | 0 | 3 | 1,625 | |
0 | none | [
"none"
] | null | null | Hongcow is ruler of the world. As ruler of the world, he wants to make it easier for people to travel by road within their own countries.
The world can be modeled as an undirected graph with *n* nodes and *m* edges. *k* of the nodes are home to the governments of the *k* countries that make up the world.
There is at most one edge connecting any two nodes and no edge connects a node to itself. Furthermore, for any two nodes corresponding to governments, there is no path between those two nodes. Any graph that satisfies all of these conditions is stable.
Hongcow wants to add as many edges as possible to the graph while keeping it stable. Determine the maximum number of edges Hongcow can add. | The first line of input will contain three integers *n*, *m* and *k* (1<=≤<=*n*<=≤<=1<=000, 0<=≤<=*m*<=≤<=100<=000, 1<=≤<=*k*<=≤<=*n*) — the number of vertices and edges in the graph, and the number of vertices that are homes of the government.
The next line of input will contain *k* integers *c*1,<=*c*2,<=...,<=*c**k* (1<=≤<=*c**i*<=≤<=*n*). These integers will be pairwise distinct and denote the nodes that are home to the governments in this world.
The following *m* lines of input will contain two integers *u**i* and *v**i* (1<=≤<=*u**i*,<=*v**i*<=≤<=*n*). This denotes an undirected edge between nodes *u**i* and *v**i*.
It is guaranteed that the graph described by the input is stable. | Output a single integer, the maximum number of edges Hongcow can add to the graph while keeping it stable. | [
"4 1 2\n1 3\n1 2\n",
"3 3 1\n2\n1 2\n1 3\n2 3\n"
] | [
"2\n",
"0\n"
] | For the first sample test, the graph looks like this:
For the second sample test, the graph looks like this: | [
{
"input": "4 1 2\n1 3\n1 2",
"output": "2"
},
{
"input": "3 3 1\n2\n1 2\n1 3\n2 3",
"output": "0"
},
{
"input": "10 3 2\n1 10\n1 2\n1 3\n4 5",
"output": "33"
},
{
"input": "1 0 1\n1",
"output": "0"
},
{
"input": "1000 0 1\n72",
"output": "499500"
},
{
... | 31 | 4,608,000 | 0 | 1,627 | |
366 | Dima and To-do List | [
"brute force",
"implementation"
] | null | null | You helped Dima to have a great weekend, but it's time to work. Naturally, Dima, as all other men who have girlfriends, does everything wrong.
Inna and Dima are now in one room. Inna tells Dima off for everything he does in her presence. After Inna tells him off for something, she goes to another room, walks there in circles muttering about how useless her sweetheart is. During that time Dima has time to peacefully complete *k*<=-<=1 tasks. Then Inna returns and tells Dima off for the next task he does in her presence and goes to another room again. It continues until Dima is through with his tasks.
Overall, Dima has *n* tasks to do, each task has a unique number from 1 to *n*. Dima loves order, so he does tasks consecutively, starting from some task. For example, if Dima has 6 tasks to do in total, then, if he starts from the 5-th task, the order is like that: first Dima does the 5-th task, then the 6-th one, then the 1-st one, then the 2-nd one, then the 3-rd one, then the 4-th one.
Inna tells Dima off (only lovingly and appropriately!) so often and systematically that he's very well learned the power with which she tells him off for each task. Help Dima choose the first task so that in total he gets told off with as little power as possible. | The first line of the input contains two integers *n*,<=*k* (1<=≤<=*k*<=≤<=*n*<=≤<=105). The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=103), where *a**i* is the power Inna tells Dima off with if she is present in the room while he is doing the *i*-th task.
It is guaranteed that *n* is divisible by *k*. | In a single line print the number of the task Dima should start with to get told off with as little power as possible. If there are multiple solutions, print the one with the minimum number of the first task to do. | [
"6 2\n3 2 1 6 5 4\n",
"10 5\n1 3 5 7 9 9 4 1 8 5\n"
] | [
"1\n",
"3\n"
] | Explanation of the first example.
If Dima starts from the first task, Inna tells him off with power 3, then Dima can do one more task (as *k* = 2), then Inna tells him off for the third task with power 1, then she tells him off for the fifth task with power 5. Thus, Dima gets told off with total power 3 + 1 + 5 = 9. If Dima started from the second task, for example, then Inna would tell him off for tasks 2, 4 and 6 with power 2 + 6 + 4 = 12.
Explanation of the second example.
In the second example *k* = 5, thus, Dima manages to complete 4 tasks in-between the telling off sessions. Thus, Inna tells Dima off for tasks number 1 and 6 (if he starts from 1 or 6), 2 and 7 (if he starts from 2 or 7) and so on. The optimal answer is to start from task 3 or 8, 3 has a smaller number, so the answer is 3. | [
{
"input": "6 2\n3 2 1 6 5 4",
"output": "1"
},
{
"input": "10 5\n1 3 5 7 9 9 4 1 8 5",
"output": "3"
},
{
"input": "20 4\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1",
"output": "1"
},
{
"input": "10 10\n8 4 5 7 6 9 2 2 3 5",
"output": "7"
},
{
"input": "50 10\n1 2 3... | 1,000 | 9,830,400 | 0 | 1,631 | |
1,011 | Stages | [
"greedy",
"implementation",
"sortings"
] | null | null | Natasha is going to fly to Mars. She needs to build a rocket, which consists of several stages in some order. Each of the stages is defined by a lowercase Latin letter. This way, the rocket can be described by the string — concatenation of letters, which correspond to the stages.
There are $n$ stages available. The rocket must contain exactly $k$ of them. Stages in the rocket should be ordered by their weight. So, after the stage with some letter can go only stage with a letter, which is at least two positions after in the alphabet (skipping one letter in between, or even more). For example, after letter 'c' can't go letters 'a', 'b', 'c' and 'd', but can go letters 'e', 'f', ..., 'z'.
For the rocket to fly as far as possible, its weight should be minimal. The weight of the rocket is equal to the sum of the weights of its stages. The weight of the stage is the number of its letter in the alphabet. For example, the stage 'a 'weighs one ton,' b 'weighs two tons, and' z' — $26$ tons.
Build the rocket with the minimal weight or determine, that it is impossible to build a rocket at all. Each stage can be used at most once. | The first line of input contains two integers — $n$ and $k$ ($1 \le k \le n \le 50$) – the number of available stages and the number of stages to use in the rocket.
The second line contains string $s$, which consists of exactly $n$ lowercase Latin letters. Each letter defines a new stage, which can be used to build the rocket. Each stage can be used at most once. | Print a single integer — the minimal total weight of the rocket or -1, if it is impossible to build the rocket at all. | [
"5 3\nxyabd\n",
"7 4\nproblem\n",
"2 2\nab\n",
"12 1\nabaabbaaabbb\n"
] | [
"29",
"34",
"-1",
"1"
] | In the first example, the following rockets satisfy the condition:
- "adx" (weight is $1+4+24=29$);- "ady" (weight is $1+4+25=30$);- "bdx" (weight is $2+4+24=30$);- "bdy" (weight is $2+4+25=31$).
Rocket "adx" has the minimal weight, so the answer is $29$.
In the second example, target rocket is "belo". Its weight is $2+5+12+15=34$.
In the third example, $n=k=2$, so the rocket must have both stages: 'a' and 'b'. This rocket doesn't satisfy the condition, because these letters are adjacent in the alphabet. Answer is -1. | [
{
"input": "5 3\nxyabd",
"output": "29"
},
{
"input": "7 4\nproblem",
"output": "34"
},
{
"input": "2 2\nab",
"output": "-1"
},
{
"input": "12 1\nabaabbaaabbb",
"output": "1"
},
{
"input": "50 13\nqwertyuiopasdfghjklzxcvbnmaaaaaaaaaaaaaaaaaaaaaaaa",
"output": ... | 109 | 0 | 0 | 1,635 | |
220 | Little Elephant and Problem | [
"implementation",
"sortings"
] | null | null | The Little Elephant has got a problem — somebody has been touching his sorted by non-decreasing array *a* of length *n* and possibly swapped some elements of the array.
The Little Elephant doesn't want to call the police until he understands if he could have accidentally changed the array himself. He thinks that he could have accidentally changed array *a*, only if array *a* can be sorted in no more than one operation of swapping elements (not necessarily adjacent). That is, the Little Elephant could have accidentally swapped some two elements.
Help the Little Elephant, determine if he could have accidentally changed the array *a*, sorted by non-decreasing, himself. | The first line contains a single integer *n* (2<=≤<=*n*<=≤<=105) — the size of array *a*. The next line contains *n* positive integers, separated by single spaces and not exceeding 109, — array *a*.
Note that the elements of the array are not necessarily distinct numbers. | In a single line print "YES" (without the quotes) if the Little Elephant could have accidentally changed the array himself, and "NO" (without the quotes) otherwise. | [
"2\n1 2\n",
"3\n3 2 1\n",
"4\n4 3 2 1\n"
] | [
"YES\n",
"YES\n",
"NO\n"
] | In the first sample the array has already been sorted, so to sort it, we need 0 swap operations, that is not more than 1. Thus, the answer is "YES".
In the second sample we can sort the array if we swap elements 1 and 3, so we need 1 swap operation to sort the array. Thus, the answer is "YES".
In the third sample we can't sort the array in more than one swap operation, so the answer is "NO". | [
{
"input": "2\n1 2",
"output": "YES"
},
{
"input": "3\n3 2 1",
"output": "YES"
},
{
"input": "4\n4 3 2 1",
"output": "NO"
},
{
"input": "3\n1 3 2",
"output": "YES"
},
{
"input": "2\n2 1",
"output": "YES"
},
{
"input": "9\n7 7 8 8 10 10 10 10 1000000000... | 155 | 8,192,000 | 3 | 1,646 | |
66 | Petya and Java | [
"implementation",
"strings"
] | A. Petya and Java | 2 | 256 | Little Petya has recently started attending a programming club. Naturally he is facing the problem of choosing a programming language. After long considerations he realized that Java is the best choice. The main argument in favor of choosing Java was that it has a very large integer data type, called BigInteger.
But having attended several classes of the club, Petya realized that not all tasks require using the BigInteger type. It turned out that in some tasks it is much easier to use small data types. That's why a question arises: "Which integer type to use if one wants to store a positive integer *n*?"
Petya knows only 5 integer types:
1) byte occupies 1 byte and allows you to store numbers from <=-<=128 to 127
2) short occupies 2 bytes and allows you to store numbers from <=-<=32768 to 32767
3) int occupies 4 bytes and allows you to store numbers from <=-<=2147483648 to 2147483647
4) long occupies 8 bytes and allows you to store numbers from <=-<=9223372036854775808 to 9223372036854775807
5) BigInteger can store any integer number, but at that it is not a primitive type, and operations with it are much slower.
For all the types given above the boundary values are included in the value range.
From this list, Petya wants to choose the smallest type that can store a positive integer *n*. Since BigInteger works much slower, Peter regards it last. Help him. | The first line contains a positive number *n*. It consists of no more than 100 digits and doesn't contain any leading zeros. The number *n* can't be represented as an empty string.
Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cout (also you may use %I64d). | Print the first type from the list "byte, short, int, long, BigInteger", that can store the natural number *n*, in accordance with the data given above. | [
"127\n",
"130\n",
"123456789101112131415161718192021222324\n"
] | [
"byte\n",
"short\n",
"BigInteger\n"
] | none | [
{
"input": "127",
"output": "byte"
},
{
"input": "130",
"output": "short"
},
{
"input": "123456789101112131415161718192021222324",
"output": "BigInteger"
},
{
"input": "6",
"output": "byte"
},
{
"input": "16",
"output": "byte"
},
{
"input": "126",
... | 154 | 0 | 3.9615 | 1,651 |
92 | Binary Number | [
"greedy"
] | B. Binary Number | 1 | 256 | Little walrus Fangy loves math very much. That's why when he is bored he plays with a number performing some operations.
Fangy takes some positive integer *x* and wants to get a number one from it. While *x* is not equal to 1, Fangy repeats the following action: if *x* is odd, then he adds 1 to it, otherwise he divides *x* by 2. Fangy knows that for any positive integer number the process ends in finite time.
How many actions should Fangy perform to get a number one from number *x*? | The first line contains a positive integer *x* in a binary system. It is guaranteed that the first digit of *x* is different from a zero and the number of its digits does not exceed 106. | Print the required number of actions. | [
"1\n",
"1001001\n",
"101110\n"
] | [
"0\n",
"12\n",
"8\n"
] | Let's consider the third sample. Number 101110 is even, which means that we should divide it by 2. After the dividing Fangy gets an odd number 10111 and adds one to it. Number 11000 can be divided by 2 three times in a row and get number 11. All that's left is to increase the number by one (we get 100), and then divide it by 2 two times in a row. As a result, we get 1. | [
{
"input": "1",
"output": "0"
},
{
"input": "1001001",
"output": "12"
},
{
"input": "101110",
"output": "8"
},
{
"input": "11",
"output": "3"
},
{
"input": "11110001101",
"output": "16"
},
{
"input": "101010100100111100011111001111100001010101111110101... | 93 | 0 | 0 | 1,652 |
63 | Sinking Ship | [
"implementation",
"sortings",
"strings"
] | A. Sinking Ship | 2 | 256 | The ship crashed into a reef and is sinking. Now the entire crew must be evacuated. All *n* crew members have already lined up in a row (for convenience let's label them all from left to right with positive integers from 1 to *n*) and await further instructions. However, one should evacuate the crew properly, in a strict order. Specifically:
The first crew members to leave the ship are rats. Then women and children (both groups have the same priority) leave the ship. After that all men are evacuated from the ship. The captain leaves the sinking ship last.
If we cannot determine exactly who should leave the ship first for any two members of the crew by the rules from the previous paragraph, then the one who stands to the left in the line leaves the ship first (or in other words, the one whose number in the line is less).
For each crew member we know his status as a crew member, and also his name. All crew members have different names. Determine the order in which to evacuate the crew. | The first line contains an integer *n*, which is the number of people in the crew (1<=≤<=*n*<=≤<=100). Then follow *n* lines. The *i*-th of those lines contains two words — the name of the crew member who is *i*-th in line, and his status on the ship. The words are separated by exactly one space. There are no other spaces in the line. The names consist of Latin letters, the first letter is uppercase, the rest are lowercase. The length of any name is from 1 to 10 characters. The status can have the following values: rat for a rat, woman for a woman, child for a child, man for a man, captain for the captain. The crew contains exactly one captain. | Print *n* lines. The *i*-th of them should contain the name of the crew member who must be the *i*-th one to leave the ship. | [
"6\nJack captain\nAlice woman\nCharlie man\nTeddy rat\nBob child\nJulia woman\n"
] | [
"Teddy\nAlice\nBob\nJulia\nCharlie\nJack\n"
] | none | [
{
"input": "6\nJack captain\nAlice woman\nCharlie man\nTeddy rat\nBob child\nJulia woman",
"output": "Teddy\nAlice\nBob\nJulia\nCharlie\nJack"
},
{
"input": "1\nA captain",
"output": "A"
},
{
"input": "1\nAbcdefjhij captain",
"output": "Abcdefjhij"
},
{
"input": "5\nA captain... | 62 | 0 | 0 | 1,653 |
30 | King's Problem? | [
"geometry",
"greedy"
] | D. King's Problem? | 3 | 256 | Every true king during his life must conquer the world, hold the Codeforces world finals, win pink panda in the shooting gallery and travel all over his kingdom.
King Copa has already done the first three things. Now he just needs to travel all over the kingdom. The kingdom is an infinite plane with Cartesian coordinate system on it. Every city is a point on this plane. There are *n* cities in the kingdom at points with coordinates (*x*1,<=0),<=(*x*2,<=0),<=...,<=(*x**n*,<=0), and there is one city at point (*x**n*<=+<=1,<=*y**n*<=+<=1).
King starts his journey in the city number *k*. Your task is to find such route for the king, which visits all cities (in any order) and has minimum possible length. It is allowed to visit a city twice. The king can end his journey in any city. Between any pair of cities there is a direct road with length equal to the distance between the corresponding points. No two cities may be located at the same point. | The first line contains two integers *n* and *k* (1<=≤<=*n*<=≤<=105,<=1<=≤<=*k*<=≤<=*n*<=+<=1) — amount of cities and index of the starting city. The second line contains *n*<=+<=1 numbers *x**i*. The third line contains *y**n*<=+<=1. All coordinates are integers and do not exceed 106 by absolute value. No two cities coincide. | Output the minimum possible length of the journey. Your answer must have relative or absolute error less than 10<=-<=6. | [
"3 1\n0 1 2 1\n1\n",
"3 1\n1 0 2 1\n1\n",
"4 5\n0 5 -1 -5 2\n3\n"
] | [
"3.41421356237309490000",
"3.82842712474619030000",
"14.24264068711928400000"
] | none | [
{
"input": "3 1\n0 1 2 1\n1",
"output": "3.41421356237309490000"
},
{
"input": "3 1\n1 0 2 1\n1",
"output": "3.82842712474619030000"
},
{
"input": "4 5\n0 5 -1 -5 2\n3",
"output": "14.24264068711928400000"
},
{
"input": "4 1\n0 5 -1 -5 2\n3",
"output": "16.858413792983193... | 372 | 11,059,200 | 3.917401 | 1,655 |
672 | Different is Good | [
"constructive algorithms",
"implementation",
"strings"
] | null | null | A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different.
Kerem recently got a string *s* consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string *s* to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba".
If string *s* has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible.
Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. | The first line of the input contains an integer *n* (1<=≤<=*n*<=≤<=100<=000) — the length of the string *s*.
The second line contains the string *s* of length *n* consisting of only lowercase English letters. | If it's impossible to change the string *s* such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. | [
"2\naa\n",
"4\nkoko\n",
"5\nmurat\n"
] | [
"1\n",
"2\n",
"0\n"
] | In the first sample one of the possible solutions is to change the first character to 'b'.
In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko". | [
{
"input": "2\naa",
"output": "1"
},
{
"input": "4\nkoko",
"output": "2"
},
{
"input": "5\nmurat",
"output": "0"
},
{
"input": "6\nacbead",
"output": "1"
},
{
"input": "7\ncdaadad",
"output": "4"
},
{
"input": "25\npeoaicnbisdocqofsqdpgobpn",
"outp... | 93 | 204,800 | 0 | 1,656 | |
271 | Beautiful Year | [
"brute force"
] | null | null | It seems like the year of 2013 came only yesterday. Do you know a curious fact? The year of 2013 is the first year after the old 1987 with only distinct digits.
Now you are suggested to solve the following problem: given a year number, find the minimum year number which is strictly larger than the given one and has only distinct digits. | The single line contains integer *y* (1000<=≤<=*y*<=≤<=9000) — the year number. | Print a single integer — the minimum year number that is strictly larger than *y* and all it's digits are distinct. It is guaranteed that the answer exists. | [
"1987\n",
"2013\n"
] | [
"2013\n",
"2014\n"
] | none | [
{
"input": "1987",
"output": "2013"
},
{
"input": "2013",
"output": "2014"
},
{
"input": "1000",
"output": "1023"
},
{
"input": "1001",
"output": "1023"
},
{
"input": "1234",
"output": "1235"
},
{
"input": "5555",
"output": "5601"
},
{
"inp... | 62 | 0 | 0 | 1,658 | |
327 | Hungry Sequence | [
"math"
] | null | null | Iahub and Iahubina went to a date at a luxury restaurant. Everything went fine until paying for the food. Instead of money, the waiter wants Iahub to write a Hungry sequence consisting of *n* integers.
A sequence *a*1, *a*2, ..., *a**n*, consisting of *n* integers, is Hungry if and only if:
- Its elements are in increasing order. That is an inequality *a**i*<=<<=*a**j* holds for any two indices *i*,<=*j* (*i*<=<<=*j*). - For any two indices *i* and *j* (*i*<=<<=*j*), *a**j* must not be divisible by *a**i*.
Iahub is in trouble, so he asks you for help. Find a Hungry sequence with *n* elements. | The input contains a single integer: *n* (1<=≤<=*n*<=≤<=105). | Output a line that contains *n* space-separated integers *a*1 *a*2, ..., *a**n* (1<=≤<=*a**i*<=≤<=107), representing a possible Hungry sequence. Note, that each *a**i* must not be greater than 10000000 (107) and less than 1.
If there are multiple solutions you can output any one. | [
"3\n",
"5\n"
] | [
"2 9 15\n",
"11 14 20 27 31\n"
] | none | [
{
"input": "3",
"output": "2 9 15"
},
{
"input": "5",
"output": "11 14 20 27 31"
},
{
"input": "1",
"output": "3"
},
{
"input": "1000",
"output": "3000 3001 3002 3003 3004 3005 3006 3007 3008 3009 3010 3011 3012 3013 3014 3015 3016 3017 3018 3019 3020 3021 3022 3023 3024 ... | 1,000 | 68,812,800 | 0 | 1,661 | |
461 | Appleman and Toastman | [
"greedy",
"sortings"
] | null | null | Appleman and Toastman play a game. Initially Appleman gives one group of *n* numbers to the Toastman, then they start to complete the following tasks:
- Each time Toastman gets a group of numbers, he sums up all the numbers and adds this sum to the score. Then he gives the group to the Appleman. - Each time Appleman gets a group consisting of a single number, he throws this group out. Each time Appleman gets a group consisting of more than one number, he splits the group into two non-empty groups (he can do it in any way) and gives each of them to Toastman.
After guys complete all the tasks they look at the score value. What is the maximum possible value of score they can get? | The first line contains a single integer *n* (1<=≤<=*n*<=≤<=3·105). The second line contains *n* integers *a*1, *a*2, ..., *a**n* (1<=≤<=*a**i*<=≤<=106) — the initial group that is given to Toastman. | Print a single integer — the largest possible score. | [
"3\n3 1 5\n",
"1\n10\n"
] | [
"26\n",
"10\n"
] | Consider the following situation in the first example. Initially Toastman gets group [3, 1, 5] and adds 9 to the score, then he give the group to Appleman. Appleman splits group [3, 1, 5] into two groups: [3, 5] and [1]. Both of them should be given to Toastman. When Toastman receives group [1], he adds 1 to score and gives the group to Appleman (he will throw it out). When Toastman receives group [3, 5], he adds 8 to the score and gives the group to Appleman. Appleman splits [3, 5] in the only possible way: [5] and [3]. Then he gives both groups to Toastman. When Toastman receives [5], he adds 5 to the score and gives the group to Appleman (he will throws it out). When Toastman receives [3], he adds 3 to the score and gives the group to Appleman (he will throws it out). Finally Toastman have added 9 + 1 + 8 + 5 + 3 = 26 to the score. This is the optimal sequence of actions. | [
{
"input": "3\n3 1 5",
"output": "26"
},
{
"input": "1\n10",
"output": "10"
},
{
"input": "10\n8 10 2 5 6 2 4 7 2 1",
"output": "376"
},
{
"input": "10\n171308 397870 724672 431255 228496 892002 542924 718337 888642 161821",
"output": "40204082"
},
{
"input": "10\... | 2,000 | 6,041,600 | 0 | 1,666 | |
453 | Little Pony and Expected Maximum | [
"probabilities"
] | null | null | Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has *m* faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the *m*-th face contains *m* dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability . Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice *n* times. | A single line contains two integers *m* and *n* (1<=≤<=*m*,<=*n*<=≤<=105). | Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10<=<=-<=4. | [
"6 1\n",
"6 3\n",
"2 2\n"
] | [
"3.500000000000\n",
"4.958333333333\n",
"1.750000000000\n"
] | Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2. 1. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1. 1. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2. 1. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value | [
{
"input": "6 1",
"output": "3.500000000000"
},
{
"input": "6 3",
"output": "4.958333333333"
},
{
"input": "2 2",
"output": "1.750000000000"
},
{
"input": "5 4",
"output": "4.433600000000"
},
{
"input": "5 8",
"output": "4.814773760000"
},
{
"input": "... | 249 | 102,400 | -1 | 1,673 | |
641 | Little Artem and Dance | [
"brute force",
"constructive algorithms",
"implementation"
] | null | null | Little Artem is fond of dancing. Most of all dances Artem likes rueda — Cuban dance that is danced by pairs of boys and girls forming a circle and dancing together.
More detailed, there are *n* pairs of boys and girls standing in a circle. Initially, boy number 1 dances with a girl number 1, boy number 2 dances with a girl number 2 and so on. Girls are numbered in the clockwise order. During the dance different moves are announced and all pairs perform this moves. While performing moves boys move along the circle, while girls always stay at their initial position. For the purpose of this problem we consider two different types of moves:
1. Value *x* and some direction are announced, and all boys move *x* positions in the corresponding direction. 1. Boys dancing with even-indexed girls swap positions with boys who are dancing with odd-indexed girls. That is the one who was dancing with the girl 1 swaps with the one who was dancing with the girl number 2, while the one who was dancing with girl number 3 swaps with the one who was dancing with the girl number 4 and so one. It's guaranteed that *n* is even.
Your task is to determine the final position of each boy. | The first line of the input contains two integers *n* and *q* (2<=≤<=*n*<=≤<=1<=000<=000, 1<=≤<=*q*<=≤<=2<=000<=000) — the number of couples in the rueda and the number of commands to perform, respectively. It's guaranteed that *n* is even.
Next *q* lines contain the descriptions of the commands. Each command has type as the integer 1 or 2 first. Command of the first type is given as *x* (<=-<=*n*<=≤<=*x*<=≤<=*n*), where 0<=≤<=*x*<=≤<=*n* means all boys moves *x* girls in clockwise direction, while <=-<=*x* means all boys move *x* positions in counter-clockwise direction. There is no other input for commands of the second type. | Output *n* integers, the *i*-th of them should be equal to the index of boy the *i*-th girl is dancing with after performing all *q* moves. | [
"6 3\n1 2\n2\n1 2\n",
"2 3\n1 1\n2\n1 -2\n",
"4 2\n2\n1 3\n"
] | [
"4 3 6 5 2 1\n",
"1 2\n",
"1 4 3 2\n"
] | none | [
{
"input": "6 3\n1 2\n2\n1 2",
"output": "4 3 6 5 2 1"
},
{
"input": "2 3\n1 1\n2\n1 -2",
"output": "1 2"
},
{
"input": "4 2\n2\n1 3",
"output": "1 4 3 2"
},
{
"input": "6 8\n1 2\n2\n2\n2\n2\n1 1\n1 -5\n2",
"output": "4 3 6 5 2 1"
},
{
"input": "6 8\n1 -1\n2\n2\n1... | 2,000 | 5,836,800 | 0 | 1,676 |
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