Datasets:
ivlu2000
/
coding-questions-seed-data

Dataset card Data Studio Files
xet
Community
1
task
stringlengths
0
154k
__index_level_0__
int64
0
39.2k
Score : 300 points Problem Statement Takahashi made N problems for competitive programming. The problems are numbered 1 to N , and the difficulty of Problem i is represented as an integer d_i (the higher, the harder). He is dividing the problems into two categories by choosing an integer K , as follows: A problem with difficulty K or higher will be for ARCs . A problem with difficulty lower than K will be for ABCs . How many choices of the integer K make the number of problems for ARCs and the number of problems for ABCs the same? Problem Statement 2 \leq N \leq 10^5 N is an even number. 1 \leq d_i \leq 10^5 All values in input are integers. Input Input is given from Standard Input in the following format: N d_1 d_2 ... d_N Output Print the number of choices of the integer K that make the number of problems for ARCs and the number of problems for ABCs the same. Sample Input 1 6 9 1 4 4 6 7 Sample Output 1 2 If we choose K=5 or 6 , Problem 1 , 5 , and 6 will be for ARCs, Problem 2 , 3 , and 4 will be for ABCs, and the objective is achieved. Thus, the answer is 2 . Sample Input 2 8 9 1 14 5 5 4 4 14 Sample Output 2 0 There may be no choice of the integer K that make the number of problems for ARCs and the number of problems for ABCs the same. Sample Input 3 14 99592 10342 29105 78532 83018 11639 92015 77204 30914 21912 34519 80835 100000 1 Sample Output 3 42685
37,960
Score: 300 points Problem Statement We have a canvas divided into a grid with H rows and W columns. The square at the i -th row from the top and the j -th column from the left is represented as (i, j) . Initially, all the squares are white. square1001 wants to draw a picture with black paint. His specific objective is to make Square (i, j) black when s_{i, j}= # , and to make Square (i, j) white when s_{i, j}= . . However, since he is not a good painter, he can only choose two squares that are horizontally or vertically adjacent and paint those squares black, for some number of times (possibly zero). He may choose squares that are already painted black, in which case the color of those squares remain black. Determine if square1001 can achieve his objective. Constraints H is an integer between 1 and 50 (inclusive). W is an integer between 1 and 50 (inclusive). For every (i, j) (1 \leq i \leq H, 1 \leq j \leq W) , s_{i, j} is # or . . Input Input is given from Standard Input in the following format: H W s_{1, 1} s_{1, 2} s_{1, 3} ... s_{1, W} s_{2, 1} s_{2, 2} s_{2, 3} ... s_{2, W} : : s_{H, 1} s_{H, 2} s_{H, 3} ... s_{H, W} Output If square1001 can achieve his objective, print Yes ; if he cannot, print No . Sample Input 1 3 3 .#. ### .#. Sample Output 1 Yes One possible way to achieve the objective is shown in the figure below. Here, the squares being painted are marked by stars. Sample Input 2 5 5 #.#.# .#.#. #.#.# .#.#. #.#.# Sample Output 2 No square1001 cannot achieve his objective here. Sample Input 3 11 11 ...#####... .##.....##. #..##.##..# #..##.##..# #.........# #...###...# .#########. .#.#.#.#.#. ##.#.#.#.## ..##.#.##.. .##..#..##. Sample Output 3 Yes
37,961
Score : 300 points Problem Statement 2N players are running a competitive table tennis training on N tables numbered from 1 to N . The training consists of rounds . In each round, the players form N pairs, one pair per table. In each pair, competitors play a match against each other. As a result, one of them wins and the other one loses. The winner of the match on table X plays on table X-1 in the next round, except for the winner of the match on table 1 who stays at table 1 . Similarly, the loser of the match on table X plays on table X+1 in the next round, except for the loser of the match on table N who stays at table N . Two friends are playing their first round matches on distinct tables A and B . Let's assume that the friends are strong enough to win or lose any match at will. What is the smallest number of rounds after which the friends can get to play a match against each other? Constraints 2 \leq N \leq 10^{18} 1 \leq A < B \leq N All input values are integers. Input Input is given from Standard Input in the following format: N A B Output Print the smallest number of rounds after which the friends can get to play a match against each other. Sample Input 1 5 2 4 Sample Output 1 1 If the first friend loses their match and the second friend wins their match, they will both move to table 3 and play each other in the next round. Sample Input 2 5 2 3 Sample Output 2 2 If both friends win two matches in a row, they will both move to table 1 .
37,962
Score : 100 points Problem Statement Takahashi is meeting up with Aoki. They have planned to meet at a place that is D meters away from Takahashi's house in T minutes from now. Takahashi will leave his house now and go straight to the place at a speed of S meters per minute. Will he arrive in time? Constraints 1 \leq D \leq 10000 1 \leq T \leq 10000 1 \leq S \leq 10000 All values in input are integers. Input Input is given from Standard Input in the following format: D T S Output If Takahashi will reach the place in time, print Yes ; otherwise, print No . Sample Input 1 1000 15 80 Sample Output 1 Yes It takes 12.5 minutes to go 1000 meters to the place at a speed of 80 meters per minute. They have planned to meet in 15 minutes so he will arrive in time. Sample Input 2 2000 20 100 Sample Output 2 Yes It takes 20 minutes to go 2000 meters to the place at a speed of 100 meters per minute. They have planned to meet in 20 minutes so he will arrive just on time. Sample Input 3 10000 1 1 Sample Output 3 No He will be late.
37,964
Problem J: Cluster Network Problem マむヅ倧孊にある倧芏暡クラスタ † 型スヌパヌコンピュヌタ通称「SAKURA」のクラスタは、$N$台のコンピュヌタノヌドず$M$本の盞互に通信が可胜な物理的通信路で構成される。たた、各ノヌドにはそれぞれ1から$N$たでの識別番号が割り圓おられおいる。 この床SAKURAの利甚を倧孊関係者だけでなく、県内の䌁業にも認めるこずずなった。それに䌎い、SAKURAを構成する各ノヌドを点怜する必芁がある。しかし、SAKURAの利甚スケゞュヌルは数ヶ月先たで埋たっおいるので、点怜䞭もシステム党䜓を停止させるこずはできない。そこで、ノヌドを1日に1台ず぀順番に点怜する。 点怜は$N$日にわたっお行われ、$i$日目にノヌド$i$を点怜する。このずき、点怜するノヌドずそのノヌドに盎接接続されおいる通信路をSAKURAのクラスタから切り離す。それによっお、SAKURAのクラスタ党䜓は1぀以䞊のクラスタに分断されるので、そのうちのいずれかをSAKURAの代わりに運甚する。圓然、点怜䞭のノヌドは運甚するこずができない。 耇数のクラスタに分断された堎合、それらの䞭で最も「総合性胜倀」の高いクラスタのみを運甚する。各クラスタの「総合性胜倀」はそれを構成する各ノヌドに蚭定された「単䜓性胜倀」の和である。 SAKURAを構成するノヌドの数、通信路の本数ず各ノヌドに蚭定された「単䜓性胜倀」が䞎えられるので、$i$日目の点怜䞭に運甚されるクラスタの「総合性胜倀」を出力せよ。 †クラスタずは、1぀以䞊のコンピュヌタを結合しおひずたずたりにしたシステムのこず。ここでは、物理的通信路で連結なノヌドの集合ずする。 Input 入力は以䞋の圢匏で䞎えられる。 $N$ $M$ $w_1$ $w_2$ ... $w_N$ $u_1$ $v_1$ $u_2$ $v_2$ ... $u_M$ $v_M$ 1行目にクラスタを構成するノヌドの数$N$ず通信路の本数$M$が空癜区切りで䞎えられる。 2行目には各ノヌドの「単䜓性胜倀」を衚す$N$個の敎数が空癜区切りで䞎えられる。$i$番目の敎数$w_i$はノヌド$i$の「単䜓性胜倀」を衚す。 3行目からの$M$行には各通信路が぀なぐ2぀のノヌドの識別番号が空癜区切りで䞎えられる。2+$i$行目の入力では、通信路がノヌド$u_i$ずノヌド$v_i$を盞互に぀なぐこずを衚す。 Constraints 入力は以䞋の条件を満たす。 $2 \leq N \leq 10^5$ $N-1 \leq M \leq min(\frac{N\times(N-1)}{2},10^5)$ $1 \leq w_i \leq 10^6$ $1 \leq u_i, v_i \leq N, u_i \ne v_i$ $(u_i,v_i) \ne (u_j,v_j), (u_i,v_i) \ne (v_j,u_j), i \ne j$ 入力は党お敎数 Output 出力は$N$行からなる。 $i$行目には、$i$日目に運甚されるクラスタの「総合性胜倀」を出力する。 Sample Input 1 9 10 1 2 3 4 5 6 7 8 9 1 2 2 3 2 4 3 4 4 5 4 6 2 7 7 8 7 9 9 1 Sample Output 1 44 25 42 30 40 39 30 37 36 Sample Input 2 16 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 2 3 3 4 3 5 1 6 6 7 6 8 7 8 8 9 8 10 10 11 11 12 12 10 1 13 13 14 14 15 15 13 14 16 15 16 Sample Output 2 63 122 124 132 131 73 129 86 127 103 125 124 78 122 121 120 Sample Input 3 2 1 1 2 1 2 Sample Output 3 2 1
37,965
Problem I: Shuffle 2 Problem $n$枚のカヌドからなる束があり、䞋から$i$番目のカヌドには$i$が曞かれおいる。この束に察しお、以䞋のように定矩されるシャッフルを$q$回行う。 束を䞋から芋たずき、奇数番目のカヌドを䞊に重ねおいっお䜜られる束$x$、偶数番目のカヌドを䞊に重ねおいっお䜜られる束$y$を考える。その埌以䞋の$2$぀のうち、奜きな操䜜を行う。 操䜜 $0$ 束$x$の䞊に束$y$をのせお$1$぀の束にする。 操䜜 $1$ 束$y$の䞊に束$x$をのせお$1$぀の束にする。 䟋えば、$6$枚のカヌドからなる束(䞋から123456)に察しお$1$回のシャッフルを行うこずを考えたずき、操䜜$0$を行った堎合に埗られる束は䞋から 246135 135246、操䜜$1$を行った堎合に埗られる束は䞋から 135246 246135である。(14:52修正) $q$回のシャッフルの埌、$k$の曞かれたカヌドが束の䞋から$d$番目にあるようにしたい。 可胜であるなら$q$回のシャッフルの操䜜を順番に出力し、䞍可胜ならば$-1$を出力せよ。 Input 入力は以䞋の圢匏で䞎えられる。 $n$ $q$ $k$ $d$ Constraints 入力は以䞋の条件を満たす。 $2 \le n \le 10^{15}$ $1 \le q \le 10^6$ $1 \le k,d \le n$ $n$は偶数 Output 条件を満たすシャッフルが可胜なら$q$行にシャッフルの操䜜を出力せよ。 䞍可胜なら$-1$を出力せよ。 Sample Input 1 4 2 1 1 Sample Output 1 0 0 Sample Input 2 4 2 3 1 Sample Output 2 0 1 Sample Input 3 4 1 1 4 Sample Output 3 -1 Sample Input 4 7834164883628 15 2189823423122 5771212644938 Sample Output 4 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0
37,966
最高のピザ (Best Pizza) 問題 K 理事長はJOI 垂の䞭心郚にある JOI ピザ店の垞連客である圌はある事情により今月から節玄生掻を始めるこずにしたそこで圌はJOI ピザ店で泚文できるピザのうち1 ドルあたりのカロリヌが最倧ずなるようなピザを泚文したいず思ったこのようなピザを「最高のピザ」ず呌ぶこずにしよう「最高のピザ」は 1 皮類ずは限らない JOI ピザでは N 皮類のトッピングから䜕皮類かを自由に遞び基本の生地の䞊に茉せたものを泚文するこずができる同皮のトッピングを 2 ぀以䞊茉せるこずはできない生地にトッピングを 1 皮類も茉せないピザも泚文できる生地の倀段は A ドルでありトッピングの倀段はいずれも B ドルであるピザの倀段は生地の倀段ず茉せたトッピングの倀段の合蚈であるすなわちトッピングを k 皮類 (0 ≩ k ≩ N) 茉せたピザの倀段は A + k × B ドルであるピザ党䜓のカロリヌは生地のカロリヌず茉せたトッピングのカロリヌの合蚈である 生地の倀段ずトッピングの倀段および生地ず各トッピングのカロリヌの倀が䞎えられたずき「最高のピザ」の 1 ドルあたりのカロリヌ数を求めるプログラムを䜜成せよ 入力 入力は N + 3 行からなる 1 行目にはトッピングの皮類数を衚す 1 ぀の敎数 N (1 ≩ N ≩ 100) が曞かれおいる2 行目には 2 ぀の敎数 A, B (1 ≩ A ≩ 10001 ≩ B ≩ 1000) が空癜を区切りずしお曞かれおいるA は生地の倀段B はトッピングの倀段を衚す3 行目には生地のカロリヌ数を衚す 1 ぀の敎数 C (1 ≩ C ≩ 10000) が曞かれおいる 3 + i 行目 (1 ≩ i ≩ N) にはi 番目のトッピングのカロリヌ数を衚す 1 ぀の敎数 D i (1 ≩ D i ≩ 10000) が曞かれおいる 出力 「最高のピザ」の 1 ドルあたりのカロリヌ数を 1 行で出力せよただし小数点以䞋は切り捚おお敎数倀で出力せよ 入出力䟋 入力䟋 1 3 12 2 200 50 300 100 出力䟋 1 37 入出力䟋 1 では2 番目ず 3 番目のトッピングを茉せるず200 + 300 + 100 = 600 カロリヌで 12 + 2 × 2 = 16 ドルのピザになる このピザは 1 ドルあたり 600 / 16 = 37.5 カロリヌになるこれが「最高のピザ」ずなるので37.5 の小数点以䞋を切り捚おた 37 を出力する 入力䟋 2 4 20 3 900 300 100 400 1300 出力䟋 2 100 問題文ず自動審刀に䜿われるデヌタは、 情報オリンピック日本委員䌚 が䜜成し公開しおいる問題文ず採点甚テストデヌタです。
37,967
Score: 200 points Problem Statement Takahashi, who works at DISCO, is standing before an iron bar. The bar has N-1 notches, which divide the bar into N sections. The i -th section from the left has a length of A_i millimeters. Takahashi wanted to choose a notch and cut the bar at that point into two parts with the same length. However, this may not be possible as is, so he will do the following operations some number of times before he does the cut: Choose one section and expand it, increasing its length by 1 millimeter. Doing this operation once costs 1 yen (the currency of Japan). Choose one section of length at least 2 millimeters and shrink it, decreasing its length by 1 millimeter. Doing this operation once costs 1 yen. Find the minimum amount of money needed before cutting the bar into two parts with the same length. Constraints 2 \leq N \leq 200000 1 \leq A_i \leq 2020202020 All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 A_3 ... A_N Output Print an integer representing the minimum amount of money needed before cutting the bar into two parts with the same length. Sample Input 1 3 2 4 3 Sample Output 1 3 The initial lengths of the sections are [2, 4, 3] (in millimeters). Takahashi can cut the bar equally after doing the following operations for 3 yen: Shrink the second section from the left. The lengths of the sections are now [2, 3, 3] . Shrink the first section from the left. The lengths of the sections are now [1, 3, 3] . Shrink the second section from the left. The lengths of the sections are now [1, 2, 3] , and we can cut the bar at the second notch from the left into two parts of length 3 each. Sample Input 2 12 100 104 102 105 103 103 101 105 104 102 104 101 Sample Output 2 0
37,968
Problem F: Traveling Cube On a small planet named Bandai, a landing party of the starship Tadamigawa discovered colorful cubes traveling on flat areas of the planet surface, which the landing party named beds. A cube appears at a certain position on a bed, travels on the bed for a while, and then disappears. After a longtime observation, a science officer Lt. Alyssa Ogawa of Tadamigawa found the rule how a cube travels on a bed. A bed is a rectangular area tiled with squares of the same size. One of the squares is colored red, one colored green, one colored blue, one colored cyan, one colored magenta, one colored yellow, one or more colored white, and all others, if any, colored black. Initially, a cube appears on one of the white squares. The cube’s faces are colored as follows. top red bottom cyan north green south magenta east blue west yellow The cube can roll around a side of the current square at a step and thus rolls on to an adjacent square. When the cube rolls on to a chromatically colored (red, green, blue, cyan, magenta or yellow) square, the top face of the cube after the roll should be colored the same. When the cube rolls on to a white square, there is no such restriction. The cube should never roll on to a black square. Throughout the travel, the cube can visit each of the chromatically colored squares only once, and any of the white squares arbitrarily many times. As already mentioned, the cube can never visit any of the black squares. On visit to the final chromatically colored square, the cube disappears. Somehow the order of visits to the chromatically colored squares is known to us before the travel starts. Your mission is to find the least number of steps for the cube to visit all the chromatically colored squares in the given order. Input The input is a sequence of datasets. A dataset is formatted as follows: w d c 11 . . . c w 1 . . . . . . c 1 d . . . c wd v 1 v 2 v 3 v 4 v 5 v 6 The first line is a pair of positive integers w and d separated by a space. The next d lines are w-character-long strings c 11 . . . c w 1 , . . . , c 1 d . . . c wd with no spaces. Each character cij is one of the letters r, g, b, c, m, y, w and k, which stands for red, green, blue, cyan, magenta, yellow, white and black respectively, or a sign #. Each of r, g, b, c, m, y and # occurs once and only once in a dataset. The last line is a six-character-long string v 1 v 2 v 3 v 4 v 5 v 6 which is a permutation of “rgbcmy”. The integers w and d denote the width (the length from the east end to the west end) and the depth (the length from the north end to the south end) of a bed. The unit is the length of a side of a square. You can assume that neither w nor d is greater than 30. Each character c ij shows the color of a square in the bed. The characters c 11 , c w 1 , c 1 d and c wd correspond to the north-west corner, the north-east corner, the south-west corner and the south- east corner of the bed respectively. If c ij is a letter, it indicates the color of the corresponding square. If c ij is a #, the corresponding square is colored white and is the initial position of the cube. The string v 1 v 2 v 3 v 4 v 5 v 6 shows the order of colors of squares to visit. The cube should visit the squares colored v 1 , v 2 , v 3 , v 4 , v 5 and v 6 in this order. The end of the input is indicated by a line containing two zeros separated by a space. Output For each input dataset, output the least number of steps if there is a solution, or "unreachable" if there is no solution. In either case, print it in one line for each input dataset. Sample Input 10 5 kkkkkwwwww w#wwwrwwww wwwwbgwwww kwwmcwwwkk kkwywwwkkk rgbcmy 10 5 kkkkkkkkkk k#kkkkkkkk kwkkkkkwwk kcmyrgbwwk kwwwwwwwwk cmyrgb 10 5 kkkkkkkkkk k#kkkkkkkk kwkkkkkwkk kcmyrgbwwk kwwwwwwwwk cmyrgb 0 0 Output for the Sample Input 9 49 unreachable
37,969
Score : 500 points Problem Statement You are given a connected undirected simple graph, which has N vertices and M edges. The vertices are numbered 1 through N , and the edges are numbered 1 through M . Edge i connects vertices A_i and B_i . Your task is to find a path that satisfies the following conditions: The path traverses two or more vertices. The path does not traverse the same vertex more than once. A vertex directly connected to at least one of the endpoints of the path, is always contained in the path. It can be proved that such a path always exists. Also, if there are more than one solution, any of them will be accepted. Constraints 2 \leq N \leq 10^5 1 \leq M \leq 10^5 1 \leq A_i < B_i \leq N The given graph is connected and simple (that is, for every pair of vertices, there is at most one edge that directly connects them). Input Input is given from Standard Input in the following format: N M A_1 B_1 A_2 B_2 : A_M B_M Output Find one path that satisfies the conditions, and print it in the following format. In the first line, print the count of the vertices contained in the path. In the second line, print a space-separated list of the indices of the vertices, in order of appearance in the path. Sample Input 1 5 6 1 3 1 4 2 3 1 5 3 5 2 4 Sample Output 1 4 2 3 1 4 There are two vertices directly connected to vertex 2 : vertices 3 and 4 . There are also two vertices directly connected to vertex 4 : vertices 1 and 2 . Hence, the path 2 → 3 → 1 → 4 satisfies the conditions. Sample Input 2 7 8 1 2 2 3 3 4 4 5 5 6 6 7 3 5 2 6 Sample Output 2 7 1 2 3 4 5 6 7
37,970
Problem I: Tatami A tatami mat, a Japanese traditional floor cover, has a rectangular form with aspect ratio 1:2. When spreading tatami mats on a floor, it is prohibited to make a cross with the border of the tatami mats, because it is believed to bring bad luck. Your task is to write a program that reports how many possible ways to spread tatami mats of the same size on a floor of given height and width. Input The input consists of multiple datasets. Each dataset cosists of a line which contains two integers H and W in this order, separated with a single space. H and W are the height and the width of the floor respectively. The length of the shorter edge of a tatami mat is regarded as a unit length. You may assume 0 < H , W ≀ 20. The last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed. Output For each dataset, print the number of possible ways to spread tatami mats in one line. Sample Input 3 4 4 4 0 0 Output for the Sample Input 4 2
37,971
Score : 200 points Problem Statement Let S(n) denote the sum of the digits in the decimal notation of n . For example, S(101) = 1 + 0 + 1 = 2 . Given an integer N , determine if S(N) divides N . Constraints 1 \leq N \leq 10^9 Input Input is given from Standard Input in the following format: N Output If S(N) divides N , print Yes ; if it does not, print No . Sample Input 1 12 Sample Output 1 Yes In this input, N=12 . As S(12) = 1 + 2 = 3 , S(N) divides N . Sample Input 2 101 Sample Output 2 No As S(101) = 1 + 0 + 1 = 2 , S(N) does not divide N . Sample Input 3 999999999 Sample Output 3 Yes
37,972
Score: 300 points Problem Statement Takahashi has decided to hold fastest-finger-fast quiz games. Kizahashi, who is in charge of making the scoreboard, is struggling to write the program that manages the players' scores in a game, which proceeds as follows. A game is played by N players, numbered 1 to N . At the beginning of a game, each player has K points. When a player correctly answers a question, each of the other N-1 players receives minus one ( -1 ) point. There is no other factor that affects the players' scores. At the end of a game, the players with 0 points or lower are eliminated, and the remaining players survive. In the last game, the players gave a total of Q correct answers, the i -th of which was given by Player A_i . For Kizahashi, write a program that determines whether each of the N players survived this game. Constraints All values in input are integers. 2 \leq N \leq 10^5 1 \leq K \leq 10^9 1 \leq Q \leq 10^5 1 \leq A_i \leq N\ (1 \leq i \leq Q) Input Input is given from Standard Input in the following format: N K Q A_1 A_2 . . . A_Q Output Print N lines. The i -th line should contain Yes if Player i survived the game, and No otherwise. Sample Input 1 6 3 4 3 1 3 2 Sample Output 1 No No Yes No No No In the beginning, the players' scores are (3, 3, 3, 3, 3, 3) . Player 3 correctly answers a question. The players' scores are now (2, 2, 3, 2, 2, 2) . Player 1 correctly answers a question. The players' scores are now (2, 1, 2, 1, 1, 1) . Player 3 correctly answers a question. The players' scores are now (1, 0, 2, 0, 0, 0) . Player 2 correctly answers a question. The players' scores are now (0, 0, 1, -1, -1, -1) . Players 1, 2, 4, 5 and 6 , who have 0 points or lower, are eliminated, and Player 3 survives this game. Sample Input 2 6 5 4 3 1 3 2 Sample Output 2 Yes Yes Yes Yes Yes Yes Sample Input 3 10 13 15 3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 Sample Output 3 No No No No Yes No No No Yes No
37,973
Score : 700 points Problem Statement We have a tree with N vertices. Vertex 1 is the root of the tree, and the parent of Vertex i ( 2 \leq i \leq N ) is Vertex P_i . To each vertex in the tree, Snuke will allocate a color, either black or white, and a non-negative integer weight. Snuke has a favorite integer sequence, X_1, X_2, ..., X_N , so he wants to allocate colors and weights so that the following condition is satisfied for all v . The total weight of the vertices with the same color as v among the vertices contained in the subtree whose root is v , is X_v . Here, the subtree whose root is v is the tree consisting of Vertex v and all of its descendants. Determine whether it is possible to allocate colors and weights in this way. Constraints 1 \leq N \leq 1 000 1 \leq P_i \leq i - 1 0 \leq X_i \leq 5 000 Inputs Input is given from Standard Input in the following format: N P_2 P_3 ... P_N X_1 X_2 ... X_N Outputs If it is possible to allocate colors and weights to the vertices so that the condition is satisfied, print POSSIBLE ; otherwise, print IMPOSSIBLE . Sample Input 1 3 1 1 4 3 2 Sample Output 1 POSSIBLE For example, the following allocation satisfies the condition: Set the color of Vertex 1 to white and its weight to 2 . Set the color of Vertex 2 to black and its weight to 3 . Set the color of Vertex 3 to white and its weight to 2 . There are also other possible allocations. Sample Input 2 3 1 2 1 2 3 Sample Output 2 IMPOSSIBLE If the same color is allocated to Vertex 2 and Vertex 3 , Vertex 2 cannot be allocated a non-negative weight. If different colors are allocated to Vertex 2 and 3 , no matter which color is allocated to Vertex 1 , it cannot be allocated a non-negative weight. Thus, there exists no allocation of colors and weights that satisfies the condition. Sample Input 3 8 1 1 1 3 4 5 5 4 1 6 2 2 1 3 3 Sample Output 3 POSSIBLE Sample Input 4 1 0 Sample Output 4 POSSIBLE
37,974
Problem C: Towns along a Highway There are several towns on a highway. The highway has no forks. Given the distances between the neighboring towns, we can calculate all distances from any town to others. For example, given five towns (A, B, C, D and E) and the distances between neighboring towns like in Figure C.1, we can calculate the distance matrix as an upper triangular matrix containing the distances between all pairs of the towns, as shown in Figure C.2. Figure C.1: An example of towns Figure C.2: The distance matrix for Figure C.1 In this problem, you must solve the inverse problem. You know only the distances between all pairs of the towns, that is, N ( N - 1)/2 numbers in the above matrix. Then, you should recover the order of the towns and the distances from each town to the next. Input The input is a sequence of datasets. Each dataset is formatted as follows. N d 1 d 2 ... d N ( N -1)/2 The first line contains an integer N (2 ≀ N ≀ 20), which is the number of the towns on the highway. The following lines contain N ( N -1)/2 integers separated by a single space or a newline, which are the distances between all pairs of the towns. Numbers are given in descending order without any information where they appear in the matrix. You can assume that each distance is between 1 and 400, inclusive. Notice that the longest distance is the distance from the leftmost town to the rightmost. The end of the input is indicated by a line containing a zero. Output For each dataset, output N - 1 integers in a line, each of which is the distance from a town to the next in the order of the towns. Numbers in a line must be separated by a single space. If the answer is not unique, output multiple lines ordered by the lexicographical order as a sequence of integers, each of which corresponds to an answer. For example, ' 2 10 ' should precede ' 10 2 '. If no answer exists, output nothing. At the end of the output for each dataset, a line containing five minus symbols ' ----- ' should be printed for human readability. No extra characters should occur in the output. For example, extra spaces at the end of a line are not allowed. Sample Input 2 1 3 5 3 2 3 6 3 2 5 9 8 7 6 6 4 3 2 2 1 6 9 8 8 7 6 6 5 5 3 3 3 2 2 1 1 6 11 10 9 8 7 6 6 5 5 4 3 2 2 1 1 7 72 65 55 51 48 45 40 38 34 32 27 25 24 23 21 17 14 13 11 10 7 20 190 189 188 187 186 185 184 183 182 181 180 179 178 177 176 175 174 173 172 171 170 169 168 167 166 165 164 163 162 161 160 159 158 157 156 155 154 153 152 151 150 149 148 147 146 145 144 143 142 141 140 139 138 137 136 135 134 133 132 131 130 129 128 127 126 125 124 123 122 121 120 119 118 117 116 115 114 113 112 111 110 109 108 107 106 105 104 103 102 101 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 19 60 59 58 56 53 52 51 50 48 48 47 46 45 45 44 43 43 42 42 41 41 40 40 40 40 40 40 40 39 39 39 38 38 38 37 37 36 36 35 35 34 33 33 32 32 32 31 31 30 30 30 29 28 28 28 28 27 27 26 26 25 25 25 25 24 24 23 23 23 23 22 22 22 22 21 21 21 21 20 20 20 20 20 20 20 20 20 20 20 20 20 19 19 19 19 19 18 18 18 18 18 17 17 17 17 16 16 16 15 15 15 15 14 14 13 13 13 12 12 12 12 12 11 11 11 10 10 10 10 10 9 9 8 8 8 8 8 8 7 7 7 6 6 6 5 5 5 5 5 5 4 4 4 3 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 0 Output for the Sample Input 1 ----- 2 3 3 2 ----- ----- 1 2 4 2 2 4 2 1 ----- 1 2 3 2 1 ----- 1 1 4 2 3 1 5 1 2 2 2 2 1 5 1 3 2 4 1 1 ----- 7 14 11 13 10 17 17 10 13 11 14 7 ----- ----- 1 1 2 3 5 8 1 1 2 3 5 8 1 1 2 3 5 8 8 5 3 2 1 1 8 5 3 2 1 1 8 5 3 2 1 1 -----
37,975
Problem E Cost Performance Flow Yayoi is a professional of money saving. Yayoi does not select items just because they are cheap; her motto is "cost performance". This is one of the reasons why she is good at cooking with bean sprouts. Due to her saving skill, Yayoi often receives requests to save various costs. This time, her task is optimization of "network flow". Network flow is a problem on graph theory. Now, we consider a directed graph $G = (V, E)$, where $V = \{1, 2, ... , |V|\}$ is a vertex set and $E \subset V \times V$ is an edge set. Each edge $e$ in $E$ has a capacity $u(e)$ and a cost $c(e)$. For two vertices $s$ and $t$, a function $f_{s,t} : E \rightarrow R$, where $R$ is the set of real numbers, is called an $s$-$t$ flow if the following conditions hold: For all $e$ in $E$, $f_{s,t}$ is non-negative and no more than $u(e)$. Namely, $0 \leq f_{s,t}(e) \leq u(e)$ holds. For all $v$ in $V \setminus \{s, t\}$, the sum of $f_{s,t}$ of out-edges from $v$ equals the sum of $f_{s,t}$ of in-edges to $v$. Namely, $\sum_{e=(u,v) \in E} f_{s,t}(e) = \sum_{e=(v,w) \in E} f_{s,t}(e)$ holds. Here, we define flow $F( f_{s,t})$ and cost $C( f_{s,t})$ of $f_{s,t}$ as $F( f_{s,t}) = \sum_{e=(s,v)\in E} f_{s,t}(e) - \sum_{e=(u,s)\in E} f_{s,t}(e)$ and $C( f_{s,t}) = \sum_{e\in E} f_{s,t}(e)c(e)$, respectively. Usually, optimization of network flow is defined as cost minimization under the maximum flow. However, Yayoi's motto is "cost performance". She defines a balanced function $B( f_{s,t})$ for $s$-$t$ flow as the sum of the square of the cost $C( f_{s,t})$ and the difference between the maximum flow $M = max_{f : s-t flow} F( f )$ and the flow $F( f_{s,t})$, i.e. $B( f_{s,t}) = C( f_{s,t})^2 + (M - F( f_{s,t}))^2$. Then, Yayoi considers that the best cost performance flow yields the minimum of $B( f_{s,t})$. Your task is to write a program for Yayoi calculating $B( f_{s,t}^*)$ for the best cost performance flow $f_{s,t}^*$. Input The input consists of a single test case. The first line gives two integers separated by a single space: the number of vertices $N$ $(2 \leq N \leq 100)$ and the number of edges $M$ $(1 \leq M \leq 1,000)$. The second line gives two integers separated by a single space: two vertices $s$ and $t$ $(1 \leq s, t \leq N, s \ne t)$. The $i$-th line of the following $M$ lines describes the $i$-th edges as four integers $a_i$, $b_i$, $u_i$, and $c_i$: the $i$-th edge from $a_i$ $(1 \leq a_i \leq N)$ to $b_i$ $(1 \leq b_i \leq N)$ has the capacity $u_i$ $(1 \leq u_i \leq 100)$ and the cost $c_i$ $(1 \leq c_i \leq 100)$ . You can assume that $a_i \ne b_i$ for all $1 \leq i \leq M$, and $a_i \ne a_j$ or $b_i \ne b_j$ if $i \ne j$ for all $1 \leq i, j \leq M$. Output Display $B( f_{s,t}^*)$, the minimum of balanced function under $s$-$t$ flow, as a fraction in a line. More precisely, output "$u/d$", where $u$ is the numerator and $d$ is the denominator of $B( f_{s,t}^*)$, respectively. Note that $u$ and $d$ must be non-negative integers and relatively prime, i.e. the greatest common divisor of $u$ and $d$ is 1. You can assume that the answers for all the test cases are rational numbers. Sample Input 1 2 1 1 2 1 2 1 1 Output for the Sample Input 1 1/2 Sample Input 2 3 3 1 2 1 2 1 1 1 3 3 1 3 2 3 2 Output for the Sample Input 2 10/1 Sample Input 3 3 3 1 2 1 2 1 1 1 3 7 1 3 2 7 1 Output for the Sample Input 3 45/1
37,976
Score : 400 points Problem Statement You are given positive integers N and M . How many sequences a of length N consisting of positive integers satisfy a_1 \times a_2 \times ... \times a_N = M ? Find the count modulo 10^9+7 . Here, two sequences a' and a'' are considered different when there exists some i such that a_i' \neq a_i'' . Constraints All values in input are integers. 1 \leq N \leq 10^5 1 \leq M \leq 10^9 Input Input is given from Standard Input in the following format: N M Output Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7 . Sample Input 1 2 6 Sample Output 1 4 Four sequences satisfy the condition: \{a_1, a_2\} = \{1, 6\}, \{2, 3\}, \{3, 2\} and \{6, 1\} . Sample Input 2 3 12 Sample Output 2 18 Sample Input 3 100000 1000000000 Sample Output 3 957870001
37,977
Problem I. Sum of QQ You received a card with an integer $S$ and a multiplication table of infinite size. All the elements in the table are integers, and an integer at the $i$-th row from the top and the $j$-th column from the left is $A_{i,j} = i \times j$ ($i,j \geq 1$). The table has infinite size, i.e., the number of the rows and the number of the columns are infinite. You love rectangular regions of the table in which the sum of numbers is $S$. Your task is to count the number of integer tuples $(a, b, c, d)$ that satisfies $1 \leq a \leq b, 1 \leq c \leq d$ and $\sum_{i=a}^b \sum_{j=c}^d A_{i,j} = S$. Input The input consists of a single test case of the following form. $S$ The first line consists of one integer $S$ ($1 \leq S \leq 10^5$), representing the summation of rectangular regions you have to find. Output Print the number of rectangular regions whose summation is $S$ in one line. Examples Sample Input 1 25 Output for Sample Input 1 10 Sample Input 2 1 Output for Sample Input 2 1 Sample Input 3 5 Output for Sample Input 3 4 Sample Input 4 83160 Output for Sample Input 4 5120
37,978
ゎヌルドバッハ予想 ゎヌルドバッハ予想ずは「6 以䞊のどんな偶数も、2 ぀の玠数 (*1) の和ずしお衚わすこずができる」ずいうものです。 たずえば、偶数の 12 は 12 = 5 + 7 、18 は 18 = 5 + 13 = 7 + 11 などず衚すこずができたす。 和が 134 ずなる 2 ぀の玠数の組み合せをすべお曞き出すず、以䞋の通りずなりたす。 134 = 3+131 = 7+127 = 31+103 = 37+97 = 61+73 = 67+67 = 131+3 = 127+7 = 103+31 = 97+37 = 73+61 䞎えられた数が倧きくなるず、いくらでも玠数の組み合せが芋぀かるような気がしたす。しかし、珟代数孊をもっおしおもこの予想を蚌明するこずも、反䟋を䜜るこずもできたせん(*2)。ちょっず䞍思議な感じがしたすね。 そこで、ゎヌルドバッハ予想を鑑賞するために、偶数 n を入力ずし、和が n ずなる 2 ぀の玠数の組み合せの数を求めるプログラムを䜜成しおください。 和が n ずなる玠数の組み合せの数ずは n = p + q か぀ p ≀ q であるような正の玠数 p , q の組み合せの数です。䞊の䟋からわかるように和が 134 ずなる玠数の組み合せは6 個です。 (*1) 玠数ずは、1 たたは自分自身以倖に玄数を持たない敎数のこずである。なお、1 は玠数ではない。 (*2) 2007 幎 2 月珟圚、5×10 17 たでの党おの偶数に぀いお成り立぀こずが確かめられおいる。(Wikipedia) Input 耇数のデヌタセットの䞊びが入力ずしお䞎えられたす。入力の終わりはれロひず぀の行で瀺されたす。 各デヌタセットずしお、぀の偶数 n (6 ≀ n ≀ 1000000) が行に䞎えられたす。 デヌタセットの数は 500 を超えたせん。 Output デヌタセット毎に玠数の組み合せの数を行に出力したす。 Sample Input 134 4330 34808 98792 0 Output for the Sample Input 6 72 274 607
37,979
Lexicographical Comparison Compare given two sequence $A = \{a_0, a_1, ..., a_{n-1}\}$ and $B = \{b_0, b_1, ..., b_{m-1}$ lexicographically. Input The input is given in the following format. $n$ $a_0 \; a_1, ..., \; a_{n-1}$ $m$ $b_0 \; b_1, ..., \; b_{m-1}$ The number of elements in $A$ and its elements $a_i$ are given in the first and second lines respectively. The number of elements in $B$ and its elements $b_i$ are given in the third and fourth lines respectively. All input are given in integers. Output Print 1 $B$ is greater than $A$, otherwise 0 . Constraints $1 \leq n, m \leq 1,000$ $0 \leq a_i, b_i \leq 1,000$ Sample Input 1 3 1 2 3 2 2 4 Sample Output 1 1 Sample Input 2 4 5 4 7 0 5 1 2 3 4 5 Sample Output 2 0 Sample Input 3 3 1 1 2 4 1 1 2 2 Sample Output 3 1
37,980
Princess, a Cryptanalyst お姫様の暗号解読 English text is not available in this practice contest. ある貧乏な囜のおおんばで勇敢なお姫様はお忍びで出かけた町である日本語で曞かれた叀文曞を手に入れたお姫様は日本語ができるためさっそくこの叀文曞を読んでみたするず驚くべき事が分かったこの叀文曞は叀の秘宝の圚凊を瀺しおいたのであるずころが秘宝の圚凊は暗号になっおおり容易には分からないようになっおいたそこでお姫様は埓者であるあなたに暗号の解読を手䌝うように呜什を䞋した あなたはお姫様を助けるため昌倜を問わず調査を行ったその結果Shortest Secret String (SSS) ず呌ばれる文字列が解読に重芁な圹割を果たすこずがわかったここで SSS ずは N 個の単語党郚を郚分文字列ずしお含みなおか぀その長さが最小であるような文字列である あなたの仕事は N 個の単語から SSS を芋぀け出す事である Input 入力は耇数のデヌタセットで䞎えられるデヌタセットの初めの䞀行はデヌタセットに含たれる単語の数 N (1≩ N ≩10)が䞎えられる続く N 行に単語が䞎えられる最埌のデヌタセットの埌に0のみを含む䞀行が䞎えられる なお入力で䞎えられる単語はアルファベット小文字のみからなり長さは高々10であるこずが保蚌されおいる Output 各デヌタセットに぀いおSSS を䞀行に出力せよたた耇数ある堎合は蟞曞匏順序で最小のものを出力せよ Sample Input 4 apple length things thin 2 icp cpc 3 zeta eta alphabet 2 until till 0 Output for the Sample Input applengthings icpc zetalphabet untill
37,982
The Enemy of My Enemy is My Friend 敵の敵は味方 English text is not available in this practice contest. 時は XXXX 幎。戊乱の䞖である。 土地や資源を巡っお、隣り合った囜同士の衝突がそこかしこで起こり、䞖の䞭の先行きは非垞に䞍透明であった。そんな䞭ずある囜が、様々な囜ず軍事同盟を結んでこの乱䞖を生き延びようず考えた。軍事同盟は次の条件をみたすように行うこずが出来る。 自囜の隣囜ずは同盟を結ぶこずは出来ない。 同盟をした囜の隣囜ずは同盟を結ぶこずは出来ない。 ただし、囜ごずにその軍事的な匷さは異なっおいる。軍事的に匷くない耇数の囜ず同盟を結ぶより、軍事的に非垞に匷い䞀囜ず同盟を結んだほうが有利であるこずも有り埗る。ここでは、同盟に含たれる囜の軍事的匷さの和が最倧になるような軍事同盟の結び方を考えたい。 Input 入力は耇数のデヌタセットからなる各デヌタセットの圢匏は次の通りである。 N A 1 B 1 C 1 D 1,1 ... D 1,C 1 A 2 B 2 C 2 D 2,1 ... D 2,C 2 ... A N B N C N D N,1 ... D N,C N 各デヌタセットでは、1行目は囜の数 N (1 ≀ N ≀ 40)が䞎えられ、2〜N+1行目には囜の詳现が䞎えられる。囜の詳现では、囜名 A i 、軍事的匷さ B i 、隣接しおいる囜の数 C i 、隣接しおいる囜のリスト D i,1 ... D i,C i が䞎えられる。自囜は1぀目の囜 A 1 である。 囜名 A i は党お異なり、それぞれ1文字以䞊16文字以䞋の倧文字あるいは小文字アルファベットからなる。軍事的匷さ B i は0以䞊1000以䞋の敎数で䞎えられる。隣接しおいる囜のリストにある囜名 D i,j は A 1 から A N のうちいずれかず䞀臎する。たた、ある囜の隣接囜リストにその囜自身が含たれるこずはなく、同じ囜名が2回以䞊重耇しお含たれるこずもない。さらに、隣接関係が察称でない堎合は入力に存圚しない。 入力の終了は0のみからなる行で衚される。 Output 各テストケヌスに぀いお、自囜を含めた軍事的匷さの和が最倧になるような同盟を考えたずき、その匷さを求め、1行で出力せよ。 Sample Input 7 INTERCAL 10 3 Chef Piet COW Chef 7 3 INTERCAL Piet COW Piet 6 2 INTERCAL Chef COW 7 2 INTERCAL Chef J 6 1 A A 12 1 J Grass 0 0 7 Qin 105 4 Zhao Wei Han Chu Zhao 81 4 Qin Wei Qi Yan Wei 70 5 Qin Zhao Han Qi Chu Han 45 3 Qin Wei Chu Qi 79 4 Zhao Wei Chu Yan Chu 102 4 Qin Wei Han Qi Yan 53 2 Zhao Qi 14 Magadha 98 8 Macedonia Kalinga Surashtra Ashmaka Kantala Andhra Gangaridai Kamapura Macedonia 79 2 Magadha Surashtra Kalinga 51 2 Magadha Andhra Surashtra 13 3 Magadha Macedonia Ashmaka Ashmaka 11 3 Magadha Surashtra Kantala Kantala 12 3 Magadha Ashmaka Andhra Andhra 14 3 Magadha Kantala Kalinga Cholas 15 3 Cheras Pandyas Anuradhapuras Cheras 8 2 Cholas Pandyas Pandyas 10 3 Cholas Cheras Anuradhapuras Anuradhapuras 7 2 Cholas Pandyas Gangaridai 20 3 Magadha Kamapura Arakan Kamapura 18 2 Magadha Gangaridai Arakan 7 1 Gangaridai 0 Output for Sample Input 22 184 120
37,983
Reflection For given three points p1, p2, p , find the reflection point x of p onto p1p2 . Input x p1 y p1 x p2 y p2 q x p 0 y p 0 x p 1 y p 1 ... x p q−1 y p q−1 In the first line, integer coordinates of p1 and p2 are given. Then, q queries are given for integer coordinates of p . Output For each query, print the coordinate of the reflection point x . The output values should be in a decimal fraction with an error less than 0.00000001. Constraints 1 ≀ q ≀ 1000 -10000 ≀ x i , y i ≀ 10000 p1 and p2 are not identical. Sample Input 1 0 0 2 0 3 -1 1 0 1 1 1 Sample Output 1 -1.0000000000 -1.0000000000 0.0000000000 -1.0000000000 1.0000000000 -1.0000000000 Sample Input 2 0 0 3 4 3 2 5 1 4 0 3 Sample Output 2 4.2400000000 3.3200000000 3.5600000000 2.0800000000 2.8800000000 0.8400000000
37,984
And Then, How Many Are There? To Mr. Solitarius, who is a famous solo play game creator, a new idea occurs like every day. His new game requires discs of various colors and sizes. To start with, all the discs are randomly scattered around the center of a table. During the play, you can remove a pair of discs of the same color if neither of them has any discs on top of it. Note that a disc is not considered to be on top of another when they are externally tangent to each other. Figure D-1: Seven discs on the table For example, in Figure D-1, you can only remove the two black discs first and then their removal makes it possible to remove the two white ones. In contrast, gray ones never become removable. You are requested to write a computer program that, for given colors, sizes, and initial placings of discs, calculates the maximum number of discs that can be removed. Input The input consists of multiple datasets, each being in the following format and representing the state of a game just after all the discs are scattered. n x 1 y 1 r 1 c 1 x 2 y 2 r 2 c 2 ... x n y n r n c n The first line consists of a positive integer n representing the number of discs. The following n lines, each containing 4 integers separated by a single space, represent the colors, sizes, and initial placings of the n discs in the following manner: ( x i , y i ), r i , and c i are the xy -coordinates of the center, the radius, and the color index number, respectively, of the i -th disc, and whenever the i -th disc is put on top of the j -th disc, i < j must be satisfied. You may assume that every color index number is between 1 and 4, inclusive, and at most 6 discs in a dataset are of the same color. You may also assume that the x - and y -coordinates of the center of every disc are between 0 and 100, inclusive, and the radius between 1 and 100, inclusive. The end of the input is indicated by a single zero. Output For each dataset, print a line containing an integer indicating the maximum number of discs that can be removed. Sample Input 4 0 0 50 1 0 0 50 2 100 0 50 1 0 0 100 2 7 12 40 8 1 10 40 10 2 30 40 10 2 10 10 10 1 20 10 9 3 30 10 8 3 40 10 7 3 2 0 0 100 1 100 32 5 1 0 Output for the Sample Input 2 4 0
37,985
Score : 500 points Problem Statement Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1) , (x_2, y_2) , and (x_3, y_3) . He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles. Constraints 0 ≀ x_i, y_i ≀ 1000 The coordinates are integers. The three points are not on the same line. Input The input is given from Standard Input in the following format: x_1 y_1 x_2 y_2 x_3 y_3 Output Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9} . Sample Input 1 0 0 1 1 2 0 Sample Output 1 0.292893218813 Sample Input 2 3 1 1 5 4 9 Sample Output 2 0.889055514217
37,986
F - 土地盞続 Problem Statement ある $N$ 人の兄匟は芪の遺産盞続の話し合いをしおいた 圌らの芪の残した莫倧な遺産の䞭には広倧な土地も含たれおいた その土地は南北に $H$ km, 東西に $W$ km に広がる長方圢の圢をしおいる この土地は 1 km 四方の区画単䜍で管理されおおり 土地の北端から $i$ 〜 $i+1$ km か぀西端から $j$ 〜 $j+1$ km の範囲にある 1 km 四方の区画を区画 $(i, j)$ ず呌ぶ $i$, $j$ は $0 \leq i < H$, $0 \leq j < W$ を満たす敎数である 土地の䟡栌は区画ごずに決たっおおり区画 $(i, j)$ の䟡栌は $a_{i, j}$ で衚される 兄匟は次のように土地を分けお盞続するこずにした $N$ 人の兄匟それぞれが区画をいく぀か遞び盞続する 各兄匟が盞続する土地が 1 ぀の長方圢を成すように区画を遞ばなければならない $N$ 人の兄匟が盞続する土地は重なっおはならない 誰も盞続しない区画があっおもよい誰も盞続しない区画は攟棄される ある人が盞続する土地の範囲に含たれる区画の䟡栌の和をその土地の䟡栌ず呌ぶ 兄匟は各々が盞続する土地の䟡栌がなるべく公平になるように土地を分けたい あなたの仕事は $N$ 人の䞭で盞続する土地の䟡栌が 最も䜎い人の土地の䟡栌を最倧にするような土地の分け方を考えるこずである そのように土地を分けた時の盞続する土地の䟡栌が最も䜎い人の土地の䟡栌を答えるプログラムを䜜成せよ Input 入力は以䞋のような圢匏で䞎えられる $H$ $W$ $N$ $a_{0,0}$ $a_{0,1}$ ... $a_{0,W-1}$ ... $a_{H-1,0}$ $a_{H-1,1}$ ... $a_{H-1,W-1}$ $H$, $W$ $(2 \leq H,W \leq 200)$ は遺産の土地の南北の長さず東西の長さをそれぞれ衚す $N$ $(2 \leq N \leq 4)$ は土地を盞続する兄匟の人数を衚す $a_{i, j}$ $(0 \leq a_{i,j} \leq 10^4)$ は区画 $(i, j)$ の䟡栌を衚す Output 盞続する土地の䟡栌が最も䜎い人の土地の䟡栌を最倧にするように分けた時の 最も䜎い土地の䟡栌を 1 行で出力せよ Sample Input 1 3 3 2 1 2 2 3 1 0 0 4 3 Output for the Sample Input 1 7 図のように分けるのが最適である Sample Input 2 3 3 2 0 1 0 1 1 1 0 1 0 Output for the Sample Input 2 1 Sample Input 3 2 5 3 8 3 0 5 6 2 5 2 5 2 Output for the Sample Input 3 11 Sample Input 4 3 3 4 3 3 4 3 3 4 3 3 4 Output for the Sample Input 4 7 Sample Input 5 4 4 4 2 2 2 2 2 1 2 1 2 2 2 2 2 1 2 1 Output for the Sample Input 5 7
37,987
かぐや いよいよ今月末に「はやぶさ」が打ち䞊げられたす。幎前に「はやぶさ」が垰っおきたずきは、日本䞭が盛り䞊がったのを芚えおいる人も倚いず思いたす。幎前には、「かぐや」が打ち䞊げられ、月の呚りを回りながらたくさんの鮮明な画像を地球に送っおくれたした。 䞊の図は、地球を原点ずした空間座暙z軞は玙面から垂盎に䞋から䞊に向いおいるものずしたすに、月の軌道ずいく぀かの月の䜍眮、月の呚りを回るかぐやの軌道を描いたものです。月の軌道は、x軞ずy軞を通る平面䞊にある、原点を䞭心ずする円ずしたす。月の呚りを回るかぐやの軌道は、x軞ずz軞を通る平面に平行な平面䞊にある円ずし、その䞭心は月の䞭心ず䞀臎したす。月は、その軌道に沿っお描かれた矢印の方向に回っおいるものずしたす。 右の図で、月の䜍眮はの぀が描かれおいたす。月を暪切る盎線がかぐやの軌道です。かぐやは月の呚りを回っおいるので軌道は円ですが、z軞の正の方向から芋おいるので、図のx軞に平行な盎線に芋えたす月の䜍眮が倉わっおも、぀ねにx軞に平行であるこずに泚意しおください。かぐやは、その軌道䞊に描かれた矢印の方向に回っおいるものずしたす。 かぐやが地球から芋お月の裏偎に隠れおしたうず、地球ず盎接通信ができなくなりたす。かぐやの管制を担圓するあなたは、かぐやが月の裏偎に隠れる時間が、䞎えられた時間の䞭でどれだけになるかをプログラムで求めようずしおいたす。 月の地球に察する䜍眮ず分単䜍での時間tが䞎えられたずき、その䜍眮から始めおt分埌たでの間に、かぐやが月の裏偎に隠れる時間を求めるプログラムを䜜成しおください。ただし、地球ずかぐやは点、月は半埄 1800 km の球ず考えたす。月は半埄 380000 km の軌道を 2500000 秒で䞀呚し、かぐやは月の衚面から高床 100 km の円䞊を時間で䞀呚するものずしたす。かぐやの最初の䜍眮は、かぐやの軌道がz座暙で最倧の倀をずる䜍眮ずしたす。 入力 入力は以䞋の圢匏で䞎えられる。 m t m (0 ≀ m < 360) は月の䜍眮を䞊の図のx軞の正の郚分からy軞の正の郚分に向かっお反時蚈回りに枬った角床を敎数で衚したものである。 t (1 ≀ t ≀ 10000) は分で枬った時間を衚す敎数である。 出力 はじめの䜍眮から t 分経過するたでの間に、かぐやが月の裏偎に隠れる時間分を実数で出力する。ただし、誀差がプラスマむナス 1.0 分を超えおはならない。この条件を満たせば小数点以䞋䜕桁衚瀺しおもよい。 入出力䟋 入力䟋 90 10 出力䟋 0.0 入力䟋 0 120 出力䟋 47.73
37,988
Problem I: A Piece of Cake In the city, there are two pastry shops. One shop was very popular because its cakes are pretty tasty. However, there was a man who is displeased at the shop. He was an owner of another shop. Although cause of his shop's unpopularity is incredibly awful taste of its cakes, he never improved it. He was just growing hate, ill, envy, and jealousy. Finally, he decided to vandalize the rival. His vandalize is to mess up sales record of cakes. The rival shop sells K kinds of cakes and sales quantity is recorded for each kind. He calculates sum of sales quantities for all pairs of cakes. Getting K ( K -1)/2 numbers, then he rearranges them randomly, and replace an original sales record with them. An owner of the rival shop is bothered. Could you write, at least, a program that finds total sales quantity of all cakes for the pitiful owner? Input Input file contains several data sets. A single data set has following format: K c 1 c 2 ... c K ×( K -1)/2 K is an integer that denotes how many kinds of cakes are sold. c i is an integer that denotes a number written on the card. The end of input is denoted by a case where K = 0. You should output nothing for this case. Output For each data set, output the total sales quantity in one line. Constraints Judge data contains at most 100 data sets. 2 ≀ K ≀ 100 0 ≀ c i ≀ 100 Sample Input 2 2 3 5 4 3 0 Output for the Sample Input 2 6
37,989
D: 日焌け - Suntan - 物語 あいずにゃんは若ヶ束高校のプログラミングコンテスト郚、通称ぷろこん郚に所属する2幎生である。倩䜿のようにかわいい。 あいずにゃんは今幎の倏フェスに参加する予定なので、聎きに行くバンドのスケゞュヌルを立おた。 ここで心配なのが日焌けだ。 ラむブはすべお野倖で行われるが、あいずにゃんは日焌けしやすい䜓質なので長時間野倖で玫倖線を济びすぎるずすぐ日焌けしおしたう。 ラむブがない間は屋内に避難するこずでできるだけ玫倖線を回避する぀もりだが、ラむブ䞭はどうしおも日に圓たっおしたう。 そこであいずにゃんは日焌け止めを塗るこずで玫倖線察策をするこずを考えた。 問題 日焌け止めを塗るず、塗った時間から T 分間だけその効果を埗るこずができる。 日焌け止めは1回しか塗るこずができないため、効果的に䜿いたい。 あいずにゃんは、ラむブの開始時刻から終了時刻たでは野倖にいお、それ以倖では屋内にいる。 あいずにゃんが聎く予定のラむブスケゞュヌルが䞎えられるので、野倖にいる間で日焌け止めの効果を埗られる最倧の時間の長さを求めよ。 入力圢匏 入力は次の圢匏で䞎えらえる。 T N s_1 t_1 ... s_N t_N 1行目では日焌け止めの効果を埗られる時間を衚す敎数 T が䞎えられる。 2行目ではあいずにゃんが聎くラむブの数を衚す敎数 N が䞎えられる。 続く N 行には、あいずにゃんが i 番目に聎くラむブの開始時刻を衚す敎数 s_i ず終了時刻を衚す敎数 t_i が空癜区切りで䞎えられる。 制玄 1 ≀ T ≀ 10^{15} 1 ≀ N ≀ 10^5 0 ≀ s_i < t_i ≀ 10^{15} ( 1 ≀ i ≀ N ) (i+1) 番目のラむブの開始時刻は i 番目のラむブの終了時刻ず同じかそれよりも遅い。すなわち、 t_i ≀ s_{i+1} ( 1 ≀ i < N ) 出力 野倖にいる間で日焌け止めの効果を埗られる最倧の時間の長さを1行で出力せよ。 入力䟋1 20 1 0 10 出力䟋1 10 入力䟋2 20 1 0 100 出力䟋2 20 入力䟋3 9 3 1 5 9 11 13 20 出力䟋3 7 入力䟋4 25 5 9 12 15 20 21 25 28 40 45 60 出力䟋4 21
37,990
塗り぀ぶしゲヌム 指で画面にタッチしお操䜜するこずのできるタブレットむンタヌフェヌスの技術は、ゲヌムの分野でも応甚され、新しい操䜜感を持぀様々な皮類のゲヌムが䜜られおいたす。珟圚、瀟が開発しおいるゲヌムもその䞀぀です。 この゜フトりェアゲヌムの芁件は以䞋の通りです。 画面には X 列× Y 行の2次元グリッドがありたす。 グリッドのセルは赀(R)、緑(G)、茶(B)の3色のいずれかで塗られおいたす。 セルの色を倉曎するボタンR、G、Bがあり、このボタンが抌䞋されるず䞀番巊䞊(0,0)のセルがその色に倉曎されたす。 䞀番巊䞊のセルの色が倉曎されるず、そのセルの元の色ず同じ色に塗られた隣接するすべおのセルが指定された色に倉わりたす。すなわち、元の色が同じ色のセルで぀ながったセルはすべお指定された色に倉曎されたす。 このようにグリッドを塗り぀ぶしおいき、最終的にグリッド党䜓を䞀色にするずいうゲヌムです。少ない手順で解くず高埗点が䞎えられたす。 瀟のプログラマヌであるあなたは、このゲヌムのロゞックの䞀郚分を開発するこずになりたした。たずは、この最高埗点を蚈算するため、このゲヌムを最短で解いた堎合、最䜎䜕回遞択ボタンを操䜜すればグリッドが䞀色になるかをもずめるプログラムを䜜るこずにしたした。 入力 耇数のデヌタセットが䞎えられたす。入力の終わりはれロふた぀で瀺されたす。各デヌタセットは以䞋の圢匏で䞎えられたす。 X Y c 1,1 c 2,1 ... c X,1 c 1,2 c 2,2 ... c X,2 : c 1,Y c 2,Y ... c X,Y 1行目にグリッドの列ず行のサむズ X , Y (2 ≀ X , Y ≀ 10) が䞎えられたす。続く Y 行に i 列目 j 行目のセルの色を衚す文字 c i,j が空癜区切りで䞎えられたす。 出力 デヌタセットごずに、ボタン操䜜の最少回数を1行に出力したす。 入力䟋 3 3 R G B G G G G B B 2 4 R G G G R B B R 4 3 G G B R G R R G B G G R 0 0 出力䟋 2 4 4
37,991
Score : 200 points Problem Statement Raccoon is fighting with a monster. The health of the monster is H . Raccoon can use N kinds of special moves. Using the i -th move decreases the monster's health by A_i . There is no other way to decrease the monster's health. Raccoon wins when the monster's health becomes 0 or below. If Raccoon can win without using the same move twice or more, print Yes ; otherwise, print No . Constraints 1 \leq H \leq 10^9 1 \leq N \leq 10^5 1 \leq A_i \leq 10^4 All values in input are integers. Input Input is given from Standard Input in the following format: H N A_1 A_2 ... A_N Output If Raccoon can win without using the same move twice or more, print Yes ; otherwise, print No . Sample Input 1 10 3 4 5 6 Sample Output 1 Yes The monster's health will become 0 or below after, for example, using the second and third moves. Sample Input 2 20 3 4 5 6 Sample Output 2 No Sample Input 3 210 5 31 41 59 26 53 Sample Output 3 Yes Sample Input 4 211 5 31 41 59 26 53 Sample Output 4 No
37,992
Score : 100 points Problem Statement There are N persons, conveniently numbered 1 through N . They will take 3y3s Challenge for N-1 seconds. During the challenge, each person must look at each of the N-1 other persons for 1 seconds, in some order. If any two persons look at each other during the challenge, the challenge ends in failure. Find the order in which each person looks at each of the N-1 other persons, to be successful in the challenge. Constraints 2 \leq N \leq 100 Input The input is given from Standard Input in the following format: N Output If there exists no way to be successful in the challenge, print -1 . If there exists a way to be successful in the challenge, print any such way in the following format: A_{1,1} A_{1,2} ... A_{1, N-1} A_{2,1} A_{2,2} ... A_{2, N-1} : A_{N,1} A_{N,2} ... A_{N, N-1} where A_{i, j} is the index of the person that the person numbered i looks at during the j -th second. Judging The output is considered correct only if all of the following conditions are satisfied: 1 \leq A_{i,j} \leq N For each i , A_{i,1}, A_{i,2}, ... , A_{i, N-1} are pairwise distinct. Let X = A_{i, j} , then A_{X, j} \neq i always holds. Sample Input 1 7 Sample Output 1 2 3 4 5 6 7 5 3 1 6 4 7 2 7 4 1 5 6 2 1 7 5 3 6 1 4 3 7 6 2 2 5 7 3 4 1 2 6 1 4 5 3 Sample Input 2 2 Sample Output 2 -1
37,993
Problem D: Smartphone Game Problem 人気のスマフォゲヌムの䞀機胜を実装しおみよう。ゲヌムは以䞋の仕様に基づく。 5*5のマスに、5皮類のブロックが蚭眮されおいる。 それぞれの皮類のブロックには埗点が蚭定されおいる。 埗点には、ブロックの埗点の他に、ボヌナス埗点が蚭定されおいる。最初のボヌナス埗点は1である。 ブロックを任意に1぀だけ決めお、最倧で n 回たで䞊䞋巊右に移動できる。移動先のブロックは移動元のブロックのあった堎所に移動する。぀たり、隣接したブロックを亀換する事になる。 移動した埌、同じ皮類のブロックが瞊3個以䞊又は暪3個以䞊に䞊んだ堎合、䞊んだブロックは党お消える。 消えるべきブロックが党お消えた埌、あるブロックの䞋に別のブロックが存圚しない堎合、そのブロックは萜䞋する。萜䞋ずは、あるブロックの぀䞊に蟿り着くたで䞋に移動する事をいう。ブロックが䞋に存圚しない堎合は䞀番䞋に移動する。 党おのブロックの萜䞋埌にボヌナス埗点が1だけ加算される。 その埌にブロックが䞊んだ堎合、さらに消え、萜䞋する。 ブロックが消える時に、ブロック぀に぀き「ブロックの埗点*ボヌナス埗点」が自分の埗点に加算される。 回のプレむで埗られる最倧の点数を求めよ。 Input 入力は耇数のデヌタセットからなる。 各デヌタセットは以䞋で衚される。 n a 11 .. a 15 . . a 51 .. a 55 score 1 .. score 5 a ij は1から5たでの数字で、ブロックの皮類を衚す。 score i は i 皮類目のブロック぀分の埗点を衚す。 n = -1 の時、入力が終了する。 Constraints 入力は以䞋の条件を満たす。 0 ≀ n ≀ 5 1 ≀ a ij ≀ 5 0 ≀ score i ≀ 100 テストケヌスの数は 10 を超えない。 入力に含たれる倀は党お敎数である。 Output 各デヌタセット毎に、答えを䞀行に出力しなさい。 Sample Input 0 1 1 1 5 5 5 5 5 5 5 5 5 1 5 5 5 1 1 1 5 5 5 5 5 5 0 0 0 0 1 2 1 2 3 4 5 2 3 4 5 5 2 3 4 5 5 3 4 5 5 1 5 4 3 2 1 100 99 98 97 96 5 1 2 3 4 5 2 3 4 5 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 5 99 79 31 23 56 -1 Sample Output 17 2040 926
37,994
Problem F: 歳の動的蚈画 ある日の倕方。い぀ものようにあなたが居間でテレビを芋おいるず、小孊幎生の効から盞談を持ち かけられた。話を聞いおみるず、今日孊校で出された算数の問題が難しくお理解できなかったので、 あなたに解き方を教えおほしいのだずいう。 効を悩たせおいる問題は、「道が碁盀目状に通っおいる街においお、家(0, 0) から孊校( N , M ) たで最短距離で進む方法は䜕通りあるか」ずいうものだった。もちろん、あなたにずっおは赀子の手をひねるよりも簡単な問題である。すぐに䞊のような図を曞いお「家(0, 0) から順番に足し算しおいけば解けるよ」ず教えおあげた。 ずころが、それを聞いおもただ、効はなにやら䞋を向いお考えこんでいる。あなたは、自分の説明の 仕方が悪かったのだろうかず思ったが、どうやらそうではないらしい。 たっぷり分ほど悩んでいただろうか。効は、おもむろに顔を䞊げるず、あなたに向かっおこう蚀っ た。 「でも、わたしだったら、きっず孊校に行く途䞭で K 回くらい寄り道しちゃうだろうな  。ねぇお 兄ちゃん、そうするず答えは䜕通りになるの」 さあ倧倉だ。兄の嚁厳を保぀ため、なんずしおもこの問題に答えねば。 この問題を定匏化するず、次のようになる。 点(0, 0) から点( N , M ) たで、碁盀目状の道を通っお進む方法は䜕通りあるか答えよ。 基本的には右か䞊にマス進むが、途䞭で、ちょうど K 回だけ寄り道をする。 「寄り道をする」ずは、巊か䞋にマス進むこずである。 K 回の寄り道をすたせおいない堎合、いったん点( N , M ) に着いた埌でも歩き続ける。途䞭で点(0, 0) に戻っおくる堎合もある。 家はこの街の隅に建っおいるので、X 座暙たたはY 座暙が負になるような点に入るこずはできない。 しかし、X 座暙が N より倧きな点、たたは、Y 座暙が M より倧きな点には入るこずができる。 Input N M K 入力の行目には、敎数N1 ≀ N ≀ 100,000ず敎数M1 ≀ M ≀ 100,000ず敎数 K 0 ≀ K ≀ 10,000が、この順に空癜区切りで曞かれおいる。敎数 N は孊校のX 座暙を、敎数 M は孊校のY座暙を、敎数 K は寄り道の回数をあらわす。 Output 点(0, 0) から点( N , M ) たで、 K 回の寄り道をしお進む方法。その総数を1,000,000,007 で割った䜙りを出力せよ。なお1,000,000,007 は玠数である。 Sample Input 1 6 4 0 Sample Output 1 210 Sample Input 2 3 3 1 Sample Output 2 448 Sample Input 3 124 218 367 Sample Output 3 817857665
37,995
Problem E : Connect r × c のグリッドが䞎えられる。 グリッドのいく぀かのマスには1から8たでの数字が曞かれおいる。 数字が曞かれおいるマスず他の数字が曞かれおいるマスを線で結ぶ必芁がある。 数字が曞かれおいるマスに぀いお、そのマスに曞かれおいる本数だけ、他のマスずの間に線を結ぶ必芁がある。 ただし、線を結べるのは䞊䞋巊右方向だけで、䞀぀の方向に぀いお、最倧本たでである。 他の数字を跚いで線で結ぶこずはできない。 たた、次のように亀差しおしたう結び方をするこずはできない。 グリッドが入力ずしお䞎えられるので、数字が曞かれおいるマス党おを正しく結ぶ方法が、䜕通りあるのかを数えお欲しい。 Input 入力は以䞋のフォヌマットで䞎えられる。 r c grid 1 . . . grid r-1 grid i は長さcの文字列で、1から8たでの数字か"."からなる。 入力は以䞋の制玄を満たす 1 ≀ r,c ≀ 10 Output 答えの倀を100,000,007で割った䜙りを1行に出力せよ Sample Input 1 3 3 .1. 1.1 .1. Sample Output 1 0 Sample Input 2 1 3 1.1 Sample Output 2 1 Sample Input 3 3 3 4.2 ... 2.. Sample Output 3 1 Sample Input 4 7 7 2.3.1.1 ....... 2...... ....... ..3.3.. ....... 2.2.4.3 Sample Output 4 10
37,997
Problem Statement You are given a rectangular board divided into square cells. The number of rows and columns in this board are $3$ and $3 M + 1$, respectively, where $M$ is a positive integer. The rows are numbered $1$ through $3$ from top to bottom, and the columns are numbered $1$ through $3 M + 1$ from left to right. The cell at the $i$-th row and the $j$-th column is denoted by $(i, j)$. Each cell is either a floor cell or a wall cell. In addition, cells in columns $2, 3, 5, 6, \ldots, 3 M - 1, 3 M$ (numbers of form $3 k - 1$ or $3 k$, for $k = 1, 2, \ldots, M$) are painted in some color. There are $26$ colors which can be used for painting, and they are numbered $1$ through $26$. The other cells (in columns $1, 4, 7, \ldots, 3 M + 1$) are not painted and each of them is a floor cell. You are going to play the following game. First, you put a token at cell $(2, 1)$. Then, you repeatedly move it to an adjacent floor cell. Two cells are considered adjacent if they share an edge. It is forbidden to move the token to a wall cell or out of the board. The objective of this game is to move the token to cell $(2, 3 M + 1)$. For this game, $26$ magical switches are available for you! Switches are numbered $1$ through $26$ and each switch corresponds to the color with the same number. When you push switch $x$, each floor cell painted in color $x$ becomes a wall cell and each wall cell painted in color $x$ becomes a floor cell, simultaneously. You are allowed to push some of the magical switches ONLY BEFORE you start moving the token. Determine whether there exists a set of switches to push such that you can achieve the objective of the game, and if there does, find such a set. Input The input is a sequence of at most $130$ datasets. Each dataset begins with a line containing an integer $M$ ($1 \le M \le 1{,}000$). The following three lines, each containing $3 M + 1$ characters, represent the board. The $j$-th character in the $i$-th of those lines describes the information of cell $(i, j)$, as follows: The $x$-th uppercase letter indicates that cell $(i, j)$ is painted in color $x$ and it is initially a floor cell. The $x$-th lowercase letter indicates that cell $(i, j)$ is painted in color $x$ and it is initially a wall cell. A period ( . ) indicates that cell $(i, j)$ is not painted and so it is a floor cell. Here you can assume that $j$ will be one of $1, 4, 7, \ldots, 3 M + 1$ if and only if that character is a period. The end of the input is indicated by a line with a single zero. Output For each dataset, output $-1$ if you cannot achieve the objective. Otherwise, output the set of switches you push in order to achieve the objective, in the following format: $n$ $s_1$ $s_2$ ... $s_n$ Here, $n$ is the number of switches you push and $s_1, s_2, \ldots, s_n$ are uppercase letters corresponding to switches you push, where the $x$-th uppercase letter denotes switch $x$. These uppercase letters $s_1, s_2, \ldots, s_n$ must be distinct, while the order of them does not matter. Note that it is allowed to output $n = 0$ (with no following uppercase letters) if you do not have to push any switches. See the sample output for clarification. If there are multiple solutions, output any one of them. Sample Input 3 .aa.cA.Cc. .bb.Bb.AC. .cc.ac.Ab. 1 .Xx. .Yy. .Zz. 6 .Aj.fA.aW.zA.Jf.Gz. .gW.GW.Fw.ZJ.AG.JW. .bZ.jZ.Ga.Fj.gF.Za. 9 .ab.gh.mn.st.yz.EF.KL.QR.WA. .cd.ij.op.uv.AB.GH.MN.ST.XB. .ef.kl.qr.wx.CD.IJ.OP.UV.yz. 2 .AC.Mo. .IC.PC. .oA.CM. 20 .QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.qb. .qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb.qb. .QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.QB.qb. 0 Output for the Sample Input 3 B C E -1 3 J A G 10 A B G H M N S T Y Z 0 2 Q B
37,998
Score : 400 points Problem Statement Takahashi has a maze, which is a grid of H \times W squares with H horizontal rows and W vertical columns. The square at the i -th row from the top and the j -th column is a "wall" square if S_{ij} is # , and a "road" square if S_{ij} is . . From a road square, you can move to a horizontally or vertically adjacent road square. You cannot move out of the maze, move to a wall square, or move diagonally. Takahashi will choose a starting square and a goal square, which can be any road squares, and give the maze to Aoki. Aoki will then travel from the starting square to the goal square, in the minimum number of moves required. In this situation, find the maximum possible number of moves Aoki has to make. Constraints 1 \leq H,W \leq 20 S_{ij} is . or # . S contains at least two occurrences of . . Any road square can be reached from any road square in zero or more moves. Input Input is given from Standard Input in the following format: H W S_{11} ... S_{1W} : S_{H1} ... S_{HW} Output Print the maximum possible number of moves Aoki has to make. Sample Input 1 3 3 ... ... ... Sample Output 1 4 If Takahashi chooses the top-left square as the starting square and the bottom-right square as the goal square, Aoki has to make four moves. Sample Input 2 3 5 ...#. .#.#. .#... Sample Output 2 10 If Takahashi chooses the bottom-left square as the starting square and the top-right square as the goal square, Aoki has to make ten moves.
38,000
Score : 100 points Problem Statement Based on some criterion, Snuke divided the integers from 1 through 12 into three groups as shown in the figure below. Given two integers x and y ( 1 ≀ x < y ≀ 12 ), determine whether they belong to the same group. Constraints x and y are integers. 1 ≀ x < y ≀ 12 Input Input is given from Standard Input in the following format: x y Output If x and y belong to the same group, print Yes ; otherwise, print No . Sample Input 1 1 3 Sample Output 1 Yes Sample Input 2 2 4 Sample Output 2 No
38,001
敎数の和 II 0 から 100 の数字から異なる n 個の数を取り出しお合蚈が s ずなる組み合わせの数を出力するプログラムを䜜成しおください。 n 個の数はおのおの 0 から 100 たでずし、぀の組み合わせに同じ数字は䜿えたせん。たずえば、 n が 3 で s が6 のずき、3 個の数字の合蚈が 6 になる組み合わせは、 1 + 2 + 3 = 6 0 + 1 + 5 = 6 0 + 2 + 4 = 6 の 3 通りずなりたす。 Input 耇数のデヌタセットが䞎えられたす。各デヌタセットに n ( 1 ≀ n ≀ 9 ) ず s ( 0 ≀ s ≀ 1000 ) が぀のスペヌスで区切られお行に䞎えられたす。 n ず s が共に 0 のずき入力の最埌ずしたす。 デヌタセットの数は 50 を超えたせん。 Output 各デヌタセットに察しお、 n 個の敎数の和が s になる組み合わせの数を行に出力しお䞋さい。 組み合わせの数が 10 10 を超える入力は䞎えられたせん。 Sample Input 3 6 3 1 0 0 Output for the Sample Input 3 0
38,002
Score : 500 points Problem Statement Let us denote by f(x, m) the remainder of the Euclidean division of x by m . Let A be the sequence that is defined by the initial value A_1=X and the recurrence relation A_{n+1} = f(A_n^2, M) . Find \displaystyle{\sum_{i=1}^N A_i} . Constraints 1 \leq N \leq 10^{10} 0 \leq X < M \leq 10^5 All values in input are integers. Input Input is given from Standard Input in the following format: N X M Output Print \displaystyle{\sum_{i=1}^N A_i} . Sample Input 1 6 2 1001 Sample Output 1 1369 The sequence A begins 2,4,16,256,471,620,\ldots Therefore, the answer is 2+4+16+256+471+620=1369 . Sample Input 2 1000 2 16 Sample Output 2 6 The sequence A begins 2,4,0,0,\ldots Therefore, the answer is 6 . Sample Input 3 10000000000 10 99959 Sample Output 3 492443256176507
38,003
Problem C: Factorization Problem ukuku1333さんはおっちょこちょいなので、 x の䞀次匏の積を展開したら、元の䞀次匏がわからなくなっおしたった。 x の n 次倚項匏が䞎えられるので、因数分解しお元のxの䞀次匏の積の圢にせよ。 x の n 次倚項匏は以䞋のBNFによっお䞎えられる。 <倚項匏> := <項> | <倚項匏>+<項> | <倚項匏>−<項> <項> := x^<指数> | <係数>x^<指数> | <係数>x | <定数> <指数> := [2-5] <係数> := [1-9][0-9]* <定数> := [1-9][0-9]* 指数及び係数が省略されおいる堎合は1ずみなす。 Input 入力は以䞋の圢匏で䞎えられる。 S x の n 次倚項匏を衚す文字列 S が䞀行に䞎えられる。 Constraints 入力は以䞋の条件を満たす。 2 ≀ n ≀ 5 䞎えられる匏の項の数を m ずするず、1 ≀ i < j ≀ m なる任意の i , j の組に察しお、 i 番目の項の次数は j 番目の項の次数より倧きいこずが保蚌される 䞎えられる x の n 次倚項匏は、 x の䞀次匏の積の圢に因数分解したもので衚すこずができるこずが保蚌される 係数、定数の絶察倀はそれぞれ2×10 3 以䞋である 次数が最倧のものの係数は1であり、省略されおいるこずが保蚌される 展開する前のそれぞれの䞀次匏の元の定数項は0ではない敎数であるこずが保蚌される 展開する前のそれぞれの䞀次匏の元の定数項は盞異なるこずが保蚌される Output S を x の䞀次匏の積の圢に因数分解したものを、定数項の小さいものから順に出力せよ。 出力の最埌には改行を入れるこず。 Sample Input 1 x^2+3x+2 Sample Output 1 (x+1)(x+2) Sample Input 2 x^2-1 Sample Output 2 (x-1)(x+1) Sample Input 3 x^5+15x^4+85x^3+225x^2+274x+120 Sample Output 3 (x+1)(x+2)(x+3)(x+4)(x+5) Sample Input 4 x^3-81x^2-1882x-1800 Sample Output 4 (x-100)(x+1)(x+18)
38,004
Toggling Cases Write a program which converts uppercase/lowercase letters to lowercase/uppercase for a given string. Input A string is given in a line. Output Print the converted string in a line. Note that you do not need to convert any characters other than alphabetical letters. Constraints The length of the input string < 1200 Sample Input fAIR, LATER, OCCASIONALLY CLOUDY. Sample Output Fair, later, occasionally cloudy.
38,005
ある孊校で修孊旅行ぞ行く蚈画がある.そのためにアンケヌト調査を行った. 生埒は 1 から n たでの生埒番号を持ち,旅行候補の堎所を 1 から m たでの番号で衚し,行きたい堎所に ○,行きたくない堎所に×の印を぀けお提出しおいる. このずき, 行きたい堎所の人数が倚い順に,堎所の番号を出力するプログラムを䜜成せよ.人数が同じずきは,堎所の番号順ずする. 入力デヌタ の 1 行目は生埒の人数 n ず旅行候補の堎所の数 m が空癜で区切られ, i + 1 行に生埒 i のアンケヌト結果を ○ は 1 で×は 0 で衚し,空癜で区切られた m 個の数字が䞊んでいる.1 ≀ n ≀ 1000, 1 ≀ m ≀ 100 ずする. 入力䟋 4 6 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 出力䟋 1 3 2 5 4 6 入力 入力は耇数のデヌタセットからなるn, m がずもに 0 のずき入力が終了するデヌタセットの数は 5 を超えない 出力 デヌタセットごずに、堎所の番号 を行に出力する 入力䟋 4 6 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 4 6 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 0 出力䟋 1 3 2 5 4 6 1 3 2 5 4 6 䞊蚘問題文ず自動審刀に䜿われるデヌタは、 情報オリンピック日本委員䌚 が䜜成し公開しおいる問題文ず採点甚テストデヌタです。
38,006
毒の沌地 あなたはレトロなロヌルプレむングゲヌムで遊んでいるこのゲヌムのフィヌルドは瞊 100 マス暪 100 マスのマス目状であるこのフィヌルドの巊から x 列目䞊から y 行目のマスは (x, y) ず衚されるあなたが操䜜するキャラクタヌはフィヌルド内のいずれかのマスの䞊におりフィヌルド内を䞊䞋巊右に 1 マスず぀移動するこずができる あなたが操䜜するキャラクタヌはいた (X 0 , Y 0 ) にいおこれから N 箇所の目的地を順番に蚪問する予定であるしかしながらあなたはキャラクタヌを操䜜するずきフィヌルドのマスの皮類に泚意しおキャラクタヌを移動させなければならないそれぞれのマスは毒のある沌地か毒のない土地のどちらかであるキャラクタヌの移動先のマスが毒のある沌地の堎合にはキャラクタヌはダメヌゞを受け移動先のマスが毒のない土地の堎合にはダメヌゞを受けないあなたはキャラクタヌぞのダメヌゞを枛らすため適切に経路を遞ぶこずでキャラクタヌがダメヌゞを受ける回数をできるだけ少なくしたいダメヌゞの有無はキャラクタヌの移動先のマスの皮類で決たるこず䟋ずしお移動元のマスが毒のある沌地で移動先のマスが毒のない土地の堎合にはキャラクタヌはダメヌゞを受けないこずに泚意せよ あなたの分析によれば巊䞊を (A, B) 右䞋を (C, D) ずする長方圢の範囲内のマスは毒のない土地でありそれ以倖のマスは毒のある沌地であるあなたのキャラクタヌが毒のある沌地からダメヌゞを受ける回数を最小化するように N 箇所の目的地を順番に蚪問したずきあなたの操䜜するキャラクタヌがダメヌゞを受ける回数を求めよ Input 入力は最倧で 50 個のデヌタセットからなる 各デヌタセットは次の圢匏で衚される N A B C D X 0 Y 0 X 1 Y 1 X 2 Y 2 ... X N Y N デヌタセットは N+3 行からなる 1 行目は目的地の数 N ( 1 ≀ N ≀ 100 ) を衚す敎数である 2 行目は毒のない土地ずなっおいる長方圢の範囲を衚す敎数 A  B  C  D であり 1 ≀ A ≀ C ≀ 100  1 ≀ B ≀ D ≀ 100 を満たすキャラクタヌの移動先のマス (x, y) が A ≀ x ≀ C ず B ≀ y ≀ D を満たすずきたたその堎合に限りキャラクタヌはダメヌゞを受けない 3 行目はあなたが操䜜するキャラクタヌが最初にいるマスの座暙 (X 0 , Y 0 ) を衚す敎数であり 1 ≀ X 0 , Y 0 ≀ 100 を満たす4 行目から続く N 行には N 箇所の目的地の座暙が䞎えられる 3+i 行目は i 番目の目的地のマスの座暙 (X i , Y i ) を衚す敎数であり 1 ≀ X i , Y i ≀ 100 を満たすキャラクタヌが最初にいるマスおよび目的地のマスの座暙はそれぞれ異なるすなわち (X j , Y j ) ≠ (X k , Y k ) (0 ≀ j < k ≀ N) を満たす 入力の終わりは1 個のれロだけからなる行で衚される Output 各デヌタセットに぀いおあなたの操䜜するキャラクタヌがダメヌゞを受ける回数を 1 行で出力せよ Sample Input 2 3 3 5 7 3 3 7 3 7 7 5 1 10 100 10 1 1 100 1 50 20 50 80 51 21 51 1 0 Output for the Sample Input 5 174 入力䟋を以䞋の図に瀺す (3, 3) から (5, 3) の間は毒のない土地であるが (6, 3) ず (7, 3) は毒のある沌地であるため1 番目の目的地に移動するたでにダメヌゞを 2 回受ける1 番目の目的地から 2 番目の目的地たで䞋方向に 4 回移動しお最短距離で移動した堎合はすべおのマスが毒のある沌地であるためダメヌゞを 4 回受ける遠回りしお毒のない土地を通った堎合は (6, 3)  (6, 7)  (7, 7) の毒のある沌地に入るためダメヌゞを 3 回受けるダメヌゞを受ける回数を最小化するような移動方法を遞んだずきダメヌゞを受ける回数は 5 回である
38,007
魔方陣 n × n の正方圢のマス目の䞭に数字のから n × n が䞀぀ず぀入っおいお、瞊のどの列のマス目の和も、暪のどの列のマス目の和も察角線のマス目の和も等しいものを魔方陣ずいいたす。 䞀蟺のマスの個数が奇数の魔方陣の䜜り方には以䞋の方法がありたす。 䞭倮のマス目のちょうど䞀぀䞋のマス目にを入れる。 次の数字を右斜め䞋のマス目に入れる。 ただし、数字を入れようずしたマス目が正方圢からはみ出しおいる堎合、すでに数字が埋たっおいる堎合は以䞋の方法に埓っお数字を入れるマス目を探す。 右にはみ出した堎合には、同じ行の巊はしに、巊にはみ出した堎合には、同じ行の右はしに、䞋にはみ出した堎合には、同じ列の䞀番䞊に数字を入れる。 数字を入れようずしたマス目が埋たっおいるずきには、その埋たっおいるマス目の巊斜め䞋のマス目に入れる。 党おのマス目が埋たるたでを繰り返す。 この方法に埓っお、䞀蟺のマス目の個数 n を入力ずしお、その倧きさの魔方陣を出力するプログラムを䜜成しお䞋さい。ただし、 n は 3 以䞊 15 以䞋の奇数ずしたす。マス目に入る各数字は右詰 4 桁で出力しおください。 入力 耇数の入力が䞎えられたす。各入力で n 正の敎数が行に䞎えられたす。入力は 0 で終了したす。入力の数は 10 を超えたせん。 出力 各入力に察しお n × n の魔方陣を出力しお䞋さい。 Sample Input 3 5 0 Output for the Sample Input 4 9 2 3 5 7 8 1 6 11 24 7 20 3 4 12 25 8 16 17 5 13 21 9 10 18 1 14 22 23 6 19 2 15
38,008
展芧䌚(Exhibition) あなたは絵の展芧䌚を開催しようずしおいる展芧䌚ではいく぀かの絵を額瞁に入れ巊から右に䞀列に䞊べお展瀺する 展芧䌚で展瀺する候補ずなる絵が$N$ 枚あり1 から$N$ たでの番号が付けられおいる絵$i$ ($1 \leq i \leq N$) の倧きさは$S_i$䟡倀は$V_i$ である たたこれらの絵を入れるための額瞁が$M$ 枚あり1 から$M$ たでの番号が付けられおいる額瞁$j$ ($1 \leq j \leq M$) の倧きさは$C_j$ である額瞁$j$ には倧きさが$C_j$ 以䞋の絵のみを入れるこずができる1 枚の額瞁には高々1 枚の絵しか入れるこずができない 展瀺する絵はすべお䜕らかの額瞁に入っおいなければならない芋栄えを良くするため展瀺する絵は以䞋の条件を満たさなければならない 巊右に隣り合うどの2 枚の絵に぀いおも右偎の絵が入っおいる額瞁の倧きさは巊偎の絵が入っおいる額瞁の倧きさ以䞊である 巊右に隣り合うどの2 枚の絵に぀いおも右偎の絵の䟡倀は巊偎の絵の䟡倀以䞊である あなたはできるだけ倚くの絵を展瀺したい 展瀺候補の絵の枚数額瞁の枚数及びそれらの倧きさや䟡倀が䞎えられたずき展瀺する絵の枚数の最倧倀を求めるプログラムを䜜成せよ 入力 入力は以䞋の圢匏で暙準入力から䞎えられる $N$ $M$ $S_1$ $V_1$ : $S_N$ $V_N$ $C_1$ : $C_M$ 出力 暙準出力に展芧䌚に展瀺する絵の枚数の最倧倀を1 行で出力せよ 制玄 $ 1 \leq N \leq 100 000$. $ 1 \leq M \leq 100 000$. $ 1 \leq S i \leq 1 000 000 000 (1 \leq i \leq N)$. $ 1 \leq V_i \leq 1 000 000 000 (1 \leq i \leq N)$. $ 1 \leq C_j \leq 1 000 000 000 (1 \leq j \leq M)$. 入出力䟋 入力䟋1 3 4 10 20 5 1 3 5 4 6 10 4 出力䟋1 2 この入出力䟋では巊から順に(çµµ2, 額瞁2)(çµµ1, 額瞁3) ず䞊べるこずで2 枚の絵を展瀺するこずができる3 枚以䞊の絵を展瀺するこずはできないので2 を出力するここで(çµµ$i$, 額瞁$j$) は額瞁$j$に入った絵$i$ を衚す 入力䟋2 3 2 1 2 1 2 1 2 1 1 出力䟋2 2 入力䟋3 4 2 28 1 8 8 6 10 16 9 4 3 出力䟋3 0 入力䟋4 8 8 508917604 35617051 501958939 840246141 485338402 32896484 957730250 357542366 904165504 137209882 684085683 775621730 552953629 20004459 125090903 607302990 433255278 979756183 28423637 856448848 276518245 314201319 666094038 149542543 出力䟋4 3 情報オリンピック日本委員䌚䜜 『第18 回日本情報オリンピック(JOI 2018/2019) 本遞』
38,009
Problem F: Connect Line Segments Your dear son Arnie is addicted to a puzzle named Connect Line Segments . In this puzzle, you are given several line segments placed on a two-dimensional area. You are allowed to add some new line segments each connecting the end points of two existing line segments. The objective is to form a single polyline, by connecting all given line segments, as short as possible. The resulting polyline is allowed to intersect itself. Arnie has solved many instances by his own way, but he is wondering if his solutions are the best one. He knows you are a good programmer, so he asked you to write a computer program with which he can verify his solutions. Please respond to your dear Arnie’s request. Input The input consists of multiple test cases. Each test case begins with a line containing a single integer n (2 ≀ n ≀ 14), which is the number of the initial line segments. The following n lines are the description of the line segments. The i -th line consists of four real numbers: x i ,1 , y i ,1 , x i ,2 , and y i ,2 (-100 ≀ x i ,1 , y i ,1 , x i ,2 , y i ,2 ≀ 100). ( x i ,1 , y i ,1 ) and ( x i ,2 , y i ,2 ) are the coordinates of the end points of the i -th line segment. The end of the input is indicated by a line with single “0”. Output For each test case, output the case number followed by the minimum length in a line. The output value should be printed with five digits after the decimal point, and should not contain an error greater than 0.00001. Sample Input 4 0 1 0 9 10 1 10 9 1 0 9 0 1 10 9 10 2 1.2 3.4 5.6 7.8 5.6 3.4 1.2 7.8 0 Output for the Sample Input Case 1: 36.24264 Case 2: 16.84508
38,010
Score : 1200 points Problem Statement Takahashi's office has N rooms. Each room has an ID from 1 to N . There are also N-1 corridors, and the i -th corridor connects Room a_i and Room b_i . It is known that we can travel between any two rooms using only these corridors. Takahashi has got lost in one of the rooms. Let this room be r . He decides to get back to his room, Room 1 , by repeatedly traveling in the following manner: Travel to the room with the smallest ID among the rooms that are adjacent to the rooms already visited, but not visited yet. Let c_r be the number of travels required to get back to Room 1 . Find all of c_2,c_3,...,c_N . Note that, no matter how many corridors he passes through in a travel, it still counts as one travel. Constraints 2 \leq N \leq 2\times 10^5 1 \leq a_i,b_i \leq N a_i \neq b_i The graph given as input is a tree. Input Input is given from Standard Input in the following format: N a_1 b_1 : a_{N-1} b_{N-1} Output Print c_r for each r , in the following format: c_2 c_3 ... c_N Sample Input 1 6 1 5 5 6 6 2 6 3 6 4 Sample Output 1 5 5 5 1 5 For example, if Takahashi was lost in Room 2 , he will travel as follows: Travel to Room 6 . Travel to Room 3 . Travel to Room 4 . Travel to Room 5 . Travel to Room 1 . Sample Input 2 6 1 2 2 3 3 4 4 5 5 6 Sample Output 2 1 2 3 4 5 Sample Input 3 10 1 5 5 6 6 10 6 4 10 3 10 8 8 2 4 7 4 9 Sample Output 3 7 5 3 1 3 4 7 4 5
38,011
Score : 200 points Problem Statement There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000 . Among them, some K consecutive stones are painted black, and the others are painted white. Additionally, we know that the stone at coordinate X is painted black. Print all coordinates that potentially contain a stone painted black, in ascending order. Constraints 1 \leq K \leq 100 0 \leq X \leq 100 All values in input are integers. Input Input is given from Standard Input in the following format: K X Output Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between. Sample Input 1 3 7 Sample Output 1 5 6 7 8 9 We know that there are three stones painted black, and the stone at coordinate 7 is painted black. There are three possible cases: The three stones painted black are placed at coordinates 5 , 6 , and 7 . The three stones painted black are placed at coordinates 6 , 7 , and 8 . The three stones painted black are placed at coordinates 7 , 8 , and 9 . Thus, five coordinates potentially contain a stone painted black: 5 , 6 , 7 , 8 , and 9 . Sample Input 2 4 0 Sample Output 2 -3 -2 -1 0 1 2 3 Negative coordinates can also contain a stone painted black. Sample Input 3 1 100 Sample Output 3 100
38,012
C - Iyasugigappa Problem Statement Three animals Frog, Kappa (Water Imp) and Weasel are playing a card game. In this game, players make use of three kinds of items: a guillotine, twelve noble cards and six action cards. Some integer value is written on the face of each noble card and each action card. Before stating the game, players put twelve noble cards in a line on the table and put the guillotine on the right of the noble cards. And then each player are dealt two action cards. Here, all the noble cards and action cards are opened, so the players share all the information in this game. Next, the game begins. Each player takes turns in turn. Frog takes the first turn, Kappa takes the second turn, Weasel takes the third turn, and Frog takes the fourth turn, etc. Each turn consists of two phases: action phase and execution phase in this order. In action phase, if a player has action cards, he may use one of them. When he uses an action card with value on the face y , y -th (1-based) noble card from the front of the guillotine on the table is moved to in front of the guillotine, if there are at least y noble cards on the table. If there are less than y cards, nothing happens. After the player uses the action card, he must discard it from his hand. In execution phase, a player just remove a noble card in front of the guillotine. And then the player scores x points, where x is the value of the removed noble card. The game ends when all the noble cards are removed. Each player follows the following strategy: Each player assume that other players would follow a strategy such that their final score is maximized. Actually, Frog and Weasel follows such strategy. However, Kappa does not. Kappa plays so that Frog's final score is minimized. Kappa knows that Frog and Weasel would play under ``wrong'' assumption: They think that Kappa would maximize his score. As a tie-breaker of multiple optimum choises for each strategy, assume that players prefer to keep as many action cards as possible at the end of the turn. If there are still multiple optimum choises, players prefer to maximuze the total value of remaining action cards. Your task in this problem is to calculate the final score of each player. Input The input is formatted as follows. x_{12} x_{11} x_{10} x_9 x_8 x_7 x_6 x_5 x_4 x_3 x_2 x_1 y_1 y_2 y_3 y_4 y_5 y_6 The first line of the input contains twelve integers x_{12} , x_{11} , 
, x_{1} ( -2 \leq x_i \leq 5 ). x_i is integer written on i -th noble card from the guillotine. Following three lines contains six integers y_1 , 
, y_6 ( 1 \leq y_j \leq 4 ). y_1 , y_2 are values on Frog's action cards, y_3 , y_4 are those on Kappa's action cards, and y_5 , y_6 are those on Weasel's action cards. Output Print three space-separated integers: the final scores of Frog, Kappa and Weasel. Sample Input 1 3 2 1 3 2 1 3 2 1 3 2 1 1 1 1 1 1 1 Output for the Sample Input 1 4 8 12 Sample Input 2 4 4 4 3 3 3 2 2 2 1 1 1 1 2 2 3 3 4 Output for the Sample Input 2 8 10 12 Sample Input 3 0 0 0 0 0 0 0 -2 0 -2 5 0 1 1 4 1 1 1 Output for the Sample Input 3 -2 -2 5
38,013
Score : 1100 points Problem Statement There is a tree with N vertices, numbered 1 through N . The i -th edge in this tree connects Vertices A_i and B_i and has a length of C_i . Joisino created a complete graph with N vertices. The length of the edge connecting Vertices u and v in this graph, is equal to the shortest distance between Vertices u and v in the tree above. Joisino would like to know the length of the longest Hamiltonian path (see Notes) in this complete graph. Find the length of that path. Notes A Hamiltonian path in a graph is a path in the graph that visits each vertex exactly once. Constraints 2 \leq N \leq 10^5 1 \leq A_i < B_i \leq N The given graph is a tree. 1 \leq C_i \leq 10^8 All input values are integers. Input Input is given from Standard Input in the following format: N A_1 B_1 C_1 A_2 B_2 C_2 : A_{N-1} B_{N-1} C_{N-1} Output Print the length of the longest Hamiltonian path in the complete graph created by Joisino. Sample Input 1 5 1 2 5 3 4 7 2 3 3 2 5 2 Sample Output 1 38 The length of the Hamiltonian path 5 → 3 → 1 → 4 → 2 is 5+8+15+10=38 . Since there is no Hamiltonian path with length 39 or greater in the graph, the answer is 38 . Sample Input 2 8 2 8 8 1 5 1 4 8 2 2 5 4 3 8 6 6 8 9 2 7 12 Sample Output 2 132
38,014
問題 F ボ〜ル 問題文 2 次元平面䞊の原点にボヌルがあり x 軞の正方向ずの角床が反時蚈回りに芋お 0 床 180 床たでの間の方向に䞀様な確率で発射されようずしおいる (発射される方向は敎数角であるずは限らない)ボヌルの倧きさは十分小さく平面䞊では点であるず芋なすこずにするこの問題における目的はこのボヌルをできるだけ高い確率で捕獲するこずである 平面䞊に N 個の堎所 (x i , y i ) が䞎えられるボヌルを捕獲するためにあなたは N 個の堎所から K 個の堎所を遞んでそれぞれの堎所に人を配眮するこずができる人は i 番目の䞎えられた堎所に察しお半埄 r i 以内の距離たで動いおボヌルを取るこずが出来る 人の配眮をうたく遞んでボヌルを捕獲できる確率を最倧にするずきその確率を出力せよ 入力圢匏 入力は以䞋の圢匏で䞎えられる N K x 1 y 1 r 1 ... x N y N r N N はボヌルを捕獲するために人を眮くための堎所の数であり K はその䞭から䜿うこずの出来る堎所の数である (x i , y i ) は i 番目の堎所の座暙であり r i はそこから動くこずの出来る距離である 出力圢匏 確率を小数衚蚘で 1 行に出力せよ小数点以䞋䜕桁でも出力しお構わないが盞察誀差あるいは絶察誀差が 10 -6 未満になっおいなければならない 制玄 1≀ N≀ 1,500, 1≀ K≀ N |x i | ≀ 1,000, |y i | ≀ 1,000, 1 ≀ r i < (x i 2 + y i 2 ) 1/2 入力倀はすべお敎数である 入出力䟋 入力䟋 1 2 1 10 10 10 -10 10 10 出力䟋 1 0.50 2 ぀堎所がありそのうちのどちらかに人を配眮できるこの堎合どちらに配眮しおも確率は 1/2 になる 入力䟋 2 2 2 10 10 10 -10 10 10 出力䟋 2 1.0 入力䟋 3 5 3 -10 -10 5 10 10 2 -10 10 3 -10 0 4 10 0 2 出力䟋 3 0.3574057314330 入力䟋 4 4 2 1 1 1 2 2 2 3 3 3 4 4 4 出力䟋 4 0.50
38,015
倕暮れ AIZU 囜の倕暮れ時は、スマヌトフォンを西の空ぞ構えお立ち止たる芳光客で賑わう。AIZU 囜は無数のビルが建ち䞊ぶ倧郜垂であり、ビルの谷間が長く連なる西の空には、ビルのシル゚ットずそれらから挏れ出す倪陜の光による絶景が広がる。 AIZU 芳光協䌚の若束氏によるず、倪陜を衚す円が、その面積のちょうど半分だけ遮られおいるずき、栌段の絶景になるずいう。 図のように、西の空を、地平線を x 軞、倪陜の䞭心の軌跡を y 軞ずするような x - y 平面で衚し、倪陜を半埄 R の円、それぞれのビルのシル゚ットを長方圢ずする。 各ビルのシル゚ットの底蟺は x 軞䞊にあり、倪陜は十分高い䜍眮から地平線に察しお垂盎に沈んでいく。倪陜はビルのシル゚ットあるいは地平線を䞊端ずする地面に遮られ、やがお地平線の䞋ぞ消えおゆく。 倪陜の半埄ず各ビルのシル゚ットの情報が䞎えられたずき、倪陜の面積のちょうど半分が遮られるような、最も高い倪陜の高さ䞭心の y 座暙を求めるプログラムを䜜成せよ。 Input 入力は以䞋の圢匏で䞎えられる。 N R x 1 w 1 h 1 x 2 w 2 h 2 : x N w N h N 行目にビルの数 N (0 ≀ N ≀ 100) ず倪陜を衚す円の半埄 R (1 ≀ R ≀ 100) が䞎えられる。続く N 行に i 番目のビルのシル゚ットの巊䞋角の x 座暙 x i (-100 ≀ x i ≀ 100, x i < x i+1 )、幅 w i (1 ≀ w i ≀ 100)、高さ h i (1 ≀ h i ≀ 100) が䞎えられる。入力はすべお敎数で䞎えられる。 入力は以䞋の条件を満たす。 ビルのシル゚ットが重なるこずはない x i + w i ≀ x i+1 。 ぀の隣接するビルのシル゚ットの高さの差は、 R を超えない。 ビルの巊偎 x 軞の負の方向たたは右偎 x 軞の正の方向に隣接するビルがない堎合、その高さは R を超えない。 Output 倪陜の高さ円の䞭心の y 座暙を行に出力する。ただし、誀差がプラスマむナス 10 -6 を超えおはならない。 Sample Input 1 0 2 Sample Output 1 0.00000000 Sample Input 2 3 2 -2 1 1 -1 1 2 0 2 1 Sample Output 2 1.25065774
38,016
Score : 400 points Problem Statement Given are integers A , B , and N . Find the maximum possible value of floor(Ax/B) - A × floor(x/B) for a non-negative integer x not greater than N . Here floor(t) denotes the greatest integer not greater than the real number t . Constraints 1 ≀ A ≀ 10^{6} 1 ≀ B ≀ 10^{12} 1 ≀ N ≀ 10^{12} All values in input are integers. Input Input is given from Standard Input in the following format: A B N Output Print the maximum possible value of floor(Ax/B) - A × floor(x/B) for a non-negative integer x not greater than N , as an integer. Sample Input 1 5 7 4 Sample Output 1 2 When x=3 , floor(Ax/B)-A×floor(x/B) = floor(15/7) - 5×floor(3/7) = 2 . This is the maximum value possible. Sample Input 2 11 10 9 Sample Output 2 9
38,017
Score : 300 points Problem Statement Mikan's birthday is coming soon. Since Mikan likes graphs very much, Aroma decided to give her a undirected graph this year too. Aroma bought a connected undirected graph, which consists of n vertices and n edges. The vertices are numbered from 1 to n and for each i (1 \leq i \leq n) , vertex i and vartex a_i are connected with an undirected edge. Aroma thinks it is not interesting only to give the ready-made graph and decided to paint it. Count the number of ways to paint the vertices of the purchased graph in k colors modulo 10^9 + 7 . Two ways are considered to be the same if the graph painted in one way can be identical to the graph painted in the other way by permutating the numbers of the vertices. Constraints 1 \leq n \leq 10^5 1 \leq k \leq 10^5 1 \leq a_i \leq n (1 \leq i \leq n) The given graph is connected The given graph contains no self-loops or multiple edges. Input Each data set is given in the following format from the standard input. n k a_1 : a_n Output Output the number of ways to paint the vertices of the given graph in k colors modulo 10^9 + 7 in one line. Sample Input 1 4 2 2 3 1 1 Sample Output 1 12 Sample Input 2 4 4 2 3 4 1 Sample Output 2 55 Sample Input 3 10 5 2 3 4 1 1 1 2 3 3 4 Sample Output 3 926250
38,018
Pile Up! There are cubes of the same size and a simple robot named Masato. Initially, all cubes are on the floor. Masato can be instructed to pick up a cube and put it on another cube, to make piles of cubes. Each instruction is of the form `pick up cube A and put it on cube B (or on the floor).' When he is to pick up a cube, he does so after taking off all the cubes on and above it in the same pile (if any) onto the floor. In contrast, when he is to put a cube on another, he puts the former on top of the pile including the latter without taking any cubes off. When he is instructed to put a cube on another cube and both cubes are already in the same pile, there are two cases. If the former cube is stacked somewhere below the latter, he put off all the cube above it onto the floor. Afterwards he puts the former cube on the latter cube. If the former cube is stacked somewhere above the latter, he just ignores the instruction. When he is instructed to put a cube on the floor, there are also two cases. If the cube is already on the floor (including the case that the cube is stacked in the bottom of some pile), he just ignores the instruction. Otherwise, he puts off all the cube on and up above the pile (if any) onto the floor before moving the cube onto the floor. He also ignores the instruction when told to put a cube on top of itself (this is impossible). Given the number of the cubes and a series of instructions, simulate actions of Masato and calculate the heights of piles when Masato has finished his job. Input The input consists of a series of data sets. One data set contains the number of cubes as its first line, and a series of instructions, each described in a separate line. The number of cubes does not exceed 100. Each instruction consists of two numbers; the former number indicates which cube to pick up, and the latter number indicates on which cube to put it. The end of the instructions is marked by two zeros. The end of the input is marked by the line containing a single zero. One data set has the following form: m I 1 J 1 I 2 J 2 ... I n J n 0 0 Each cube is identified by its number (1 through m ). I k indicates which cube to pick up and J k indicates on which cube to put it. The latter may be zero, instructing to put the cube on the floor. Output Output the height of each pile (the number of cubes in the pile) in ascending order, separated by newlines. A single cube by itself also counts as "a pile." End of output for one data set should be marked by a line containing the character sequence `end' by itself. Sample Input 3 1 3 2 0 0 0 4 4 1 3 1 1 2 0 0 5 2 1 3 1 4 1 3 2 1 1 0 0 0 Output for the Sample Input 1 2 end 1 1 2 end 1 4 end
38,019
坑道数匏 ある日廃坑を探怜しおいたあなたは、坑道に長い数匏 S が曞かれおいるのを発芋した。倧きな数が奜きなあなたは、チョヌクを取り出し、数匏を蚈算した結果ができるだけ倧きくなるように ( たたは ) を曞き加えるこずにした。曞き加えた埌も数匏になっおいなければならないずするず、最倧でいく぀にできるか。 文字ず文字の間は十分広く空いおいお、 ( たたは ) であればいく぀でも曞き加えるこずができる。最終的に数匏になっおいれば、最初のかっこの察応が厩れるように ( たたは ) を曞いおもよいSample 2参照。 たた、ここでは以䞋のBNFで定矩される<expr>を数匏ず呌ぶ。数匏䞭の数は党お䞀桁である。 <expr> ::= "(" <expr> ")" | <term> "+" <term> | <term> "-" <term> <term> ::= <digit> | <expr> <digit> ::= "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" Constraints 3 ≀ |S| ≀ 200 S は数匏を衚す。 Input Format 入力は以䞋の圢匏で暙準入力から䞎えられる。 S Output Format 答えを敎数で出力せよ。 Sample Input 1 1-(2+3-4+5) Sample Output 1 5 1-(2+3-(4+5))が最倧ずなる。 Sample Input 2 1-(2+3+4) Sample Output 2 0 (1-(2+3)+4)が最倧ずなる。 Sample Input 3 1-(2+3) Sample Output 3 -4 1-(2)+(3)はここでいう数匏ではないこずに泚意。
38,020
宝探し 倪郎君はある広堎にお宝を探しにやっおきたした。この広堎にはたくさんのお宝が埋められおいたすが、倪郎君は最新の機械を持っおいるので、どこにお宝が埋たっおいるかをすべお知っおいたす。広堎はずおも広いので倪郎君は領域を決めおお宝を探すこずにしたしたが、お宝はたくさんあるためどのお宝がその領域の䞭にあるかすぐにわかりたせん。そこで倪郎君はその領域の䞭にあるお宝の数を数えるこずにしたした。 Input n m x 1 y 1 x 2 y 2 ... x n y n x 11 y 11 x 12 y 12 x 21 y 21 x 22 y 22 ... x m1 y m1 x m2 y m2 n は広堎に埋たっおいるお宝の数を衚す m は調べる領域の数を衚す 2行目から n+1 行目はそれぞれのお宝が埋たっおいる座暙を衚す n+2 行目から n+m+1 行目はそれぞれの調べる領域を衚す x軞の正の方向が東、y軞の正の方向が北を衚す それぞれの領域は長方圢であり、 x i1 ず y i1 は長方圢の南西の頂点の座暙、 x i2 ず y i2 は長方圢の北東の頂点の座暙を衚す Constraints 1 ≀ n ≀ 5000 1 ≀ m ≀ 5×10 5 |x i |, |y i | ≀ 10 9 (1 ≀ i ≀ n) |x i1 |, |y i1 |, |x i2 |, |y i2 | ≀ 10 9 (1 ≀ i ≀ m) x i1 ≀ x i2 , y i1 ≀ y i2 (1 ≀ i ≀ m) すべおの入力は敎数で䞎えられる Output C 1 C 2 ... C m それぞれの領域に含たれるお宝の数を各行に出力せよ Sample Input 1 3 1 1 1 2 4 5 3 0 0 5 5 Output for the Sample Input 1 3 領域の境界線䞊にあるお宝も領域に含たれるものずみなす Sample Input 2 4 2 -1 1 0 3 4 0 2 1 -3 1 5 1 4 0 4 0 Output for the Sample Input 2 2 1 領域は盎線や点のようになる堎合もある Sample Input 3 2 3 0 0 0 0 -1 -1 1 1 0 0 2 2 1 1 4 4 Output for the Sample Input 3 2 2 0 同じ堎所に耇数のお宝が存圚する堎合もある Sample Input 4 5 5 10 5 -3 -8 2 11 6 0 -1 3 -3 1 3 13 -1 -1 9 5 -3 -8 10 11 0 0 5 5 -10 -9 15 10 Output for the Sample Input 4 2 2 5 0 4
38,021
Score : 300 points Problem Statement You are given a string S of length N consisting of A , C , G and T . Answer the following Q queries: Query i ( 1 \leq i \leq Q ): You will be given integers l_i and r_i ( 1 \leq l_i < r_i \leq N ). Consider the substring of S starting at index l_i and ending at index r_i (both inclusive). In this string, how many times does AC occurs as a substring? Notes A substring of a string T is a string obtained by removing zero or more characters from the beginning and the end of T . For example, the substrings of ATCODER include TCO , AT , CODER , ATCODER and (the empty string), but not AC . Constraints 2 \leq N \leq 10^5 1 \leq Q \leq 10^5 S is a string of length N . Each character in S is A , C , G or T . 1 \leq l_i < r_i \leq N Input Input is given from Standard Input in the following format: N Q S l_1 r_1 : l_Q r_Q Output Print Q lines. The i -th line should contain the answer to the i -th query. Sample Input 1 8 3 ACACTACG 3 7 2 3 1 8 Sample Output 1 2 0 3 Query 1 : the substring of S starting at index 3 and ending at index 7 is ACTAC . In this string, AC occurs twice as a substring. Query 2 : the substring of S starting at index 2 and ending at index 3 is CA . In this string, AC occurs zero times as a substring. Query 3 : the substring of S starting at index 1 and ending at index 8 is ACACTACG . In this string, AC occurs three times as a substring.
38,022
Origami, or the art of folding paper Master Grus is a famous origami (paper folding) artist, who is enthusiastic about exploring the possibility of origami art. For future creation, he is now planning fundamental experiments to establish the general theory of origami. One rectangular piece of paper is used in each of his experiments. He folds it horizontally and/or vertically several times and then punches through holes in the folded paper. The following figure illustrates the folding process of a simple experiment, which corresponds to the third dataset of the Sample Input below. Folding the 10 × 8 rectangular piece of paper shown at top left three times results in the 6 × 6 square shape shown at bottom left. In the figure, dashed lines indicate the locations to fold the paper and round arrows indicate the directions of folding. Grid lines are shown as solid lines to tell the sizes of rectangular shapes and the exact locations of folding. Color densities represent the numbers of overlapping layers. Punching through holes at A and B in the folded paper makes nine holes in the paper, eight at A and another at B. Your mission in this problem is to write a computer program to count the number of holes in the paper, given the information on a rectangular piece of paper and folding and punching instructions. Input The input consists of at most 1000 datasets, each in the following format. n m t p d 1 c 1 ... d t c t x 1 y 1 ... x p y p n and m are the width and the height, respectively, of a rectangular piece of paper. They are positive integers at most 32. t and p are the numbers of folding and punching instructions, respectively. They are positive integers at most 20. The pair of d i and c i gives the i -th folding instruction as follows: d i is either 1 or 2. c i is a positive integer. If d i is 1, the left-hand side of the vertical folding line that passes at c i right to the left boundary is folded onto the right-hand side. If d i is 2, the lower side of the horizontal folding line that passes at c i above the lower boundary is folded onto the upper side. After performing the first i −1 folding instructions, if d i is 1, the width of the shape is greater than c i . Otherwise the height is greater than c i . ( x i + 1/2, y i + 1/2) gives the coordinates of the point where the i -th punching instruction is performed. The origin (0, 0) is at the bottom left of the finally obtained shape. x i and y i are both non-negative integers and they are less than the width and the height, respectively, of the shape. You can assume that no two punching instructions punch holes at the same location. The end of the input is indicated by a line containing four zeros. Output For each dataset, output p lines, the i -th of which contains the number of holes punched in the paper by the i -th punching instruction. Sample Input 2 1 1 1 1 1 0 0 1 3 2 1 2 1 2 1 0 0 10 8 3 2 2 2 1 3 1 1 0 1 3 4 3 3 3 2 1 2 2 1 1 1 0 1 0 0 0 0 0 0 Output for the Sample Input 2 3 8 1 3 6
38,023
Score : 300 points Problem Statement You are given two integer sequences of length N : a_1,a_2,..,a_N and b_1,b_2,..,b_N . Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal. Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously : Add 2 to a_i . Add 1 to b_j . Constraints 1 ≀ N ≀ 10 000 0 ≀ a_i,b_i ≀ 10^9 ( 1 ≀ i ≀ N ) All input values are integers. Input Input is given from Standard Input in the following format: N a_1 a_2 .. a_N b_1 b_2 .. b_N Output If we can repeat the operation zero or more times so that the sequences a and b become equal, print Yes ; otherwise, print No . Sample Input 1 3 1 2 3 5 2 2 Sample Output 1 Yes For example, we can perform three operations as follows to do our job: First operation: i=1 and j=2 . Now we have a = \{3,2,3\} , b = \{5,3,2\} . Second operation: i=1 and j=2 . Now we have a = \{5,2,3\} , b = \{5,4,2\} . Third operation: i=2 and j=3 . Now we have a = \{5,4,3\} , b = \{5,4,3\} . Sample Input 2 5 3 1 4 1 5 2 7 1 8 2 Sample Output 2 No Sample Input 3 5 2 7 1 8 2 3 1 4 1 5 Sample Output 3 No
38,024
Problem H: Oh, My Goat! 倪郎君は、次郎君に叀文のノヌトを借りた。 明日の叀文の宿題を写させおもらうためだ。 倪郎君は、甚心深い性栌をしおいるため、䞇が䞀のこずを考えお、近所のコンビニで次郎君のノヌトのコピヌを取っお自宅ぞ垰った。 倪郎君は、自宅で宿題を始めようずしたずきに、慌おた。 次郎君から借りたノヌトが鞄に入っおいなかったからだ。 どうやら、コンビニに忘れおきおしたったようだ。 倪郎君は、急いでコンビニに匕き返した。 コピヌ機ずその呚蟺を懞呜に捜玢したが、ノヌトを芋぀けるこずはできなかった。 困り果おた倪郎君は、コンビニの店長に助けを求めた。 䜙談だが、店長は地球環境に優しい人で、癜ダギさんを飌っおいる。 店長は、地球環境に気を配る心遣いを持っおいるため、垞日頃から、ペットの癜ダギさんに、逌ずしおコピヌ機呚蟺の客の忘れものを䞎えおいる。 店長によるず、ノヌトは、今晩の癜ダギさんの晩埡飯であり、癜ダギさんは珟圚食事䞭だそうである。 倪郎君は癜ダギさんに頌みこみ、食べかけのノヌトを取り返すこずはできたが、ノヌトはビリビリに砎れがろがろである。 倪郎君は、急いで自宅に匕き返した。 自宀の机ずその呚蟺を懞呜に捜玢したが、ノヌトのコピヌを芋぀けるこずはできなかった。 困り果おた倪郎君は、お母さんに助けを求めた。 䜙談だが、倪郎君のお母さんは地球環境に優しい人で、黒ダギさんを飌っおいる。 倪郎君のお母さんは、地球環境に気を配る心遣いを持っおいるため、垞日頃から、ペットの黒ダギさんに、逌ずしお倪郎君の宿題を䞎えおいる。 お母さんによるず、ノヌトのコピヌは、今晩の黒ダギさんの晩埡飯であり、黒ダギさんは珟圚食事䞭だそうである。 倪郎君は黒ダギさんに頌みこみ、食べかけのノヌトを取り返すこずはできたが、ノヌトのコピヌはビリビリに砎れがろがろである。 次郎君のノヌトずそのコピヌをビリビリのがろがろにされおしたった倪郎君は、ノヌトを可胜な限り埩元しようず考えた。 そこで、繋がりそうなノヌトの切れ端同士を繋ぎ合わせお、「繋ぎ合せたノヌト」を䜜成した。 同様に、繋がりそうなノヌトのコピヌの切れ端同士を繋き合わせお、「繋ぎ合せたノヌトのコピヌ」を䜜成した。 倪郎君は、あらゆる可胜性を考えるために、繋がりそうな切れ端同士を぀なぎ合わせた。 このため、1぀の切れ目に2぀以䞊の切れ端が繋がれおしたった箇所もあった。 繋ぎ合わせ方の䟋を図1に瀺す。 図1は、7぀の切れ端ず6぀の切れ目からなる。 図1 切れ端"haru"ず"natsu"に続く切れ目には、切れ端"wa"が繋がり、文章が合流しおいる。 切れ端"wa"に続く切れ目には、切れ端"ake"ず"saron"が繋がり、文章が分岐しおいる。 このような合流や切れ端があるため、図1は次のような4぀の文章を衚す。 haruwaakebono haruwasaronpusu natsuwaakebono natsuwasaronpusu ノヌトやノヌトのコピヌは、癜ダギさんや黒ダギさんが、食べおしたったため、埩元できない郚分があったり、圌らのご飯に混ざっおいた関係のない曞類の切れ端が混圚しおいるこずもある。 倪郎君の代わりに、「繋ぎ合わせたノヌト」ず「繋ぎ合わせたノヌトのコピヌ」の2぀を入力ずしお受け取っお、䞡方に共通しお珟れる文章の数を求めるプログラムを䜜成せよ。 Input 入力の1行目では、デヌタセットの数 T ( 1 ≀ T ≀ 100 )が䞎えられる。 デヌタセットは、「繋ぎ合せたノヌト」の情報ず、「繋ぎ合せたノヌトのコピヌ」の情報から成る。 「繋ぎ合せたノヌト」の情報ずしお、 1行目に n ( 2 ≀ n ≀ 500 )ず m ( 1 ≀ m ≀ 600 )が䞎えられる。 n は、切れ端ず切れ端を繋ぎ合せる切れ目の数である。 続く m 行で繋ぎ合せ方が䞎えられる。 各行は、切れ端の䞊端に繋がる切れ目の番号 a 、切れ端の䞋端に぀ながる切れ目の番号 b 、切れ端を衚す文字列 s からなる。 ただし、 0 ≀ a < b < n が満たされる。 s は長さが1以䞊5以䞋の文字列で、アルファベットの小文字のみから成る。 「繋ぎ合せたノヌトのコピヌ」も「繋ぎ合せたノヌト」ず同じ圢匏で䞎えられる。 なお、0番目の切れ目から繋ぎ合せ情報を蟿り、 n-1 番目の切れ目に到達する過皋で埗られる文字列を連結したもののみを文章ず呌ぶものずする。 たた、それぞれの繋ぎ合せの䞭で同じ文章が2぀以䞊出珟するこずはない。 Output それぞれのデヌタセット毎に、答えの敎数を1,000,000,007で割った䜙りを1行で出力せよ。 Sample Input 4 2 1 0 1 a 2 2 0 1 a 0 1 b 5 5 0 1 a 0 2 b 1 3 a 2 3 c 3 4 e 3 3 0 1 aa 0 2 bce 1 2 a 2 4 0 1 abc 0 1 def 0 1 ghi 0 1 jkl 2 4 0 1 ghi 0 1 jkl 0 1 mno 0 1 pqr 6 7 0 1 haru 0 1 natsu 1 2 wa 2 3 ake 2 4 saron 3 5 bono 4 5 pusu 5 4 0 1 haruw 1 2 aakeb 2 3 o 3 4 no Output for Sample Input 1 1 2 1
38,025
Score : 200 points Problem Statement We have a grid with N rows and M columns of squares. Initially, all the squares are white. There is a button attached to each row and each column. When a button attached to a row is pressed, the colors of all the squares in that row are inverted; that is, white squares become black and vice versa. When a button attached to a column is pressed, the colors of all the squares in that column are inverted. Takahashi can freely press the buttons any number of times. Determine whether he can have exactly K black squares in the grid. Constraints 1 \leq N,M \leq 1000 0 \leq K \leq NM Input Input is given from Standard Input in the following format: N M K Output If Takahashi can have exactly K black squares in the grid, print Yes ; otherwise, print No . Sample Input 1 2 2 2 Sample Output 1 Yes Press the buttons in the order of the first row, the first column. Sample Input 2 2 2 1 Sample Output 2 No Sample Input 3 3 5 8 Sample Output 3 Yes Press the buttons in the order of the first column, third column, second row, fifth column. Sample Input 4 7 9 20 Sample Output 4 No
38,026
Score : 200 points Problem Statement You are given a string S of length N consisting of lowercase English letters, and an integer K . Print the string obtained by replacing every character in S that differs from the K -th character of S , with * . Constraints 1 \leq K \leq N\leq 10 S is a string of length N consisting of lowercase English letters. N and K are integers. Input Input is given from Standard Input in the following format: N S K Output Print the string obtained by replacing every character in S that differs from the K -th character of S , with * . Sample Input 1 5 error 2 Sample Output 1 *rr*r The second character of S is r . When we replace every character in error that differs from r with * , we get the string *rr*r . Sample Input 2 6 eleven 5 Sample Output 2 e*e*e* Sample Input 3 9 education 7 Sample Output 3 ******i**
38,027
Bomb Removal Problem 瞊 H ×暪 W のグリッド䞊に N 個の点火された導火線ずそれぞれに察する1぀の爆匟が配眮されおいる。それぞれの導火線ず爆匟は、 L i 個のマスからなる path i 䞊に配眮され、 path i の j 番目のマスを( px ij , py ij )ずする。各爆匟は path i の最埌のマス( px iL i , py iL i )に存圚する。導火線の火は初期状態(0秒時点)でマス( px i1 , py i1 )にあり、1秒間に1マス進む(( px i1 , py i1 ),( px i2 , py i2 ),...,( px iL i , py iL i )の順に進む)。 最初、ロボットがマス( sx , sy ) にいる。このロボットは今いるマスの隣接する8方向のマスに1進む、たたは、そのマスに留たるのに1秒かかる。ただし、グリッドの倖や爆匟のあるマスには移動するこずができない。ロボットは導火線の火があるマス䞊にいるずき消火するこずができる(同じマスに2぀以䞊の導火線の火がある堎合はそれら党おを消すこずができる)。 爆匟は導火線の火がマス( px iL i , py iL i )に到達したずきに爆発する( path i の途䞭で導火線の火がマス( px iL i , py iL i )を通過したずきは爆匟は爆発しない)。 党おの爆匟を爆発させずに党おの導火線の火を消火させるための最短の時間を出力せよ。ただし、どのように移動しおも爆匟を爆発させおしたう堎合は-1を出力せよ。なお、初期状態(0秒時点)でロボットが導火線の火の䞊にいる堎合、消火するこずができる。 Input 入力は以䞋の圢匏で䞎えられる。 W H N sx sy L 1 path 1 L 2 path 2 ... L N path N 1行目に3぀の敎数 W , H , N が空癜区切りで䞎えられる。2行目に2぀の敎数 sx , sy が空癜区切りで䞎えられる。3行目から N +2行目に L i ず path i が䞎えられる。 path i は以䞋の圢匏で䞎えられる。 px i1 py i1 px i2 py i2 ... px iL i py iL i Constraints 2 ≀ H , W ≀ 20 1 ≀ N ≀ 5 1 ≀ sx ≀ W 1 ≀ sy ≀ H 2 ≀ L i ≀ H + W 1 ≀ px ij ≀ W 1 ≀ py ij ≀ H path i の隣り合うマスは䞊䞋巊右に隣接しおいる。 導火線は互いに独立しおいる(他の導火線に圱響しない)。 爆匟はマス( sx , sy )には眮かれない。 Output ロボットが党おの導火線の火を消火させるための最短時間たたは -1 を出力せよ。 Sample Input 1 2 2 1 2 1 3 1 1 1 2 2 2 Sample Output 1 1 サンプル1に察応する図は以䞋の通りである。 ロボットは1秒埌に巊䞋の(1, 2)のマスに移動するこずにより消火するこずができる。 Sample Input 2 2 2 1 2 1 2 1 1 1 2 Sample Output 2 -1 サンプル2に察応する図は以䞋の通りである。 ロボットは、(1, 1)たたは(2, 2)のマスに移動する、たたは今いるマス(2, 1)に留たるこずができるがいずれにせよ1秒埌に爆匟が爆発しおしたう。 Sample Input 3 3 3 2 1 3 3 2 3 2 2 2 1 5 2 1 1 1 1 2 2 2 3 2 Sample Output 3 2 サンプル3に察応する図は以䞋の通りである。 ロボットは、(2, 2)のマスに移動し、(1, 2)のマスに移動するこずにより2秒で党おの導火線の火を消火するこずができる。 Sample Input 4 3 3 1 2 2 2 2 2 2 1 Sample Output 4 0 ロボットは、初期状態(0秒時点)で(2, 2)のマスにいお、導火線の火も(2, 2)のマスにあるので0秒で消火するこずができる。
38,028
秋のむルミネヌション 四角圢が倧奜きな人が倚く䜏む四角町では、四角圢の電光板を組み合わせたむルミネヌションで町䞭を圩るお祭りが開催されたす。 この電光板は電気を流すず発光し、発光しおいる板に接しおいる板も発光したす。したがっお、電光板を䜕枚䜿っおも、すべおがひずかたたりに接しおいれば電源がひず぀で枈むずいう優れものです。 お祭り実行委員䌚では、四角圢を組み合わせたデザむンを町民から募集し倚数のむルミネヌションを䜜成したす。各むルミネヌションは、デザむンを構成する四角圢の配眮によっお必芁ずなる電源の個数が倉わるため、必芁な電源の個数を把握する䜜業に 倧きな手間がかかりたす。 そこで、 あなたは四角圢の配眮を調べ、必芁な電源の個数を蚈算するプログラムを䜜成しお実行委員䌚を手助けするこずにしたした。 むルミネヌションの個数、各むルミネヌションを構成する四角圢の情報を入力ずし、むルミネヌションごずに必芁な電源の個数を出力するプログラムを䜜成しおください。重なっおいたり接しおいたりする四角圢を 1 ぀のたずたりず考え、1 ぀のたずたりに察しお電源の個数は 1 ぀ず数えおください。 Input 耇数のデヌタセットの䞊びが入力ずしお䞎えられたす。入力の終わりはれロひず぀の行で瀺されたす。各デヌタセットは以䞋の圢匏で䞎えられたす。 N M 1 xa 1 ya 1 xb 1 yb 1 xc 1 yc 1 xd 1 yd 1 xa 2 ya 2 xb 2 yb 2 xc 2 yc 2 xd 2 yd 2 : xa M 1 ya M 1 xb M 1 yb M 1 xc M 1 yc M 1 xd M 1 yd M 1 M 2 : : M N : : 1 行目にむルミネヌションの個数 N (1 ≀ N ≀ 100) が䞎えられたす。続いお、 N 個のむルミネヌションの情報が䞎えられたす。第 i のむルミネヌションの情報ずしお、むルミネヌションを構成する四角圢の個数 M i (1 ≀ M i ≀ 100) が行に䞎えられたす。続く M i 行に j 個目の四角圢の頂点 xa j , ya j , xb j , yb j , xc j , yc j , xd j , yd j (-1000 以䞊 1000 以䞋の敎数) が䞎えられたす。 入力される四角圢の頂点座暙は、時蚈回りの順に埓っお入力されたす。ただし、入力デヌタの四角圢はすべお凞な四角圢ずしたす。 デヌタセットの数は 10 を超えたせん。 Output 入力デヌタセットごずに、むルミネヌションごずに必芁な電源の個数を出力したす。出力する電源の個数は各むルミネヌションが入力された順番に埓っおください。 Sample Input 3 1 0 0 0 1 1 1 1 0 2 0 0 0 1 1 1 1 0 100 100 100 200 200 200 200 100 2 0 0 0 100 100 100 100 0 10 10 10 20 20 20 20 10 2 1 30 40 40 50 40 20 20 10 1 30 40 40 50 40 20 20 10 0 Output for the Sample Input 1 2 1 1 1
38,029
b
38,030
Dice I Write a program to simulate rolling a dice, which can be constructed by the following net. As shown in the figures, each face is identified by a different label from 1 to 6. Write a program which reads integers assigned to each face identified by the label and a sequence of commands to roll the dice, and prints the integer on the top face. At the initial state, the dice is located as shown in the above figures. Input In the first line, six integers assigned to faces are given in ascending order of their corresponding labels. In the second line, a string which represents a sequence of commands, is given. The command is one of ' E ', ' N ', ' S ' and ' W ' representing four directions shown in the above figures. Output Print the integer which appears on the top face after the simulation. Constraints $0 \leq $ the integer assigned to a face $ \leq 100$ $0 \leq $ the length of the command $\leq 100$ Sample Input 1 1 2 4 8 16 32 SE Sample Output 1 8 You are given a dice where 1, 2, 4, 8, 16 are 32 are assigned to a face labeled by 1, 2, ..., 6 respectively. After you roll the dice to the direction S and then to the direction E , you can see 8 on the top face. Sample Input 2 1 2 4 8 16 32 EESWN Sample Output 2 32
38,031
Problem H: Winter Bells The best night ever in the world has come! It's 8 p.m. of December 24th, yes, the night of Cristmas Eve. Santa Clause comes to a silent city with ringing bells. Overtaking north wind, from a sleigh a reindeer pulls she shoot presents to soxes hanged near windows for children. The sleigh she is on departs from a big christmas tree on the fringe of the city. Miracle power that the christmas tree spread over the sky like a web and form a paths that the sleigh can go on. Since the paths with thicker miracle power is easier to go, these paths can be expressed as undirected weighted graph. Derivering the present is very strict about time. When it begins dawning the miracle power rapidly weakens and Santa Clause can not continue derivering any more. Her pride as a Santa Clause never excuses such a thing, so she have to finish derivering before dawning. The sleigh a reindeer pulls departs from christmas tree (which corresponds to 0th node), and go across the city to the opposite fringe ( n -1 th node) along the shortest path. Santa Clause create presents from the miracle power and shoot them from the sleigh the reindeer pulls at his full power. If there are two or more shortest paths, the reindeer selects one of all shortest paths with equal probability and go along it. By the way, in this city there are p children that wish to see Santa Clause and are looking up the starlit sky from their home. Above the i -th child's home there is a cross point of the miracle power that corresponds to c [ i ]-th node of the graph. The child can see Santa Clause if (and only if) Santa Clause go through the node. Please find the probability that each child can see Santa Clause. Input Input consists of several datasets. The first line of each dataset contains three integers n , m , p , which means the number of nodes and edges of the graph, and the number of the children. Each node are numbered 0 to n -1. Following m lines contains information about edges. Each line has three integers. The first two integers means nodes on two endpoints of the edge. The third one is weight of the edge. Next p lines represent c [ i ] respectively. Input terminates when n = m = p = 0. Output For each dataset, output p decimal values in same order as input. Write a blank line after that. You may output any number of digit and may contain an error less than 1.0e-6. Constraints 3 ≀ n ≀ 100 There are no parallel edges and a edge whose end points are identical. 0 < weight of the edge < 10000 Sample Input 3 2 1 0 1 2 1 2 3 1 4 5 2 0 1 1 0 2 1 1 2 1 1 3 1 2 3 1 1 2 0 0 0 Output for the Sample Input 1.00000000 0.50000000 0.50000000
38,032
Score: 500 points Problem Statement We have caught N sardines. The deliciousness and fragrantness of the i -th sardine is A_i and B_i , respectively. We will choose one or more of these sardines and put them into a cooler. However, two sardines on bad terms cannot be chosen at the same time. The i -th and j -th sardines (i \neq j) are on bad terms if and only if A_i \cdot A_j + B_i \cdot B_j = 0 . In how many ways can we choose the set of sardines to put into the cooler? Since the count can be enormous, print it modulo 1000000007 . Constraints All values in input are integers. 1 \leq N \leq 2 \times 10^5 -10^{18} \leq A_i, B_i \leq 10^{18} Input Input is given from Standard Input in the following format: N A_1 B_1 : A_N B_N Output Print the count modulo 1000000007 . Sample Input 1 3 1 2 -1 1 2 -1 Sample Output 1 5 There are five ways to choose the set of sardines, as follows: The 1 -st The 1 -st and 2 -nd The 2 -nd The 2 -nd and 3 -rd The 3 -rd Sample Input 2 10 3 2 3 2 -1 1 2 -1 -3 -9 -8 12 7 7 8 1 8 2 8 4 Sample Output 2 479
38,033
Window In the building of Jewelry Art Gallery (JAG), there is a long corridor in the east-west direction. There is a window on the north side of the corridor, and $N$ windowpanes are attached to this window. The width of each windowpane is $W$, and the height is $H$. The $i$-th windowpane from the west covers the horizontal range between $W\times(i-1)$ and $W\times i$ from the west edge of the window. Figure A1. Illustration of the window You received instructions from the manager of JAG about how to slide the windowpanes. These instructions consist of $N$ integers $x_1, x_2, ..., x_N$, and $x_i \leq W$ is satisfied for all $i$. For the $i$-th windowpane, if $i$ is odd, you have to slide $i$-th windowpane to the east by $x_i$, otherwise, you have to slide $i$-th windowpane to the west by $x_i$. You can assume that the windowpanes will not collide each other even if you slide windowpanes according to the instructions. In more detail, $N$ windowpanes are alternately mounted on two rails. That is, the $i$-th windowpane is attached to the inner rail of the building if $i$ is odd, otherwise, it is attached to the outer rail of the building. Before you execute the instructions, you decide to obtain the area where the window is open after the instructions. Input The input consists of a single test case in the format below. $N$ $H$ $W$ $x_1$ ... $x_N$ The first line consists of three integers $N, H,$ and $W$ ($1 \leq N \leq 100, 1 \leq H, W \leq 100$). It is guaranteed that $N$ is even. The following line consists of $N$ integers $x_1, ..., x_N$ while represent the instructions from the manager of JAG. $x_i$ represents the distance to slide the $i$-th windowpane ($0 \leq x_i \leq W$). Output Print the area where the window is open after the instructions in one line. Sample Input 1 4 3 3 1 1 2 3 Output for Sample Input 1 9 Sample Input 2 8 10 18 2 12 16 14 18 4 17 16 Output for Sample Input 2 370 Sample Input 3 6 2 2 0 2 2 2 2 0 Output for Sample Input 3 8 Sample Input 4 4 1 4 3 3 2 2 Output for Sample Input 4 6 Sample Input 5 8 7 15 5 0 9 14 0 4 4 15 Output for Sample Input 5 189 Figure A2. Illustration of Sample Input 1
38,034
Problem F: nCm Problem æ•Žæ•° n が䞎えられた時、 nCm (異なる n 個のものから m 個を遞ぶ組み合わせの数)が偶数ずなるような最小の m を出力せよ。 Input 入力は以䞋の圢匏で䞎えられる。 n Constraints 入力は以䞋の条件を満たす。 1 ≀ n ≀ 10 18 Output nCm が偶数ずなるような最小の m を1行に出力する。 Sample Input 1 2 Sample Output 1 1 Sample Input 2 111 Sample Output 2 16 Sample Input 3 3 Sample Output 3 4
38,035
Score : 100 points Problem Statement In the Kingdom of AtCoder, people use a language called Taknese, which uses lowercase English letters. In Taknese, the plural form of a noun is spelled based on the following rules: If a noun's singular form does not end with s , append s to the end of the singular form. If a noun's singular form ends with s , append es to the end of the singular form. You are given the singular form S of a Taknese noun. Output its plural form. Constraints S is a string of length 1 between 1000 , inclusive. S contains only lowercase English letters. Input Input is given from Standard Input in the following format: S Output Print the plural form of the given Taknese word. Sample Input 1 apple Sample Output 1 apples apple ends with e , so its plural form is apples . Sample Input 2 bus Sample Output 2 buses bus ends with s , so its plural form is buses . Sample Input 3 box Sample Output 3 boxs
38,036
線察称 平面䞊の異なる 3 点 P1(x1,y1) , P2(x2,y2) , Q(xq,yq) の座暙の組を読み蟌んで、点 P1 点 P2 を通る盎線を察称軞ずしお点 Q ず線察称の䜍眮にある点 R(x,y) を出力するプログラムを䜜成しおください。なお、点 Q は、その察称軞䞊にないものずしたす。 入力 入力は耇数のデヌタセットからなりたす。各デヌタセットは以䞋の圢匏で䞎えられたす。 x1 , y1 , x2 , y2 , xq , yq x1 , y1 , x2 , y2 , xq , yq (-100 以䞊 100 以䞋の実数) がカンマ区切りで行に䞎えられたす。 デヌタセットの数は 50 を超えない。 出力 デヌタセットごずに、 x , y を空癜区切りで 1 行に出力する。出力は実数で 0.0001 以䞋の誀差を含んでもよい。 Sample Input 1.0,0.0,-1.0,0.0,1.0,1.0 1.0,0.0,0.0,-1.0,3.0,0.0 0.0,1.0,0.0,-1.0,1.0,1.0 Output for the Sample Input 1.000000 -1.000000 1.000000 2.000000 -1.000000 1.000000
38,037
Score : 700 points Problem Statement Nuske has a grid with N rows and M columns of squares. The rows are numbered 1 through N from top to bottom, and the columns are numbered 1 through M from left to right. Each square in the grid is painted in either blue or white. If S_{i,j} is 1 , the square at the i -th row and j -th column is blue; if S_{i,j} is 0 , the square is white. For every pair of two blue square a and b , there is at most one path that starts from a , repeatedly proceeds to an adjacent (side by side) blue square and finally reaches b , without traversing the same square more than once. Phantom Thnook, Nuske's eternal rival, gives Q queries to Nuske. The i -th query consists of four integers x_{i,1} , y_{i,1} , x_{i,2} and y_{i,2} and asks him the following: when the rectangular region of the grid bounded by (and including) the x_{i,1} -th row, x_{i,2} -th row, y_{i,1} -th column and y_{i,2} -th column is cut out, how many connected components consisting of blue squares there are in the region? Process all the queries. Constraints 1 ≀ N,M ≀ 2000 1 ≀ Q ≀ 200000 S_{i,j} is either 0 or 1 . S_{i,j} satisfies the condition explained in the statement. 1 ≀ x_{i,1} ≀ x_{i,2} ≀ N(1 ≀ i ≀ Q) 1 ≀ y_{i,1} ≀ y_{i,2} ≀ M(1 ≀ i ≀ Q) Input The input is given from Standard Input in the following format: N M Q S_{1,1} .. S_{1,M} : S_{N,1} .. S_{N,M} x_{1,1} y_{i,1} x_{i,2} y_{i,2} : x_{Q,1} y_{Q,1} x_{Q,2} y_{Q,2} Output For each query, print the number of the connected components consisting of blue squares in the region. Sample Input 1 3 4 4 1101 0110 1101 1 1 3 4 1 1 3 1 2 2 3 4 1 2 2 4 Sample Output 1 3 2 2 2 In the first query, the whole grid is specified. There are three components consisting of blue squares, and thus 3 should be printed. In the second query, the region within the red frame is specified. There are two components consisting of blue squares, and thus 2 should be printed. Note that squares that belong to the same component in the original grid may belong to different components. Sample Input 2 5 5 6 11010 01110 10101 11101 01010 1 1 5 5 1 2 4 5 2 3 3 4 3 3 3 3 3 1 3 5 1 1 3 4 Sample Output 2 3 2 1 1 3 2
38,038
Problem B: Make a Sequence Your company’s next product will be a new game, which is a three-dimensional variant of the classic game “Tic-Tac-Toe”. Two players place balls in a three-dimensional space (board), and try to make a sequence of a certain length. People believe that it is fun to play the game, but they still cannot fix the values of some parameters of the game. For example, what size of the board makes the game most exciting? Parameters currently under discussion are the board size (we call it n in the following) and the length of the sequence ( m ). In order to determine these parameter values, you are requested to write a computer simulator of the game. You can see several snapshots of the game in Figures 1-3. These figures correspond to the three datasets given in the Sample Input. Figure 1: A game with n = m = 3 Here are the precise rules of the game. Two players, Black and White, play alternately. Black plays first. There are n × n vertical pegs. Each peg can accommodate up to n balls. A peg can be specified by its x - and y -coordinates (1 ≀ x , y ≀ n ). A ball on a peg can be specified by its z -coordinate (1 ≀ z ≀ n ). At the beginning of a game, there are no balls on any of the pegs. Figure 2: A game with n = m = 3 (White made a 3-sequence before Black) On his turn, a player chooses one of n × n pegs, and puts a ball of his color onto the peg. The ball follows the law of gravity. That is, the ball stays just above the top-most ball on the same peg or on the floor (if there are no balls on the peg). Speaking differently, a player can choose x - and y -coordinates of the ball, but he cannot choose its z -coordinate. The objective of the game is to make an m -sequence. If a player makes an m -sequence or longer of his color, he wins. An m -sequence is a row of m consecutive balls of the same color. For example, black balls in positions (5, 1, 2), (5, 2, 2) and (5, 3, 2) form a 3-sequence. A sequence can be horizontal, vertical, or diagonal. Precisely speaking, there are 13 possible directions to make a sequence, categorized as follows. Figure 3: A game with n = 4, m = 3 (Black made two 4-sequences) (a) One-dimensional axes. For example, (3, 1, 2), (4, 1, 2) and (5, 1, 2) is a 3-sequence. There are three directions in this category. (b) Two-dimensional diagonals. For example, (2, 3, 1), (3, 3, 2) and (4, 3, 3) is a 3-sequence. There are six directions in this category. (c) Three-dimensional diagonals. For example, (5, 1, 3), (4, 2, 4) and (3, 3, 5) is a 3- sequence. There are four directions in this category. Note that we do not distinguish between opposite directions. As the evaluation process of the game, people have been playing the game several times changing the parameter values. You are given the records of these games. It is your job to write a computer program which determines the winner of each recorded game. Since it is difficult for a human to find three-dimensional sequences, players often do not notice the end of the game, and continue to play uselessly. In these cases, moves after the end of the game, i.e. after the winner is determined, should be ignored. For example, after a player won making an m -sequence, players may make additional m -sequences. In this case, all m -sequences but the first should be ignored, and the winner of the game is unchanged. A game does not necessarily end with the victory of one of the players. If there are no pegs left to put a ball on, the game ends with a draw. Moreover, people may quit a game before making any m-sequence. In such cases also, the game ends with a draw. Input The input consists of multiple datasets each corresponding to the record of a game. A dataset starts with a line containing three positive integers n , m , and p separated by a space. The relations 3 ≀ m ≀ n ≀ 7 and 1 ≀ p ≀ n 3 hold between them. n and m are the parameter values of the game as described above. p is the number of moves in the game. The rest of the dataset is p lines each containing two positive integers x and y . Each of these lines describes a move, i.e. the player on turn puts his ball on the peg specified. You can assume that 1 ≀ x ≀ n and 1 ≀ y ≀ n . You can also assume that at most n balls are put on a peg throughout a game. The end of the input is indicated by a line with three zeros separated by a space. Output For each dataset, a line describing the winner and the number of moves until the game ends should be output. The winner is either “Black” or “White”. A single space should be inserted between the winner and the number of moves. No other extra characters are allowed in the output. In case of a draw, the output line should be “Draw”. Sample Input 3 3 3 1 1 1 1 1 1 3 3 7 2 2 1 3 1 1 2 3 2 1 3 3 3 1 4 3 15 1 1 2 2 1 1 3 3 3 3 1 1 3 3 3 3 4 4 1 1 4 4 4 4 4 4 4 1 2 2 0 0 0 Output for the Sample Input Draw White 6 Black 15
38,039
Score : 500 points Problem Statement For two sequences S and T of length N consisting of 0 and 1 , let us define f(S, T) as follows: Consider repeating the following operation on S so that S will be equal to T . f(S, T) is the minimum possible total cost of those operations. Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i , where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change. There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1 . Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7) . Constraints 1 \leq N \leq 2 \times 10^5 1 \leq C_i \leq 10^9 All values in input are integers. Input Input is given from Standard Input in the following format: N C_1 C_2 \cdots C_N Output Print the sum of f(S, T) , modulo (10^9+7) . Sample Input 1 1 1000000000 Sample Output 1 999999993 There are two pairs (S, T) of different sequences of length 2 consisting of 0 and 1 , as follows: S = (0), T = (1): by changing S_1 to 1 , we can have S = T at the cost of 1000000000 , so f(S, T) = 1000000000 . S = (1), T = (0): by changing S_1 to 0 , we can have S = T at the cost of 1000000000 , so f(S, T) = 1000000000 . The sum of these is 2000000000 , and we should print it modulo (10^9+7) , that is, 999999993 . Sample Input 2 2 5 8 Sample Output 2 124 There are 12 pairs (S, T) of different sequences of length 3 consisting of 0 and 1 , which include: S = (0, 1), T = (1, 0) In this case, if we first change S_1 to 1 then change S_2 to 0 , the total cost is 5 \times 2 + 8 = 18 . We cannot have S = T at a smaller cost, so f(S, T) = 18 . Sample Input 3 5 52 67 72 25 79 Sample Output 3 269312
38,040
Score : 600 points Problem Statement There are 2N balls, N white and N black, arranged in a row. The integers from 1 through N are written on the white balls, one on each ball, and they are also written on the black balls, one on each ball. The integer written on the i -th ball from the left ( 1 ≀ i ≀ 2N ) is a_i , and the color of this ball is represented by a letter c_i . c_i = W represents the ball is white; c_i = B represents the ball is black. Takahashi the human wants to achieve the following objective: For every pair of integers (i,j) such that 1 ≀ i < j ≀ N , the white ball with i written on it is to the left of the white ball with j written on it. For every pair of integers (i,j) such that 1 ≀ i < j ≀ N , the black ball with i written on it is to the left of the black ball with j written on it. In order to achieve this, he can perform the following operation: Swap two adjacent balls. Find the minimum number of operations required to achieve the objective. Constraints 1 ≀ N ≀ 2000 1 ≀ a_i ≀ N c_i = W or c_i = B . If i ≠ j , (a_i,c_i) ≠ (a_j,c_j) . Input Input is given from Standard Input in the following format: N c_1 a_1 c_2 a_2 : c_{2N} a_{2N} Output Print the minimum number of operations required to achieve the objective. Sample Input 1 3 B 1 W 2 B 3 W 1 W 3 B 2 Sample Output 1 4 The objective can be achieved in four operations, for example, as follows: Swap the black 3 and white 1 . Swap the white 1 and white 2 . Swap the black 3 and white 3 . Swap the black 3 and black 2 . Sample Input 2 4 B 4 W 4 B 3 W 3 B 2 W 2 B 1 W 1 Sample Output 2 18 Sample Input 3 9 W 3 B 1 B 4 W 1 B 5 W 9 W 2 B 6 W 5 B 3 W 8 B 9 W 7 B 2 B 8 W 4 W 6 B 7 Sample Output 3 41
38,041
D - Disciple Life is Hard / 匟子は぀らいよ Story Dのひずはドヌナツを愛しおやたない。垞にドヌナツを欲しおいる。しかし、垫匠であるぶなしめじたんに䜓を鍛えるこずを呜じられたDのひずは、摂取カロリヌを制限しなければならない。そこでDのひずは基瀎代謝も考慮し、その日トレヌニングによっお消費したカロリヌの分たでドヌナツを食べおもよいこずにした。Dのひずはドヌナツを愛しおやたないずはいえ、奜みはあるので、食べるドヌナツによっお埗られる幞犏感は倉わる。たた、その日の䜓力によっお行えるトレヌニングも倉わっおくるため、トレヌニングの皮類、ドヌナツの皮類、䜓力を考慮し、 D 日間で埗られる幞犏を最倧化するこずを詊みた。 Problem T 皮類のトレヌニングず N 皮類のドヌナツのデヌタが䞎えられる。 i 番目のトレヌニングに必芁な䜓力は e_i 、消費カロリヌは c_i である。トレヌニングは 1 日にちょうど U 皮類だけ行わなければならず、同じトレヌニングは 1 日に 1 床しか行えない。トレヌニングに必芁な䜓力の総和はその日の䜓力以䞋でなければならない。その日の䜓力からトレヌニングに必芁な䜓力の総和を匕いた差分は残った䜓力ずなり、翌日に匕き継がれる。 j 番目のドヌナツで埗られる幞犏床は h_j 、摂取カロリヌは a_j である。 1 日に同じドヌナツを耇数個食べおもよい。 1 日に埗られる幞犏は食べたドヌナツの幞犏床の和である。摂取カロリヌの総和はその日のトレヌニングによる消費カロリヌの総和以䞋でなければならない。その日のトレヌニングによる消費カロリヌの総和から摂取カロリヌの総和を匕いた差分が䜙った消費カロリヌずなるが、これは翌日に匕き継がない。 䜓力の䞊限は S であり、毎日䜓力は O だけ回埩する。初日の始めの䜓力は S である。 D 日間で埗られる幞犏の和の最倧倀を求めよ。どうやっおもトレヌニングをちょうど U 回行えない日が生じる堎合、- 1 ず出力せよ。 Input 入力は以䞋の圢匏からなる。 S T U N O D e_1 c_1 ... e_T c_T h_1 a_1 ... h_N a_N 1 行目は 6 ぀の敎数からなり、それぞれ䜓力の䞊限 S 、トレヌニングの皮類 T 、 1 日に行うトレヌニングの皮類数 U 、ドヌナツの皮類 N 、 1 日に回埩する䜓力量 O 、日数 D が空癜 1 文字区切りで䞊んでいる。 続く T 行はトレヌニングの情報を衚す。 i+1 行目( 1 \leq i \leq T )は 2 ぀の敎数からなり、それぞれトレヌニングに必芁な䜓力 e_i 、消費カロリヌ c_i が空癜 1 文字区切りで䞊んでいる。 続く N 行はドヌナツの情報を衚す。 j+T+1 行目( 1 \leq j \leq N )は 2 ぀の敎数からなり、それぞれ埗られる幞犏床 h_j 、摂取カロリヌ a_j が空癜 1 文字区切りで䞊んでいる。 制玄: 1 \leq O \leq S \leq 100 1 \leq U \leq T \leq 100 1 \leq N \leq 100 1 \leq D \leq 100 1 \leq e_i, c_i, h_j, a_j \leq 100 Output D 日間で埗られる幞犏の総和の最倧倀を 1 行に出力せよ。 ただし、どうやっおもトレヌニングをちょうど U 回行えない日が生じる堎合、- 1 ず出力せよ。 行の最埌では必ず改行を行うこず。 Sample Input 1 10 1 1 1 4 3 6 10 5 8 Sample Output 1 15 1日目は1番目のトレヌニングを行い1番目のドヌナツを食べるこずで、䜓力が残り4、幞犏床5を埗る。 2日目はたず䜓力が4回埩し、8ずなる。 1番目のトレヌニングを行い1番目のドヌナツを食べるこずで、䜓力が残り2、幞犏床5を埗る。 3日目はたず䜓力が4回埩し、6ずなる。 1番目のトレヌニングを行い1番目のドヌナツを食べるこずで、䜓力が残り0、幞犏床5を埗る。 よっお、3日間合蚈で幞犏15を埗る。 Sample Input 2 10 3 2 3 3 2 4 10 3 4 3 5 3 4 4 5 5 7 Sample Output 2 19 1日目に1,3番目ずのトレヌニングを行うず、䜓力が残り3、消費カロリヌが15ずなる。 2番目のドヌナツを3個食べるこずで、摂取カロリヌが15で幞犏が12埗られる。 2日目にはたず䜓力が3回埩し、6ずなる。 2,3番目ずのトレヌニングを行うず、䜓力が残り0、消費カロリヌが9ずなる。 1番目のトレヌニングだけ行った方が倚くのカロリヌを消費でき、䜓力も倚く残るが、1日には必ず2皮類のトレヌニングを行う必芁があるため、これはできない。 1,2番目のドヌナツを1個ず぀食べるず摂取カロリヌが9で幞犏が7埗られる。 2日間の幞犏の合蚈は19ずなり、これが最倧である。 Sample Input 3 10 3 2 3 5 3 4 10 2 2 3 5 4 3 5 4 7 5 Sample Output 3 58 Sample Input 4 10 1 1 1 1 1 13 13 13 13 Sample Output 4 -1 䜓力の䞊限が10しかないため、䜓力が13必芁なトレヌニングを行うこずができない。 よっお、1日に行うべきトレヌニングの皮類数を満たすこずができないため、-1を出力する。
38,042
Twin Trees Bros. To meet the demand of ICPC (International Cacao Plantation Consortium), you have to check whether two given trees are twins or not. Example of two trees in the three-dimensional space. The term tree in the graph theory means a connected graph where the number of edges is one less than the number of nodes. ICPC, in addition, gives three-dimensional grid points as the locations of the tree nodes. Their definition of two trees being twins is that, there exists a geometric transformation function which gives a one-to-one mapping of all the nodes of one tree to the nodes of the other such that for each edge of one tree, there exists an edge in the other tree connecting the corresponding nodes. The geometric transformation should be a combination of the following transformations: translations, in which coordinate values are added with some constants, uniform scaling with positive scale factors, in which all three coordinate values are multiplied by the same positive constant, and rotations of any amounts around either $x$-, $y$-, and $z$-axes. Note that two trees can be twins in more than one way, that is, with different correspondences of nodes. Write a program that decides whether two trees are twins or not and outputs the number of different node correspondences. Hereinafter, transformations will be described in the right-handed $xyz$-coordinate system. Trees in the sample inputs 1 through 4 are shown in the following figures. The numbers in the figures are the node numbers defined below. For the sample input 1, each node of the red tree is mapped to the corresponding node of the blue tree by the transformation that translates $(-3, 0, 0)$, rotates $-\pi / 2$ around the $z$-axis, rotates $\pi / 4$ around the $x$-axis, and finally scales by $\sqrt{2}$. By this mapping, nodes #1, #2, and #3 of the red tree at $(0, 0, 0)$, $(1, 0, 0)$, and $(3, 0, 0)$ correspond to nodes #6, #5, and #4 of the blue tree at $(0, 3, 3)$, $(0, 2, 2)$, and $(0, 0, 0)$, respectively. This is the only possible correspondence of the twin trees. For the sample input 2, red nodes #1, #2, #3, and #4 can be mapped to blue nodes #6, #5, #7, and #8. Another node correspondence exists that maps nodes #1, #2, #3, and #4 to #6, #5, #8, and #7. For the sample input 3, the two trees are not twins. There exist transformations that map nodes of one tree to distinct nodes of the other, but the edge connections do not agree. For the sample input 4, there is no transformation that maps nodes of one tree to those of the other. Input The input consists of a single test case of the following format. $n$ $x_1$ $y_1$ $z_1$ . . . $x_n$ $y_n$ $z_n$ $u_1$ $v_1$ . . . $u_{n−1}$ $v_{n−1}$ $x_{n+1}$ $y_{n+1}$ $z_{n+1}$ . . . $x_{2n}$ $y_{2n}$ $z_{2n}$ $u_n$ $v_n$ . . . $u_{2n−2}$ $v_{2n−2}$ The input describes two trees. The first line contains an integer $n$ representing the number of nodes of each tree ($3 \leq n \leq 200$). Descriptions of two trees follow. Description of a tree consists of $n$ lines that give the vertex positions and $n - 1$ lines that show the connection relation of the vertices. Nodes are numbered $1$ through $n$ for the first tree, and $n + 1$ through $2n$ for the second tree. The triplet $(x_i, y_i, z_i)$ gives the coordinates of the node numbered $i$. $x_i$, $y_i$, and $z_i$ are integers in the range between $-1000$ and $1000$, inclusive. Nodes of a single tree have distinct coordinates. The pair of integers $(u_j , v_j )$ means that an edge exists between nodes numbered $u_j$ and $v_j$ ($u_j \ne v_j$). $1 \leq u_j \leq n$ and $1 \leq v_j \leq n$ hold for $1 \leq j \leq n - 1$, and $n + 1 \leq u_j \leq 2n$ and $n + 1 \leq v_j \leq 2n$ hold for $n \leq j \leq 2n - 2$. Output Output the number of different node correspondences if two trees are twins. Output a zero, otherwise. Sample Input 1 3 0 0 0 1 0 0 3 0 0 1 2 2 3 0 0 0 0 2 2 0 3 3 4 5 5 6 Sample Output 1 1 Sample Input 2 4 1 0 0 2 0 0 2 1 0 2 -1 0 1 2 2 3 2 4 0 1 1 0 0 0 0 2 0 0 0 2 5 6 5 7 5 8 Sample Output 2 2
38,043
問題 J : 乱択平衡分二分探玢朚 ずころでG○○gle Code Jam の地区倧䌚で右の垭に座っおいた男の ID は rng_58 ず蚀うらしい 東京倧孊時代の蚘憶に䌌たような ID の仲間が居た芚えがあるが僕の仲間は䞀人残さず矎少女だったはずだ 圌女はいわゆる無衚情䞍思議系キャラだったような気がする ずいうこずは圌は知らない男だrng ずは䜕の略だろう おそらく Random Number Generator に違いない 乱択アルゎリズムを埗意ずするのだろう ずころで乱数を甚いた平衡二分探玢朚である Treap は 2011 幎頃のプログラミングコンテストではしばしば甚いられおいたようだが 20XX 幎の今ではあたり䜿甚されおいない 圓時 Treap は実装が平易であるずいう理由により Splay 朚や Scapegoat 朚ず䞊んでよく䜿われおいた 20XX 幎の今呜をかけたプログラミングコンテストが日垞的に行われるこの䞖界では 実装が倚少平易になるずいうような甘い根拠での遞択は到底考えられない 皆少しでもプログラムが高速になるよう考えおいるし 䞖界倧䌚出堎者ずもなればLeft-leaning 赀黒朚皋床なら十数秒で蚘述できるのが圓然だ 䟋えばTreap が赀黒朚よりも遅くなっおしたうのは 高さの定数倍が効いおくるからであるず蚀われおいる ここは萜ち着いおそれを数倀的に考察するこずにより粟神の安定を取り戻そう 問題 キヌを実数ずする Treap に N 個のランダムな芁玠を挿入した際に 高さが h ( h = 0, 1, 
, N - 1 ) ずなる確率を求めよ 以䞋より詳しく説明する Treap ずは乱数を甚いた平衡二分探玢朚である 各ノヌドはキヌの他に優先床ずいう倀を持぀ ここではキヌず優先床は 0 から 1 たでの実数倀ずする Treap では以䞋の 2 ぀の条件が垞に保たれる キヌに関する条件 各ノヌドに関しお巊の子以䞋のノヌドは自分より小さなキヌを持぀ 各ノヌドに関しお右の子以䞋のノヌドは自分より倧きなキヌを持぀ 優先床に関する条件 各ノヌドに関しお子のノヌドは自分より小さな優先床を持぀ 䞋図はTreap の䟋である 各ノヌドの䞊郚にキヌが䞋郚に優先床が曞かれおいる 7 ぀のノヌドからなる Treap の䟋 挿入の操䜜は以䞋のように行われる 挿入するキヌ を x ずおく 挿入する新しいノヌドの優先床 p を 0 から 1 たでの䞀様分垃よりランダムに決定する 通垞の二分探玢朚ず同様にたずは優先床を無芖し新しいノヌドを挿入する 優先床の条件を満たすように新しいノヌドを䞊に持ち䞊げるような回転操䜜を必芁なだけ繰り返す 朚の回転操䜜に関しおは補足の節に詳しく蚘述したので参考にせよ 䞋図は先ほどの䟋にキヌずしお 0.5優先床ずしお 0.7 を持぀頂点を挿入した過皋の䟋である たずは優先床が無芖されノヌドが挿入される 回転を行い新しいノヌドが䞊ぞ行く さらに回転を行うず優先床の条件が満たされるので挿入は終了する 空の Treap に N 個のキヌを やはり 0 から 1 たでの䞀様分垃よりランダムに遞び挿入しおゆくずする 最終的に高さが h ずなる確率を 各 h = 0, 1, 
, N - 1 に぀いお求めよ なお実数は十分な粟床を持っお扱われるずし 䟋えば 2 ぀のノヌドの優先床が等しくなる確率は 0 ずしおよい たた高さずは根のノヌドから各ノヌドに至るために通らなければならない蟺の本数の最倧倀である 入力 1 ぀の敎数 N が曞かれおいる 出力 出力は N 行から成る i 行目に高さが i - 1 ずなる確率を出力せよ 倀は小数点以䞋䜕桁衚瀺しおも構わない 制玄 1 ≀ N ≀ 3 × 10 4 出力する倀は 10 - 5 以䞋の誀差を含んでいおも構わない 入出力䟋 入力䟋 1: 1 入力䟋 1 に察する出力䟋: 1.0 入力䟋 2: 2 入力䟋 2 に察する出力䟋: 0.0000000000 1.0000000000 補足 朚の回転操䜜には右回転ず巊回転がある 右回転ずは以䞋の 2 ぀の図の 1 ぀めの状態を 2 ぀めの状態にする操䜜であり 巊回転ずは以䞋の 2 ぀の図の 2 ぀めの状態を 1 ぀めの状態にする操䜜である 右回転をする前たたは巊回転をした埌 右回転をした埌たたは巊回転をする前 Treap においおは持ち䞊げたいノヌドがその芪ノヌドの巊の子であった堎合 持ち䞊げたいノヌドを䞊図の P ずするような右回転を適甚し 持ち䞊げたいノヌドがその芪ノヌドの右の子であった堎合 持ち䞊げたいノヌドを䞊図の Q ずするような巊回転を適甚する 朚の回転操䜜に぀いおより詳しくは䟋えば以䞋を参照せよ http://ja.wikipedia.org/wiki/%E6%9C%A8%E3%81%AE%E5%9B%9E%E8%BB%A2 Treap に぀いおより詳しくは䟋えば以䞋を参照せよ http://en.wikipedia.org/wiki/Treap http://www.prefield.com/algorithm/container/treap.html
38,044
Score : 1200 points Problem Statement There are infinitely many cards, numbered 1 , 2 , 3 , ... Initially, Cards x_1 , x_2 , ... , x_N are face up, and the others are face down. Snuke can perform the following operation repeatedly: Select a prime p greater than or equal to 3 . Then, select p consecutive cards and flip all of them. Snuke's objective is to have all the cards face down. Find the minimum number of operations required to achieve the objective. Constraints 1 ≀ N ≀ 100 1 ≀ x_1 < x_2 < ... < x_N ≀ 10^7 Input Input is given from Standard Input in the following format: N x_1 x_2 ... x_N Output Print the minimum number of operations required to achieve the objective. Sample Input 1 2 4 5 Sample Output 1 2 Below is one way to achieve the objective in two operations: Select p = 5 and flip Cards 1 , 2 , 3 , 4 and 5 . Select p = 3 and flip Cards 1 , 2 and 3 . Sample Input 2 9 1 2 3 4 5 6 7 8 9 Sample Output 2 3 Below is one way to achieve the objective in three operations: Select p = 3 and flip Cards 1 , 2 and 3 . Select p = 3 and flip Cards 4 , 5 and 6 . Select p = 3 and flip Cards 7 , 8 and 9 . Sample Input 3 2 1 10000000 Sample Output 3 4
38,045
Score : 600 points Problem Statement Given are a prime number p and a sequence of p integers a_0, \ldots, a_{p-1} consisting of zeros and ones. Find a polynomial of degree at most p-1 , f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \ldots + b_0 , satisfying the following conditions: For each i (0 \leq i \leq p-1) , b_i is an integer such that 0 \leq b_i \leq p-1 . For each i (0 \leq i \leq p-1) , f(i) \equiv a_i \pmod p . Constraints 2 \leq p \leq 2999 p is a prime number. 0 \leq a_i \leq 1 Input Input is given from Standard Input in the following format: p a_0 a_1 \ldots a_{p-1} Output Print b_0, b_1, \ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between. It can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted. Sample Input 1 2 1 0 Sample Output 1 1 1 f(x) = x + 1 satisfies the conditions, as follows: f(0) = 0 + 1 = 1 \equiv 1 \pmod 2 f(1) = 1 + 1 = 2 \equiv 0 \pmod 2 Sample Input 2 3 0 0 0 Sample Output 2 0 0 0 f(x) = 0 is also valid. Sample Input 3 5 0 1 0 1 0 Sample Output 3 0 2 0 1 3
38,046
Score : 300 points Problem Statement You are given an integer N . Among the integers between 1 and N (inclusive), how many Shichi-Go-San numbers (literally "Seven-Five-Three numbers") are there? Here, a Shichi-Go-San number is a positive integer that satisfies the following condition: When the number is written in base ten, each of the digits 7 , 5 and 3 appears at least once, and the other digits never appear. Constraints 1 \leq N < 10^9 N is an integer. Input Input is given from Standard Input in the following format: N Output Print the number of the Shichi-Go-San numbers between 1 and N (inclusive). Sample Input 1 575 Sample Output 1 4 There are four Shichi-Go-San numbers not greater than 575 : 357, 375, 537 and 573 . Sample Input 2 3600 Sample Output 2 13 There are 13 Shichi-Go-San numbers not greater than 3600 : the above four numbers, 735, 753, 3357, 3375, 3537, 3557, 3573, 3575 and 3577 . Sample Input 3 999999999 Sample Output 3 26484
38,047
What Color Is The Universe? On a clear night, a boy, Campanella looked up at the sky, there were many stars which have different colors such as red, yellow, green, blue, purple, etc. He was watching the stars and just lost track of time. Presently, he wondered, "There are many stars in the space. What color is the universe if I look up it from outside?" Until he found the answer to this question, he couldn't sleep. After a moment's thought, he proposed a hypothesis, "When I observe the stars in the sky, if more than half of the stars have the same color, that is the color of the universe." He has collected data of stars in the universe after consistently observing them. However, when he try to count the number of star, he was in bed sick with a cold. You decided to help him by developing a program to identify the color of the universe. You are given an array A . Let | A | be the number of element in A , and let N m be the number of m in A . For example, if A = {3, 1, 2, 3, 3, 1, 5, 3}, | A | = 8, N 3 = 4, N 1 = 2, N 5 = 1. Your program have to find m such that: N m > (| A | / 2 ) If there is no such m , you also have to report the fact. There is no such m for the above example, but for a array A = {5, 2, 5, 3, 4, 5, 5}, 5 is the answer. Input There are several test cases. For each test case, in the first line | A | is given. In the next line, there will be | A | integers. The integers are less than 2 31 and | A | < 1,000,000. The input terminate with a line which contains single 0. Output For each test case, output m in a line. If there is no answer, output "NO COLOR" in a line. Sample Input 8 3 1 2 3 3 1 5 3 7 5 2 5 3 4 5 5 0 Output for the Sample Input NO COLOR 5
38,048
B: Hokkaido University Hard 泚意 問題蚭定は A 問題ず同䞀のものですが、制玄のみが異なりたすのでご泚意ください。 物語 北海道倧孊に合栌し、新たな生掻の始たりに心を躍らせるほむらちゃん。しかし圌女の前には、ずお぀もなく広いキャンパスが埅ち受けおいた...。 「え...次の授業に間に合わないんだけど...」 問題 北海道倧孊札幌キャンパスは異垞に広いこずで有名です。札幌キャンパスは瞊に H マス、暪に W マス䞊んだ長方圢のマス目で衚珟されたす。北から i マス、西から j マス進んだマスを (i,j) で衚すこずにしたす。キャンパス内にはいく぀か建物があり、マス (i,j) で衚される䜍眮に建物がある堎合は 'B' 、ない堎合は '.' が c_{i,j} に曞かれおいたす。 北海道倧孊の新入生のほむらちゃんは、キャンパスのあたりの広さに驚愕し、建物間の移動が心配になっおきたした。そこで、建物のある 2 ぀のマスのうち、最も遠い組はどれくらい離れおいるのかが気になりたした。ここで、 2 ぀のマスの組 (i,j) , (i',j') の間の距離を |i-i'|+|j-j'| ず定矩したす。 ほむらちゃんは、自分にはこの問題は難しいず思い、同玚生のあなたに助けを求めおきたした。ほむらちゃんの代わりに答えを求めおください。 入力圢匏 H W c_{11} c_{12} ... c_{1W} : c_{H1} c_{H2} ... c_{HW} 制玄 2 \leq H,W \leq 10^3 H,W は敎数 c_{i,j} は 'B' か '.' のいずれかである。 c_{i,j} のうち少なくずも 2 ぀は 'B' である。 出力圢匏 答えを衚す敎数を 1 行に出力せよ。 入力䟋 1 3 3 B.B ..B .BB 出力䟋 1 4 (1,1) ず (3,3) の 2 点間が最長です。 入力䟋 2 4 3 B.. B.. ... ... 出力䟋 2 1 隣り合う䜍眮が最長になる堎合もありたす。 入力䟋 3 6 6 ...B.. B.B.B. .B.B.B ...B.B .B..B. ..B... 出力䟋 3 7
38,049
Print a Rectangle Draw a rectangle which has a height of H cm and a width of W cm. Draw a 1-cm square by single '#'. Input The input consists of multiple datasets. Each dataset consists of two integers H and W separated by a single space. The input ends with two 0 (when both H and W are zero). Output For each dataset, print the rectangle made of H × W '#'. Print a blank line after each dataset. Constraints 1 ≀ H ≀ 300 1 ≀ W ≀ 300 Sample Input 3 4 5 6 2 2 0 0 Sample Output #### #### #### ###### ###### ###### ###### ###### ## ##
38,050
Folding a Ribbon Think of repetitively folding a very long and thin ribbon. First, the ribbon is spread out from left to right, then it is creased at its center, and one half of the ribbon is laid over the other. You can either fold it from the left to the right, picking up the left end of the ribbon and laying it over the right end, or from the right to the left, doing the same in the reverse direction. To fold the already folded ribbon, the whole layers of the ribbon are treated as one thicker ribbon, again from the left to the right or the reverse. After folding the ribbon a number of times, one of the layers of the ribbon is marked, and then the ribbon is completely unfolded restoring the original state. Many creases remain on the unfolded ribbon, and one certain part of the ribbon between two creases or a ribbon end should be found marked. Knowing which layer is marked and the position of the marked part when the ribbon is spread out, can you tell all the directions of the repeated folding, from the left or from the right? The figure below depicts the case of the first dataset of the sample input. Input The input consists of at most 100 datasets, each being a line containing three integers. n i j The three integers mean the following: The ribbon is folded n times in a certain order; then, the i -th layer of the folded ribbon, counted from the top, is marked; when the ribbon is unfolded completely restoring the original state, the marked part is the j -th part of the ribbon separated by creases, counted from the left. Both i and j are one-based, that is, the topmost layer is the layer 1 and the leftmost part is numbered 1. These integers satisfy 1 ≀ n ≀ 60, 1 ≀ i ≀ 2 n , and 1 ≀ j ≀ 2 n . The end of the input is indicated by a line with three zeros. Output For each dataset, output one of the possible folding sequences that bring about the result specified in the dataset. The folding sequence should be given in one line consisting of n characters, each being either L or R . L means a folding from the left to the right, and R means from the right to the left. The folding operations are to be carried out in the order specified in the sequence. Sample Input 3 3 2 12 578 2214 59 471605241352156968 431565444592236940 0 0 0 Output for the Sample Input LRR RLLLRRRLRRLL LRRRLRRLLRRRRLLLLRLLRRRLRRLLRLLLLLLRLRLLRLRLLLRLRLLRLLRRRLL
38,051
Score : 800 points Problem Statement You are given a simple connected undirected graph consisting of N vertices and M edges. The vertices are numbered 1 to N , and the edges are numbered 1 to M . Edge i connects Vertex a_i and b_i bidirectionally. Determine if three circuits (see Notes) can be formed using each of the edges exactly once. Notes A circuit is a cycle allowing repetitions of vertices but not edges. Constraints All values in input are integers. 1 \leq N,M \leq 10^{5} 1 \leq a_i, b_i \leq N The given graph is simple and connected. Input Input is given from Standard Input in the following format: N M a_1 b_1 : a_M b_M Output If three circuits can be formed using each of the edges exactly once, print Yes ; if they cannot, print No . Sample Input 1 7 9 1 2 1 3 2 3 1 4 1 5 4 5 1 6 1 7 6 7 Sample Output 1 Yes Three circuits can be formed using each of the edges exactly once, as follows: Sample Input 2 3 3 1 2 2 3 3 1 Sample Output 2 No Three circuits are needed. Sample Input 3 18 27 17 7 12 15 18 17 13 18 13 6 5 7 7 1 14 5 15 11 7 6 1 9 5 4 18 16 4 6 7 2 7 11 6 3 12 14 5 2 10 5 7 8 10 15 3 15 9 8 7 15 5 16 18 15 Sample Output 3 Yes
38,052
Convex-Cut N個の頂点からなる凞倚角圢が䞎えられる。各頂点の座暙は反時蚈呚りに(X 1 , Y 1 ), (X 2 ,Y 2 ), 

, (X N , Y N )で衚わされる。 点Pを通るどのような盎線で凞倚角圢を切断しおも、切断埌に埗られる2぀の凞倚角圢の面積が等しいような点Pの座暙を求めよ。 Input 入力は以䞋の圢匏で䞎えられる。 N X 1 Y 1 X 2 Y 2 

 X N Y N Constraints 入力は党お敎数である 3 ≀ N ≀ 50 0 ≀ |X i |, |Y i | ≀ 1000000 入力の倚角圢は単玔な凞倚角圢である。 出力は、出力座暙を(X, Y)、厳密解を(cX, cY)ずした時にmax(|X-cX|, |Y-cY|) ≀ 0.0001を満たす必芁がある Output 問題文の条件を満たす点があるのならば、その点の座暙を X Y の圢匏で出力せよ。 点が存圚しない堎合は"NA"ず1行に出力せよ。 Sample Input 1 4 100 100 0 100 0 0 100 0 以䞋の図に察応する。 Output for the Sample Input 1 50.00000 50.00000 Sample Input 2 3 100 100 0 100 0 0 Output for the Sample Input 2 NA 以䞋の図に察応する。
38,053
Alternate Escape アリスハりス AliceずBobはボヌドゲヌムで遊んでいる このボヌドゲヌムは H 行 W 列のマス目が曞かれた盀面ず1぀のコマを䜿っお遊ぶ このゲヌムでは盀面の巊䞊のマスを1行1列目ずしお䞋方向に行を右方向に列を数える マス同士が隣接する蟺ずマスが盀面の倖偎ず接する蟺には壁を眮けるようになっおいおゲヌムの開始時にはそれぞれの蟺に぀いお壁の有無が指定されおいるたたゲヌムの開始時にはコマが盀面のマスのいずれか1箇所に眮かれおいる AliceずBobは亀互に手番をこなすこずでゲヌムを進める ゲヌムはAliceの手番から始たる Aliceの目的はコマを盀面の倖たで動かしお迷路から脱出させるこずである Aliceが1手でできる行動はコマを今ある䜍眮のマスから䞊䞋巊右に隣接するマスのうち間の蟺に壁がない方向のいずれかに移動させるこずである コマの今あるマスが盀面の倖偎に接しおいお間の蟺に壁がない堎合そこからコマを脱出させるこずができる 䞀方Bobの目的はコマの脱出を劚害するこずである Bobの手番では壁の有無を反転させるか䜕もせずに手番を終えるかを遞ぶこずができる 壁の有無を反転させるこずを遞んだ堎合盀面のすべおのマスの蟺に぀いお壁の有無が反転する 盀面の初期状態ずコマの初期䜍眮が䞎えられるのでAliceずBobの䞡者が最適な行動をずったずきにAliceがコマを盀面から脱出させられるか刀定せよ ただしAliceの手番においおコマが4方向ずも壁で囲たれおしたった堎合は脱出できないずみなす Input 入力は40個以䞋のデヌタセットからなる それぞれのデヌタセットは次の圢匏で䞎えられる H W R C Horz 1,1 Horz 1,2 ... Horz 1, W Vert 1,1 Vert 1,2 ... Vert 1, W +1 ... Vert H ,1 Vert H ,2 ... Vert H , W +1 Horz H +1,1 Horz H +1,2 ... Horz H +1, W 1行目には4぀の敎数 H , W (1 ≀ H , W ≀ 500), R , C (1 ≀ R ≀ H , 1 ≀ C ≀ W ) が䞎えられる これらは盀面が H 行 W 列のマス目からなりコマの初期䜍眮が R 行 C 列目であるこずを衚す 続く 2 H + 1 行には盀面の初期状態が䞎えられる 2 i 行目 (1 ≀ i ≀ H + 1) は W 個の敎数 Horz i ,1 , Horz i ,2 , ..., Horz i , W を含む Horz i , j は i 行 j 列目のマスの䞊偎の蟺に壁が有るずき1で無いずき0である ただし Horz H +1, j は H 行 j 列目のマスの䞋偎の蟺における壁の有無を衚す 2 i + 1 行目 (1 ≀ i ≀ H ) は W + 1 個の敎数 Vert i ,1 , Vert i ,2 , ..., Vert i , W +1 を含む Vert i , j は i 行 j 列目のマスの巊偎の蟺に壁が有るずき1で無いずき0である ただし Vert i , W +1 は i 行 W 列目のマスの右偎の蟺における壁の有無を衚す 入力の終わりは4぀のれロからなる1行で瀺される Output それぞれのデヌタセットに぀いおAliceがコマを盀面から脱出させられる堎合は" Yes "できない堎合は" No "ず1行に出力せよ Sample Input 3 3 2 2 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 3 3 2 2 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 3 1 1 1 1 1 1 0 0 1 1 0 1 2 2 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 Output for Sample Input Yes No Yes No Hint 1぀目のデヌタセットではAliceは次のように動くこずでコマを脱出させられる。 初期状態 Aliceがコマを巊に動かす Bobは脱出を阻止するために壁を反転させる Aliceがコマを䞊に動かす Bobが次の手番で壁の有無を反転させおもさせなくおも、 Aliceは次の手番でコマを脱出させられる。
38,054
Score : 300 points Problem Statement Snuke has a calculator. It has a display and two buttons. Initially, the display shows an integer x . Snuke wants to change this value into another integer y , by pressing the following two buttons some number of times in arbitrary order: Button A: When pressed, the value on the display is incremented by 1 . Button B: When pressed, the sign of the value on the display is reversed. Find the minimum number of times Snuke needs to press the buttons to achieve his objective. It can be shown that the objective is always achievable regardless of the values of the integers x and y . Constraints x and y are integers. |x|, |y| ≀ 10^9 x and y are different. Input The input is given from Standard Input in the following format: x y Output Print the minimum number of times Snuke needs to press the buttons to achieve his objective. Sample Input 1 10 20 Sample Output 1 10 Press button A ten times. Sample Input 2 10 -10 Sample Output 2 1 Press button B once. Sample Input 3 -10 -20 Sample Output 3 12 Press the buttons as follows: Press button B once. Press button A ten times. Press button B once.
38,055
Problem B: Polygonal Line Search Multiple polygonal lines are given on the xy -plane. Given a list of polygonal lines and a template, you must find out polygonal lines which have the same shape as the template. A polygonal line consists of several line segments parallel to x -axis or y -axis. It is defined by a list of xy -coordinates of vertices from the start-point to the end-point in order, and always turns 90 degrees at each vertex. A single polygonal line does not pass the same point twice. Two polygonal lines have the same shape when they fully overlap each other only with rotation and translation within xy -plane (i.e. without magnification or a flip). The vertices given in reverse order from the start-point to the end-point is the same as that given in order. Figure 1 shows examples of polygonal lines. In this figure, polygonal lines A and B have the same shape. Write a program that answers polygonal lines which have the same shape as the template. Figure 1: Polygonal lines Input The input consists of multiple datasets. The end of the input is indicated by a line which contains a zero. A dataset is given as follows. n Polygonal line 0 Polygonal line 1 Polygonal line 2 ... Polygonal line n n is the number of polygonal lines for the object of search on xy -plane. n is an integer, and 1 <= n <= 50. Polygonal line 0 indicates the template. A polygonal line is given as follows. m x 1 y 1 x 2 y 2 ... x m y m m is the number of the vertices of a polygonal line (3 <= m <= 10). x i and y i , separated by a space, are the x - and y -coordinates of a vertex, respectively (-10000 < x i < 10000, -10000 < y i < 10000). Output For each dataset in the input, your program should report numbers assigned to the polygonal lines that have the same shape as the template, in ascending order. Each number must be written in a separate line without any other characters such as leading or trailing spaces. Five continuous "+"s must be placed in a line at the end of each dataset. Sample Input 5 5 0 0 2 0 2 1 4 1 4 0 5 0 0 0 2 -1 2 -1 4 0 4 5 0 0 0 1 -2 1 -2 2 0 2 5 0 0 0 -1 2 -1 2 0 4 0 5 0 0 2 0 2 -1 4 -1 4 0 5 0 0 2 0 2 1 4 1 4 0 4 4 -60 -75 -60 -78 -42 -78 -42 -6 4 10 3 10 7 -4 7 -4 40 4 -74 66 -74 63 -92 63 -92 135 4 -12 22 -12 25 -30 25 -30 -47 4 12 -22 12 -25 30 -25 30 47 3 5 -8 5 -8 2 0 2 0 4 8 4 5 -3 -1 0 -1 0 7 -2 7 -2 16 5 -1 6 -1 3 7 3 7 5 16 5 5 0 1 0 -2 8 -2 8 0 17 0 0 Output for the Sample Input 1 3 5 +++++ 3 4 +++++ +++++
38,056
Score : 100 points Problem Statement This contest is CODE FESTIVAL . However, Mr. Takahashi always writes it CODEFESTIVAL , omitting the single space between CODE and FESTIVAL . So he has decided to make a program that puts the single space he omitted. You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s . Constraints s contains exactly 12 letters. All letters in s are uppercase English letters. Input The input is given from Standard Input in the following format: s Output Print the string putting a single space between the first 4 letters and last 8 letters in the string s . Put a line break at the end. Sample Input 1 CODEFESTIVAL Sample Output 1 CODE FESTIVAL Putting a single space between the first 4 letters and last 8 letters in CODEFESTIVAL makes it CODE FESTIVAL . Sample Input 2 POSTGRADUATE Sample Output 2 POST GRADUATE Sample Input 3 ABCDEFGHIJKL Sample Output 3 ABCD EFGHIJKL
38,057
Score: 600 points Problem Statement There is a grass field that stretches infinitely. In this field, there is a negligibly small cow. Let (x, y) denote the point that is x\ \mathrm{cm} south and y\ \mathrm{cm} east of the point where the cow stands now. The cow itself is standing at (0, 0) . There are also N north-south lines and M east-west lines drawn on the field. The i -th north-south line is the segment connecting the points (A_i, C_i) and (B_i, C_i) , and the j -th east-west line is the segment connecting the points (D_j, E_j) and (D_j, F_j) . What is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print INF instead. Constraints All values in input are integers between -10^9 and 10^9 (inclusive). 1 \leq N, M \leq 1000 A_i < B_i\ (1 \leq i \leq N) E_j < F_j\ (1 \leq j \leq M) The point (0, 0) does not lie on any of the given segments. Input Input is given from Standard Input in the following format: N M A_1 B_1 C_1 : A_N B_N C_N D_1 E_1 F_1 : D_M E_M F_M Output If the area of the region the cow can reach is infinite, print INF ; otherwise, print an integer representing the area in \mathrm{cm^2} . (Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite.) Sample Input 1 5 6 1 2 0 0 1 1 0 2 2 -3 4 -1 -2 6 3 1 0 1 0 1 2 2 0 2 -1 -4 5 3 -2 4 1 2 4 Sample Output 1 13 The area of the region the cow can reach is 13\ \mathrm{cm^2} . Sample Input 2 6 1 -3 -1 -2 -3 -1 1 -2 -1 2 1 4 -2 1 4 -1 1 4 1 3 1 4 Sample Output 2 INF The area of the region the cow can reach is infinite.
38,058
勢力の予想 信倫くんず静倫くんは長方圢の島で領地を取り合うゲヌムをしおいたす。䞋の図①のように、島党䜓は栌子状に区切られた正方圢の区画でできおおり、区画にはそこから生じる損埗が敎数で瀺されおいたす。 このゲヌムでは぀の駒を動かしお領地の境界線を決めおいきたす。ゲヌム開始時、駒は島の北西端にありたす図①。この駒を島の南東端たで動かしおいったずきの駒の軌跡が領地の境界線ずなりたす。二人のプレヌダヌは亀互に駒を動かしたす。駒は南隣の栌子点か東隣の栌子点にのみ動かすこずができたす図②。駒が島の端に到達した堎合は、南か東のうち動かせる方向に動かしたす。駒が南東端に到達したらゲヌム終了です。 ゲヌム終了埌の境界線から北東偎の領域が先攻プレヌダヌの領域、南西偎の領域が埌攻プレヌダヌの領 域です図③。各プレヌダヌの領域内に含たれる、区画から生じる損埗の合蚈がそのプレヌダヌのス コアずなりたす。二人ずもゲヌムにはかなり慣れおおり、最終的に自分のスコアから盞手のスコアをひ いた倀が䞀番倧きくなるように正確に駒を動かしたす。 島の倧きさずそれぞれの区画から生じる損埗が䞎えられたずき、ゲヌム終了時の結果を蚈算するプログラムを䜜成せよ。結果は、信倫くんず静倫くんのスコアの差の絶察倀ずする。 Input 入力は以䞋の圢匏で䞎えられる。 W H s 1,1 s 1,2 ... s 1,W s 2,1 s 2,2 ... s 2,W : s H,1 s H,2 ... s H,W 行目に島に含たれる東西方向ず南北方向の区画の数 W , H (1 ≀ W , H ≀ 1000) が䞎えられる。続く H 行に i 行 j 列目の区画から生じる損埗 s i,j (-1000 ≀ s i,j ≀ 1000) が䞎えられる。ただし、 i の倀が増加する方向を南、 j の倀が増加する方向を東ずする。 Output 信倫くんず静倫くんのスコアの差の絶察倀を行に出力する。 Sample Input 1 2 1 -2 1 Sample Output 1 1 Sample Input 2 2 2 2 -3 3 -1 Sample Output 2 3 Sample Input 3 5 4 5 3 2 -5 2 2 -4 2 8 -4 2 3 -7 6 7 3 -4 10 -3 -3 Sample Output 3 5
38,059
C たったひず぀の郚分列 - Unique Subsequence - 問題 ある日えびちゃんは、机の䞊に長さ n のテキスト文字列 T ず長さ m のパタヌン文字列 P ( m \leq n ) が眮かれおいるこずに気づきたした。えびちゃんは、文字列に珟れる「たったひず぀の郚分列」が倧奜きであるため、 P が T のたったひず぀の郚分列であるかどうかをすぐに調査し始めたした。 P が T のたったひず぀の郚分列であるずいう性質は以䞋のように衚されたす。ここで、文字列 X の i 文字目を X_i ず曞きたす。 長さ m の数列 S = (s_1, ..., s_m) (ただし、 s_1 < s_2 < ... < s_m ) で、各 i ( i = 1, ..., m ) に぀いお T_{s_i} = P_i である数列 S が䞀意に定たる。 調査を始めおから数時間、えびちゃんは文字列をぐっず睚んでいたしたが、文字列が長すぎるために疲れおしたったようです。それを芋かねたあなたは、えびちゃんを手䌝っおあげるこずにしたした。えびちゃんのために、 P が T のたったひず぀の郚分列であるならば “yes” を、そうでないならば “no” を出力するプログラムを䜜成しおください。 入力圢匏 T P 1 行目には、テキスト文字列 T が䞎えられる。 2 行目には、パタヌン文字列 P が䞎えられる。 制玄 1 \leq |P| \leq |T| \leq 5 \times 10^5 T および P は英字小文字 ‘a’-’z’ で構成される。 出力圢匏 P が T のたったひず぀の郚分列であるならば “yes” を、そうでないならば “no” を1行に出力しおください。 入力䟋1 aizucamp azu 出力䟋1 yes 入力䟋2 abracadabra rada 出力䟋2 no 入力䟋3 hokkaido dekai 出力䟋3 no
38,060
Problem F: Cutting a Chocolate Turtle Shi-ta and turtle Be-ko decided to divide a chocolate. The shape of the chocolate is rectangle. The corners of the chocolate are put on (0,0), ( w ,0), ( w , h ) and (0, h ). The chocolate has lines for cutting. They cut the chocolate only along some of these lines. The lines are expressed as follows. There are m points on the line connected between (0,0) and (0, h ), and between ( w ,0) and ( w , h ). Each i -th point, ordered by y value ( i = 0 then y =0), is connected as cutting line. These lines do not share any point where 0 < x < w . They can share points where x = 0 or x = w . However, (0, l i ) = (0, l j ) and ( w , r i ) = ( w , r j ) implies i = j . The following figure shows the example of the chocolate. There are n special almonds, so delicious but high in calories on the chocolate. Almonds are circle but their radius is too small. You can ignore radius of almonds. The position of almond is expressed as ( x , y ) coordinate. Two turtles are so selfish. Both of them have requirement for cutting. Shi-ta's requirement is that the piece for her is continuous. It is possible for her that she cannot get any chocolate. Assume that the minimum index of the piece is i and the maximum is k . She must have all pieces between i and k . For example, chocolate piece 1,2,3 is continuous but 1,3 or 0,2,4 is not continuous. Be-ko requires that the area of her chocolate is at least S . She is worry about her weight. So she wants the number of almond on her chocolate is as few as possible. They doesn't want to make remainder of the chocolate because the chocolate is expensive. Your task is to compute the minumum number of Beko's almonds if both of their requirment are satisfied. Input Input consists of multiple test cases. Each dataset is given in the following format. n m w h S l 0 r 0 ... l m-1 r m-1 x 0 y 0 ... x n-1 y n-1 The last line contains five 0s. n is the number of almonds. m is the number of lines. w is the width of the chocolate. h is the height of the chocolate. S is the area that Be-ko wants to eat. Input is integer except x i y i . Input satisfies following constraints. 1 ≀ n ≀ 30000 1 ≀ m ≀ 30000 1 ≀ w ≀ 200 1 ≀ h ≀ 1000000 0 ≀ S ≀ w*h If i < j then l i ≀ l j and r i ≀ r j and then i -th lines and j -th lines share at most 1 point. It is assured that l m-1 and r m-1 are h . x i y i is floating point number with ten digits. It is assured that they are inside of the chocolate. It is assured that the distance between points and any lines is at least 0.00001. Output You should output the minumum number of almonds for Be-ko. Sample input 2 3 10 10 50 3 3 6 6 10 10 4.0000000000 4.0000000000 7.0000000000 7.0000000000 2 3 10 10 70 3 3 6 6 10 10 4.0000000000 4.0000000000 7.0000000000 7.0000000000 2 3 10 10 30 3 3 6 6 10 10 4.0000000000 4.0000000000 7.0000000000 7.0000000000 2 3 10 10 40 3 3 6 6 10 10 4.0000000000 4.0000000000 7.0000000000 7.0000000000 2 3 10 10 100 3 3 6 6 10 10 4.0000000000 4.0000000000 7.0000000000 7.0000000000 0 0 0 0 0 Sample output 1 1 0 1 2
38,061
Print Many Hello World Write a program which prints 1000 "Hello World". Input There is no input for this problem. Output The output consists of 1000 lines. Print "Hello World" in each line. Sample Input No input Sample Output Hello World Hello World Hello World Hello World Hello World Hello World Hello World . . . . . . Hello World
38,062
䞊叞のおごり 䌚接倪郎さんの䌚瀟には、割り切れない事が倧嫌いな䞊叞がいたす。倪郎さんがその䞊叞ず食事に行くずきは、割り勘で䌚蚈をしおいるのですが、支払金額が参加人数で割り切れないずきは、い぀も䞊叞がおごっおくれおいたす。 ある日、倪郎さんは食事䌚の幹事になりたした。お金の少ない倪郎さんは、その䞊叞を誘っおなんずかおごっおもらえるように出来ないか考えたした。もう料理屋に泚文をしなければならないのですが、ただ䜕人参加するかは分からないので、どんな人数が参加しおもおごっおもらえるような泚文をしおおきたいようです。倪郎さんの同期で、同じく食事䌚に参加する予定のあなたは、倪郎さんに協力しお、予算額以䞋で最倧のどんな人数でも割り切れない金額を算出するこずにしたした。 料理の皮類、各料理の料金、予算額を入力ずし、予算額以䞋で最倧のどんな数字でも割り切れない合蚈金額(ただし、 1 ず合蚈金額は陀く)を出力するプログラムを䜜成しおください。なお、各皮類の料理は耇数個泚文できたすが、党皮類の料理を泚文する必芁はありたせん。ただし、このような合蚈金額がない堎合は、 NA ず出力しおください。 Input 耇数のデヌタセットの䞊びが入力ずしお䞎えられたす。 入力の終わりはれロふた぀の行で瀺されたす。 各デヌタセットは以䞋の圢匏で䞎えられたす。 n x v 1 v 2 : v n 1 行目に料理の皮類 n (1 ≀ n ≀ 30) ず予算額 x (1 ≀ x ≀ 1000000) が空癜区切りで䞎えられたす。続く n 行に i 皮類目の料理の金額を衚す敎数 v i (1 ≀ v i ≀ 1000000) が䞎えられたす。 デヌタセットの数は 100 を超えたせん。 Output 入力デヌタセットごずに、予算額に最も近い合蚈金額、たたは NA を行に出力したす。 Sample Input 4 15000 305 260 129 500 3 400 10 20 30 3 200909 5 9 12 0 0 Output for the Sample Input 14983 NA 200909
38,063