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문제

상근이는 토끼 N마리를 키우고 있다. 그는 매일 매일 토끼에게 다양한 야채와 과일을 먹이로 주고 있었다. 그러나, 상근이의 토끼는 딸기를 가장 좋아한다. 하지만 겨울에는 딸기를 구하기가 매우 어렵고, 가격도 비싸다. 따라서 상근이는 일부 토끼에게만 딸기를 주기로 했다.

상근이 토끼의 이름은 숫자이고, 1번부터 N번이다. 상근이는 각 토끼가 먹는 딸기의 양을 기록을 하기 위해서 다음과 같은 방법을 이용한다.

매일 상근이는 딸기 S개를 구매한다. 그러고 난 뒤, A번 토끼에게 첫 번째 딸기를, A+1번 토끼에게 두 번째 딸기를, A+2번 토끼에게 세 번째 딸기를,.... 준다.

모든 토끼는 비어있는 성냥갑을 가지고 있고, 이 성냥갑은 한 줄로 놓여져 있다.

K·K ≤ N을 만족하는 가장 큰 K를 고른다. 그 다음 첫 성냥갑부터 K개씩 그룹을 지어준다. 각 성냥갑의 앞에는 컵을 하나씩 놓는다. 이렇게 연속하는 K개 성냥갑과 컵을 블록이라고 한다.

토끼에게 딸기를 준 다음에, 상근이는 딸기를 받은 토끼의 성냥갑에 성냥을 넣는다. 이때, 어떤 블록에 모든 성냥갑에 성냥을 넣어야된다면, 성냥갑 대신에 컵에 성냥을 넣는다. 

위의 방법을 사용하면, 각 토끼가 지금까지 먹은 딸기의 수는 성냥갑과 컵에 들어있는 성냥의 수가 된다.

예를 들어, 위와 같이 토끼가 11마리 있다고하자. 그럼 N = 11이 된다. 이때, K를 구하면 K = 3이 된다. 따라서, 총 네 개의 블록이 있을 것이고, 마지막 블록에는 성냥갑이 2개만 있을 것이다. 만약, 상근이가 딸기를 6개 사왔고, 5번 토끼부터 딸기를 준다면, 성냥갑과 컵에 들어있는 성냥은 아래와 같이 된다.

토끼의 수 N이 주어지고, M일동안 구매한 딸기의 수와 토끼에게 준 방법이 주어진다. 이때, 상근이가 그날 성냥을 넣은 성냥갑과 컵에 들어있는 성냥의 수를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 N과 M이 공백으로 구분되어 주어진다. (1 ≤ N, M ≤ 100000)

다음 M개 줄에는 각 날 상근이가 구매한 딸기의 수 S와 딸기를 주기 시작하는 토끼의 번호 A가 주어진다. (1 ≤ A ≤ N, 1 ≤ A+S–1 ≤ N)

출력

출력은 총 M개의 숫자를 출력해야 한다. k번째 줄에는 k번째 날에 성냥을 넣은 성냥갑과 컵에 들어있는 성냥의 수를 출력해야 한다.

예제 입력 1

11 3
6 5
3 1
11 1

예제 출력 1

4
1
6

예제 입력 2

16 3
2 2
12 3
6 11

예제 출력 2

2
7
3

힌트

예제 1의 경우에는 토끼가 11마리 있고, 블록이 4개있는 경우이다. (그림과 같은 경우)

첫째 날 상근이가 딸기를 주는 토끼의 번호는 5번부터 10번이다. 성냥갑 5,6,10번에는 성냥을 넣을 것이고, 세 번째 컵에 성냥갑을 넣는다. 첫째 날이기 때문에, 원래 성냥이 들어있는 성냥갑과 컵은 없다. 따라서 정답은 4가 된다.

둘째 날 상근이는 1번부터 3번토끼에게 딸기를 준다. 첫 번째 컵에 성냥을 넣으면 된다.

셋째 날에는 모든 토끼에게 딸기를 준다. 이런 경우에는 모든 컵에 성냥을 하나씩 넣으면 된다. 따라서, 정답은 6이 된다.

[{"problem_id":"2943","problem_lang":"0","title":"\ud1a0\ub07c","description":"<p>\uc0c1\uadfc\uc774\ub294 \ud1a0\ub07c N\ub9c8\ub9ac\ub97c \ud0a4\uc6b0\uace0 \uc788\ub2e4. \uadf8\ub294 \ub9e4\uc77c \ub9e4\uc77c \ud1a0\ub07c\uc5d0\uac8c \ub2e4\uc591\ud55c \uc57c\ucc44\uc640 \uacfc\uc77c\uc744 \uba39\uc774\ub85c \uc8fc\uace0 \uc788\uc5c8\ub2e4. \uadf8\ub7ec\ub098, \uc0c1\uadfc\uc774\uc758 \ud1a0\ub07c\ub294 \ub538\uae30\ub97c \uac00\uc7a5 \uc88b\uc544\ud55c\ub2e4. \ud558\uc9c0\ub9cc \uaca8\uc6b8\uc5d0\ub294 \ub538\uae30\ub97c \uad6c\ud558\uae30\uac00 \ub9e4\uc6b0 \uc5b4\ub835\uace0, \uac00\uaca9\ub3c4 \ube44\uc2f8\ub2e4. \ub530\ub77c\uc11c \uc0c1\uadfc\uc774\ub294 \uc77c\ubd80 \ud1a0\ub07c\uc5d0\uac8c\ub9cc \ub538\uae30\ub97c \uc8fc\uae30\ub85c \ud588\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774 \ud1a0\ub07c\uc758 \uc774\ub984\uc740 \uc22b\uc790\uc774\uace0, 1\ubc88\ubd80\ud130 N\ubc88\uc774\ub2e4. \uc0c1\uadfc\uc774\ub294 \uac01 \ud1a0\ub07c\uac00 \uba39\ub294 \ub538\uae30\uc758 \uc591\uc744 \uae30\ub85d\uc744 \ud558\uae30 \uc704\ud574\uc11c \ub2e4\uc74c\uacfc \uac19\uc740 \ubc29\ubc95\uc744 \uc774\uc6a9\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub9e4\uc77c \uc0c1\uadfc\uc774\ub294 \ub538\uae30 S\uac1c\ub97c \uad6c\ub9e4\ud55c\ub2e4. \uadf8\ub7ec\uace0 \ub09c \ub4a4, A\ubc88 \ud1a0\ub07c\uc5d0\uac8c \uccab \ubc88\uc9f8 \ub538\uae30\ub97c, A+1\ubc88 \ud1a0\ub07c\uc5d0\uac8c \ub450 \ubc88\uc9f8 \ub538\uae30\ub97c, A+2\ubc88 \ud1a0\ub07c\uc5d0\uac8c \uc138 \ubc88\uc9f8 \ub538\uae30\ub97c,.... \uc900\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ud1a0\ub07c\ub294 \ube44\uc5b4\uc788\ub294 \uc131\ub0e5\uac11\uc744 \uac00\uc9c0\uace0 \uc788\uace0, \uc774 \uc131\ub0e5\uac11\uc740 \ud55c \uc904\ub85c \ub193\uc5ec\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>K&middot;K &le; N\uc744 \ub9cc\uc871\ud558\ub294 \uac00\uc7a5 \ud070 K\ub97c \uace0\ub978\ub2e4. \uadf8 \ub2e4\uc74c \uccab \uc131\ub0e5\uac11\ubd80\ud130 K\uac1c\uc529 \uadf8\ub8f9\uc744 \uc9c0\uc5b4\uc900\ub2e4. \uac01 \uc131\ub0e5\uac11\uc758 \uc55e\uc5d0\ub294 \ucef5\uc744 \ud558\ub098\uc529 \ub193\ub294\ub2e4. \uc774\ub807\uac8c \uc5f0\uc18d\ud558\ub294 K\uac1c \uc131\ub0e5\uac11\uacfc \ucef5\uc744 \ube14\ub85d\uc774\ub77c\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ud1a0\ub07c\uc5d0\uac8c \ub538\uae30\ub97c \uc900 \ub2e4\uc74c\uc5d0, \uc0c1\uadfc\uc774\ub294 \ub538\uae30\ub97c \ubc1b\uc740 \ud1a0\ub07c\uc758 \uc131\ub0e5\uac11\uc5d0 \uc131\ub0e5\uc744 \ub123\ub294\ub2e4. \uc774\ub54c, \uc5b4\ub5a4 \ube14\ub85d\uc5d0 \ubaa8\ub4e0 \uc131\ub0e5\uac11\uc5d0 \uc131\ub0e5\uc744 \ub123\uc5b4\uc57c\ub41c\ub2e4\uba74, \uc131\ub0e5\uac11 \ub300\uc2e0\uc5d0 \ucef5\uc5d0 \uc131\ub0e5\uc744 \ub123\ub294\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uc704\uc758 \ubc29\ubc95\uc744 \uc0ac\uc6a9\ud558\uba74, \uac01 \ud1a0\ub07c\uac00 \uc9c0\uae08\uae4c\uc9c0 \uba39\uc740 \ub538\uae30\uc758 \uc218\ub294 \uc131\ub0e5\uac11\uacfc \ucef5\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc131\ub0e5\uc758 \uc218\uac00 \ub41c\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/4086d9b2-59ee-4da9-b214-e84cc774266e\/-\/preview\/\" style=\"width: 494px; height: 143px;\" \/><\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, \uc704\uc640 \uac19\uc774 \ud1a0\ub07c\uac00 11\ub9c8\ub9ac \uc788\ub2e4\uace0\ud558\uc790. \uadf8\ub7fc N = 11\uc774 \ub41c\ub2e4. \uc774\ub54c, K\ub97c \uad6c\ud558\uba74 K = 3\uc774 \ub41c\ub2e4. \ub530\ub77c\uc11c, \ucd1d \ub124 \uac1c\uc758 \ube14\ub85d\uc774 \uc788\uc744 \uac83\uc774\uace0, \ub9c8\uc9c0\ub9c9 \ube14\ub85d\uc5d0\ub294 \uc131\ub0e5\uac11\uc774 2\uac1c\ub9cc \uc788\uc744 \uac83\uc774\ub2e4. \ub9cc\uc57d, \uc0c1\uadfc\uc774\uac00 \ub538\uae30\ub97c 6\uac1c \uc0ac\uc654\uace0, 5\ubc88 \ud1a0\ub07c\ubd80\ud130 \ub538\uae30\ub97c \uc900\ub2e4\uba74, \uc131\ub0e5\uac11\uacfc \ucef5\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc131\ub0e5\uc740 \uc544\ub798\uc640 \uac19\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/a1f2e754-f870-42d6-abe1-e5137138c12d\/-\/preview\/\" style=\"width: 494px; height: 144px;\" \/><\/p>\r\n\r\n<p>\ud1a0\ub07c\uc758 \uc218 N\uc774 \uc8fc\uc5b4\uc9c0\uace0, M\uc77c\ub3d9\uc548 \uad6c\ub9e4\ud55c \ub538\uae30\uc758 \uc218\uc640 \ud1a0\ub07c\uc5d0\uac8c \uc900 \ubc29\ubc95\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub54c, \uc0c1\uadfc\uc774\uac00 \uadf8\ub0a0 \uc131\ub0e5\uc744 \ub123\uc740 \uc131\ub0e5\uac11\uacfc \ucef5\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc131\ub0e5\uc758 \uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 N\uacfc M\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; N, M &le; 100000)<\/p>\r\n\r\n<p>\ub2e4\uc74c M\uac1c \uc904\uc5d0\ub294 \uac01 \ub0a0 \uc0c1\uadfc\uc774\uac00 \uad6c\ub9e4\ud55c \ub538\uae30\uc758 \uc218 S\uc640 \ub538\uae30\ub97c \uc8fc\uae30 \uc2dc\uc791\ud558\ub294 \ud1a0\ub07c\uc758 \ubc88\ud638 A\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; A &le; N, 1 &le; A+S&ndash;1 &le; N)<\/p>\r\n","output":"<p>\ucd9c\ub825\uc740 \ucd1d M\uac1c\uc758 \uc22b\uc790\ub97c \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4. k\ubc88\uc9f8 \uc904\uc5d0\ub294 k\ubc88\uc9f8 \ub0a0\uc5d0 \uc131\ub0e5\uc744 \ub123\uc740 \uc131\ub0e5\uac11\uacfc \ucef5\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc131\ub0e5\uc758 \uc218\ub97c \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uc608\uc81c 1\uc758 \uacbd\uc6b0\uc5d0\ub294 \ud1a0\ub07c\uac00 11\ub9c8\ub9ac \uc788\uace0, \ube14\ub85d\uc774 4\uac1c\uc788\ub294 \uacbd\uc6b0\uc774\ub2e4. (\uadf8\ub9bc\uacfc \uac19\uc740 \uacbd\uc6b0)<\/p>\r\n\r\n<p>\uccab\uc9f8 \ub0a0 \uc0c1\uadfc\uc774\uac00 \ub538\uae30\ub97c \uc8fc\ub294 \ud1a0\ub07c\uc758 \ubc88\ud638\ub294 5\ubc88\ubd80\ud130 10\ubc88\uc774\ub2e4. \uc131\ub0e5\uac11 5,6,10\ubc88\uc5d0\ub294 \uc131\ub0e5\uc744 \ub123\uc744 \uac83\uc774\uace0, \uc138 \ubc88\uc9f8 \ucef5\uc5d0 \uc131\ub0e5\uac11\uc744 \ub123\ub294\ub2e4. \uccab\uc9f8 \ub0a0\uc774\uae30 \ub54c\ubb38\uc5d0, \uc6d0\ub798 \uc131\ub0e5\uc774 \ub4e4\uc5b4\uc788\ub294 \uc131\ub0e5\uac11\uacfc \ucef5\uc740 \uc5c6\ub2e4. \ub530\ub77c\uc11c \uc815\ub2f5\uc740 4\uac00 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\ub458\uc9f8 \ub0a0 \uc0c1\uadfc\uc774\ub294 1\ubc88\ubd80\ud130 3\ubc88\ud1a0\ub07c\uc5d0\uac8c \ub538\uae30\ub97c \uc900\ub2e4. \uccab \ubc88\uc9f8 \ucef5\uc5d0 \uc131\ub0e5\uc744 \ub123\uc73c\uba74 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc14b\uc9f8 \ub0a0\uc5d0\ub294 \ubaa8\ub4e0 \ud1a0\ub07c\uc5d0\uac8c \ub538\uae30\ub97c \uc900\ub2e4. \uc774\ub7f0 \uacbd\uc6b0\uc5d0\ub294 \ubaa8\ub4e0 \ucef5\uc5d0 \uc131\ub0e5\uc744 \ud558\ub098\uc529 \ub123\uc73c\uba74 \ub41c\ub2e4. \ub530\ub77c\uc11c, \uc815\ub2f5\uc740 6\uc774 \ub41c\ub2e4.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"2943","problem_lang":"1","title":"JAGODA","description":"<p>Slavko has N rabbits that he feeds every day with various fruits and vegetables. Rabbits, however, prefer strawberries above all else. Strawberries are hard to find and expensive in the middle of winter, so Slavko only gives strawberries to part of his rabbits.&nbsp;<\/p>\r\n\r\n<p>Slavko numbered the rabbits 1 through N. To help keep track of how many strawberries each of the rabbits got, Slavko decided on the following strawberry allocation procedure.&nbsp;<\/p>\r\n\r\n<p>Every day Slavko purchases some number S of strawberries and chooses some rabbit A to get the first strawberry. Rabbit A+1 will get the second strawberry, rabbit A+2 the third etc.&nbsp;<\/p>\r\n\r\n<p>Every rabbit is assigned an initially empty matchbox, the N matchboxes forming a single row.&nbsp;<\/p>\r\n\r\n<p>Let K be the largest integer such that K&middot;K &le; N. Every group of K matchboxes (starting with the first) will also have a cup next to them. We say that K consecutive matchboxes with their cup form a block.&nbsp;<\/p>\r\n\r\n<p>After giving the rabbits their strawberries, Slavko will put a single match into the matchbox of every rabbit that got a strawberry, unless he would be putting a match into all matchboxes in a block. Instead of putting matches into all matchboxes in a block, he will put a single match in the appropriate cup.&nbsp;<\/p>\r\n\r\n<p>The total number of strawberries received by a rabbit can be calculated as the number of matches in its matchbox plus the number of matches in its cup.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/4086d9b2-59ee-4da9-b214-e84cc774266e\/-\/preview\/\" style=\"width: 494px; height: 143px;\" \/><\/p>\r\n\r\n<p>For example, assume that there are 11 rabbits, that is N=11. The number three is the largest integer which, when squared, gives a result of at most 11, so K=3. There will be four blocks, the last of them incomplete with only two matchboxes. If Slavko buys 6 strawberries and gives the first of them to rabbit 5, the state in the cups and matchboxes will be:&nbsp;<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/a1f2e754-f870-42d6-abe1-e5137138c12d\/-\/preview\/\" style=\"width: 494px; height: 144px;\" \/><\/p>\r\n\r\n<p>Write a program that simulates the above procedure, knowing the number of rabbits N, the number of days M and the numbers S and A for each of the M days.&nbsp;<\/p>\r\n\r\n<p>For every day, output the total number of matches in all matchboxes and cups that Slavko added matches to on that day.&nbsp;<\/p>\r\n","input":"<p>The first line contains the integers N and M separated by a space (1 &le; N, M &le; 100000), the number of rabbits and days.&nbsp;<\/p>\r\n\r\n<p>Each of the following M lines contains two integers S and A separated by a space. These numbers mean that Slavko purchased S strawberries that day and that rabbit A will receive the first one (1 &le; A &le; N, 1 &le; A+S&ndash;1 &le; N).&nbsp;<\/p>\r\n","output":"<p>Output M numbers, each on a separate line. The k-th line should contain the total number of matches in all matchboxes and cups that Slavko used on day k.&nbsp;<\/p>\r\n","hint":"<p>In the first example, there are 11 rabbits and matchboxes, and four blocks, as shown in the image on the previous page.&nbsp;<\/p>\r\n\r\n<ol>\r\n\t<li>On the first day, Slavko gives strawberries to rabbits 5 through 10, putting matches into matchboxes 5, 6 and 10, and one into the third cup. Before this there were no other matches in the matchboxes and cups he used, so the output is four.&nbsp;<\/li>\r\n\t<li>On the second day, Slavko gives strawberries to rabbits 1 through 3, putting just one match into the first cup.&nbsp;<\/li>\r\n\t<li>On the third day, Slavko gives strawberries to all his rabbits, putting one match into every cup. After putting the four matches into cups, there is a total of six matches in the cups he used, so the output is six.&nbsp;<\/li>\r\n<\/ol>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

Contest > Croatian Open Competition in Informatics > COCI 2008/2009 > Contest #5 3번