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문제

민혁이가 휴학을 한 이유는 집에서 게임을 실컷 하기 위해서이다. 민혁이가 주로 하는 게임은 FPS 게임이다. 이 게임은 맵을 돌아다니면서 상대방을 물총으로 쏘는 게임이다. 지금 민혁이네 팀에는 총 N명의 플레이어가 게임을 하고 있다. 각 플레이어는 두 능력치 속도와 사정거리가 있다. 플레이어 A가 B보다 게임을 잘하려면 A의 두 능력치가 모두 B의 능력치보다 커야 한다.

민혁이는 게임을 더욱 재밌게 하기 위해서 봇 K개를 게임에 추가하려고 한다. 봇은 컴퓨터가 조정하며, 인간 플레이어와 동일한 방법으로 게임에 참가한다. 각 봇도 인간 플레이어와 같이 두 개의 능력치가 있다. 또, 봇의 능력치가 봇끼리 겹치는 경우는 없다. 즉, (1, 2)를 가진 봇을 선택한다면, 속도가 1이거나 사정거리가 2인 봇은 선택할 수 없다. (인간 플레이어와는 겹칠 수도 있다) 또, 봇이 너무 강력해서 게임이 재미 없어지는 것을 막기 위해서 각각의 봇보다 게임을 잘하는 인간 플레이어가 적어도 한 명은 있다. 

봇을 추가 하기 전에 민혁이네 팀은 지금 한 명을 기다리고 있다. 민혁이네 팀에 들어오고 싶어하는 플레이어는 총 Q명이다. 민혁이는 후보자 중 각각을 추가했을 때, 봇 K개를 선택하는 방법의 수를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 N과 K가 주어진다. (2 ≤ N ≤ 100,000, 1 ≤ K ≤ 30)

다음 N개 줄에는 각 플레이어의 속도와 사정거리 Vi와 Ri가 주어진다. (1 ≤ Vi, Ri ≤ 100,000)

다음 줄에는 민혁이네 팀에 들어오려고 하는 사람의 수 Q가 주어진다. (1 ≤ Q ≤ 100,000)

다음 Q개 줄에는 민혁이네 팀에 들어오려고 하는 플레이어의 속도와 사정거리 Vi와 Ri가 주어진다. (1 ≤ Vi, Ri ≤ 100,000)

출력

총 Q개 줄에 각각의 후보가 민혁이네 참가했을 때, 봇 K개를 선택하는 방법의 수를 10009로 나눈 나머지를 출력한다.

예제 입력 1

2 1
2 5
3 3
1
4 2

예제 출력 1

7

힌트

능력치가 (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (3, 1)인 봇을 추가할 수 있다.

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(2 &le; N &le; 100,000, 1 &le; K &le; 30)<\/p>\r\n\r\n<p>\ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 \uac01 \ud50c\ub808\uc774\uc5b4\uc758 \uc18d\ub3c4\uc640 \uc0ac\uc815\uac70\ub9ac Vi\uc640 Ri\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; Vi, Ri &le; 100,000)<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\uc5d0\ub294 \ubbfc\ud601\uc774\ub124 \ud300\uc5d0 \ub4e4\uc5b4\uc624\ub824\uace0 \ud558\ub294 \uc0ac\ub78c\uc758 \uc218 Q\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; Q &le; 100,000)<\/p>\r\n\r\n<p>\ub2e4\uc74c Q\uac1c \uc904\uc5d0\ub294 \ubbfc\ud601\uc774\ub124 \ud300\uc5d0 \ub4e4\uc5b4\uc624\ub824\uace0 \ud558\ub294 \ud50c\ub808\uc774\uc5b4\uc758 \uc18d\ub3c4\uc640 \uc0ac\uc815\uac70\ub9ac Vi\uc640 Ri\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; Vi, Ri &le; 100,000)<\/p>\r\n","output":"<p>\ucd1d Q\uac1c \uc904\uc5d0 \uac01\uac01\uc758 \ud6c4\ubcf4\uac00 \ubbfc\ud601\uc774\ub124 \ucc38\uac00\ud588\uc744 \ub54c, \ubd07 K\uac1c\ub97c \uc120\ud0dd\ud558\ub294 \ubc29\ubc95\uc758 \uc218\ub97c 10009\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\ub2a5\ub825\uce58\uac00&nbsp;(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (3, 1)\uc778 \ubd07\uc744 \ucd94\uac00\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3084","problem_lang":"1","title":"MULTI","description":"<p>One infamous online multiplayer video game is currently being played by N people. The goal of the game is to move around the map and shoot other players with water guns of all sorts. Every player can move with certain speed and has a single gun of determined range. We can say that player A is much better than player B if both of these parameters (speed and gun range) are strictly greater for player A than for player B.&nbsp;<\/p>\r\n\r\n<p>To make the game more interesting, the programmers will add K bots into the game. Bots are controlled by a computer and participate in the game in the same manner as normal players. Each bot is determined by same two parameters as normal players, but to make them distinguishable, they all must have distinct speeds and distinct gun ranges (this doesn&#39;t include players). In order for bots not to be overpowered, for each bot there must be a normal player that is much better than that bot.&nbsp;<\/p>\r\n\r\n<p>Before the bots are added, the players are waiting for one more normal player to join the game. Your task is that for each of Q candidate new players determine the following: if that player joins the N existing players, on how many distinct ways can you select and add K bots to the game? Two bot selections are considered different if there is a single bot in one selection that doesn&#39;t exist in the other selection. This number can be quite huge, so write it modulo 10 009.<\/p>\r\n","input":"<p>First line contains two integers N and K (2 &le; N &le; 100 000, 1 &le; K &le; 30), the number of players and the number of bots.&nbsp;<\/p>\r\n\r\n<p>The following N lines contain parameters for the players, V<sub>i<\/sub> and R<sub>i<\/sub> (1 &le; V<sub>i<\/sub>, R<sub>i<\/sub> &le; 100 000), speed and gun range for player i.&nbsp;<\/p>\r\n\r\n<p>Next line contains one integer Q (1 &le; Q &le; 100 000), number of candidate players that could join the game.&nbsp;<\/p>\r\n\r\n<p>Last Q lines contain game parameters for the candidate players, V<sub>i<\/sub> and R<sub>i<\/sub> (1 &le; V<sub>i<\/sub>, R<sub>i<\/sub> &le; 100 000), speed and gun range for candidate player i.&nbsp;<\/p>\r\n","output":"<p>You need to output a total of Q lines, one for each candidate player.&nbsp;<\/p>\r\n\r\n<p>For each candidate player J output one line containing the number of ways (modulo 10009) to select K bots if that candidate player would join the other N players.&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]