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문제

개미 N마리가 막대 위에 올라가 있다. 일부 개미는 왼쪽을 바라보고 있고, 나머지 개미는 오른쪽을 바라보고 있다. 모든 개미는 매우 작아서 크기가 없는 점으로 나타낼 수 있다. 시작 신호가 주어지면, 개미는 바라보고 있는 방향으로 행진을 시작한다. 모든 개미는 동일한 속도 초속 1mm로 이동한다. 두 개미가 한 점에서 충돌하는 경우가 발생할 수 있다. 이 경우에 두 개미는 행진하는 방향을 반대 방향으로 바꾸고, 행진을 계속하게 된다. 개미가 방향을 바꾸는데 걸리는 시간은 없다. 개미가 막대의 끝에 도착하는 경우에는, 막대에서 떨어지게 된다. 막대는 땅 위에 떠있다고 가정한다.

처음에 모든 개미의 위치는 서로 다르다. 즉, 두 개미가 막대 위의 한 점에 같이 있는 경우는 없다. 개미는 부호 있는 정수로 나타낼 수 있다. 이 정수를 개미의 ID라고 한다. 개미의 ID의 부호는 개미가 처음에 바라보고 있는 방향이다. -는 왼쪽을 바라보고 있는 것이고, +는 오른쪽을 바라보고 있는 것이다. 개미의 ID의 절댓값은 1부터 109까지의 정수 중 하나이다. 또, 모든 개미의 ID의 절댓값은 서로 다르다. 아래 그림에는 개미가 총 6마리가 있고, ID는 {+4, +5, -1, -3, -2, +6}이다. 각 개미의 초기 위치는 {5, 8, 19, 22, 24, 25}이며, 막대의 길이 L = 30이다. 화살표는 처음에 개미가 바라보고 있는 방향을 나타낸다. 왼쪽 끝의 좌표는 0이고, 오른쪽 끝의 좌표는 30이다. ID가 +6인 개미는 시간 t = 5일 때, 막대의 오른쪽 끝에 도착하며, t = 6에 막대에서 떨어지게 된다.

개미가 행진을 시작하기 전의 상태 (ID와 막대 상의 위치)가 주어진다. 두 개미가 동시에 막대의 양 끝에서 떨어지는 경우에는, ID가 작은 개미가 조금 더 먼저 떨어진다고 한다. 아래 그림은 이와 같은 경우를 나타낸 그림이다. 두 개미 {-1, +2}는 끝에 동시에 도착하게 된다. -1 < +2 이기 때문에, ID가 -1인 개미가 +2인 개미보다 조금 더 먼저 떨어지게 된다. 따라서, 아래 그림의 네 개미가 떨어지는 순서는 {-1, 2, 4, 3}이 된다.

양의 정수 1 ≤ k ≤ n이 주어졌을 때, k번째로 떨어지는 개미를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스의 첫째 줄에는 N, L, k가 주어진다. 다음 N개 줄에는 pi와 ai가 주어진다. ai는 개미의 ID이고, pi는 그 개미의 초기 위치이다. 항상 pi가 증가하는 순서로 (pi<pi+1) 주어진다. (1 ≤ pi ≤ L-1, 3 ≤ N ≤ 100,000, 10 ≤ L ≤ 5,000,000, 1 ≤ k ≤ N)

출력

각 테스트 케이스마다, N마리 개미 중에서 k번째로 떨어지는 개미의 ID를 출력한다. 개미의 ID가 양수인 경우에 +를 출력하면 안 된다.

예제 입력 1

2
6 30 3
5 4
8 5
19 -1
22 -3
24 -2
25 6
4 35 2
5 -1
12 3
20 4
30 2

예제 출력 1

-2
2
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ID\uac00 +6\uc778 \uac1c\ubbf8\ub294 \uc2dc\uac04 t = 5\uc77c \ub54c, \ub9c9\ub300\uc758 \uc624\ub978\ucabd \ub05d\uc5d0 \ub3c4\ucc29\ud558\uba70, t = 6\uc5d0 \ub9c9\ub300\uc5d0\uc11c \ub5a8\uc5b4\uc9c0\uac8c \ub41c\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/ant1(1).png\" style=\"height:184px; width:646px\" \/><\/p>\r\n\r\n<p>\uac1c\ubbf8\uac00 \ud589\uc9c4\uc744 \uc2dc\uc791\ud558\uae30 \uc804\uc758 \uc0c1\ud0dc (ID\uc640 \ub9c9\ub300 \uc0c1\uc758 \uc704\uce58)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub450 \uac1c\ubbf8\uac00 \ub3d9\uc2dc\uc5d0 \ub9c9\ub300\uc758 \uc591 \ub05d\uc5d0\uc11c \ub5a8\uc5b4\uc9c0\ub294 \uacbd\uc6b0\uc5d0\ub294, ID\uac00 \uc791\uc740 \uac1c\ubbf8\uac00 \uc870\uae08 \ub354 \uba3c\uc800&nbsp;\ub5a8\uc5b4\uc9c4\ub2e4\uace0 \ud55c\ub2e4. \uc544\ub798 \uadf8\ub9bc\uc740 \uc774\uc640 \uac19\uc740 \uacbd\uc6b0\ub97c \ub098\ud0c0\ub0b8 \uadf8\ub9bc\uc774\ub2e4. \ub450 \uac1c\ubbf8 {-1, +2}\ub294 \ub05d\uc5d0 \ub3d9\uc2dc\uc5d0 \ub3c4\ucc29\ud558\uac8c \ub41c\ub2e4. -1 &lt; +2 \uc774\uae30 \ub54c\ubb38\uc5d0, ID\uac00 -1\uc778 \uac1c\ubbf8\uac00 +2\uc778 \uac1c\ubbf8\ubcf4\ub2e4 \uc870\uae08 \ub354 \uba3c\uc800 \ub5a8\uc5b4\uc9c0\uac8c \ub41c\ub2e4. \ub530\ub77c\uc11c, \uc544\ub798 \uadf8\ub9bc\uc758 \ub124 \uac1c\ubbf8\uac00 \ub5a8\uc5b4\uc9c0\ub294 \uc21c\uc11c\ub294 {-1, 2, 4, 3}\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/ant2(1).png\" style=\"height:156px; width:539px\" \/><\/p>\r\n\r\n<p>\uc591\uc758 \uc815\uc218 1 &le; k &le; n\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, k\ubc88\uc9f8\ub85c \ub5a8\uc5b4\uc9c0\ub294 \uac1c\ubbf8\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 N, L, k\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 p<sub>i<\/sub>\uc640&nbsp;a<sub>i<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. a<sub>i<\/sub>\ub294 \uac1c\ubbf8\uc758 ID\uc774\uace0, p<sub>i<\/sub>\ub294 \uadf8 \uac1c\ubbf8\uc758 \ucd08\uae30 \uc704\uce58\uc774\ub2e4. \ud56d\uc0c1 p<sub>i<\/sub>\uac00 \uc99d\uac00\ud558\ub294 \uc21c\uc11c\ub85c (p<sub>i<\/sub>&lt;p<sub>i+1<\/sub>) \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; p<sub>i<\/sub> &le; L-1, 3 &le; N &le; 100,000, 10 &le; L &le; 5,000,000, 1 &le; k &le; N)<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4, N\ub9c8\ub9ac \uac1c\ubbf8 \uc911\uc5d0\uc11c k\ubc88\uc9f8\ub85c \ub5a8\uc5b4\uc9c0\ub294 \uac1c\ubbf8\uc758 ID\ub97c \ucd9c\ub825\ud55c\ub2e4. \uac1c\ubbf8\uc758 ID\uac00 \uc591\uc218\uc778 \uacbd\uc6b0\uc5d0 +\ub97c \ucd9c\ub825\ud558\uba74 \uc548 \ub41c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"3163","problem_lang":"1","title":"Falling Ants","description":"<p>N ants are on a stick where some facing right and some facing left. You can assume all ants are so tiny compared to the distance between them, that they can be considered moving points without volume. From a start signal, all ants begin to march in whichever direction they are currently facing. All ants march in a constant speed such as 1mm per second. If two different ants collide on a point, then they bounce and reverse their previous direction. Bouncing and reversing movement does not take any time. When an ant is reaching the end of stick, that ant falls off from the stick and down to the ground. We assume the stick is floating over a floor.&nbsp;<\/p>\r\n\r\n<p>Initially all ants are placed in distinct positions, that means no two ants are placed at a same point of the stick. We represent each ant using a signed integer, called an ant ID. The sign of the ant ID denotes the facing direction in the intial state, where &#39;-&#39;(&#39;+&#39;) means facing the left (right). The absolute value of the ant ID is one of N integers 1, 2, \u22ef , N. So the absolute values of the ant ID are all distinct. In Figure 1, you can see that there are 6 ants with the signed ID {+4, +5, -1, -3, -2, +6} whose corresponding positions are &nbsp;{5,8,19,22,24,25} on a long stick with length L = 30. The arrow assigned for each ant shows the facing direction in the initial state. The position of the left end is 0, and the position of the right end is 30. It is easy to see that the ant of ID +6 will arrive at the right end of the stick at time t = 5, and then it falls off the stick at t =6.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/ant1.png\" style=\"height:184px; opacity:0.9; width:646px\" \/><\/p>\r\n\r\n<p>You are given information of ants before marching; ant ID and the corresponding position on a stick. If two ants are falling simultaneously from both sides (left and right), then we will break the tie of falling order such that the ant with smaller ID number falls off slightly earlier than the other. Let us give one example for this case. In Figure 2, if two ants with ID = {-1, +2} will reach each end simultaneously, the ant of ID = -1 will fall off earlier than the ant of ID = +2 since -1 &lt; +2. So the falling sequence of four ants in Figure 2 is \u3008-1, 2, 4, 3\u3009, i.e., the ant of ID = -1 falls off the first and the ant of ID = 3 falls off the last.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/ant2.png\" style=\"height:156px; opacity:0.9; width:539px\" \/><\/p>\r\n\r\n<p>Given a positive integer 1 &le; k &le; n, you should find the k-th ant in the falling sequence, i.e., the k-th falling ant.&nbsp;<\/p>\r\n","input":"<p>Your program is to read from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case starts with three integer numbers N, L and k, where N is the total number of the ants, L is the length of the stick, and k is the falling order we are concerned with k &le; N. Each line in the following has two integer numbers, p<sub>i<\/sub> and a<sub>i<\/sub>, where p<sub>i<\/sub> is the initial position of the ant a<sub>i<\/sub>. Note that p<sub>i<\/sub> is increasing such as p<sub>i<\/sub> &lt; p<sub>i+1<\/sub> . Note that 1 &le; p<sub>i<\/sub> &le; L - 1, 3 &le; N &le; 100,000, 10 &le; L &le; 5,000,000 and 1 &le; k &le; N.&nbsp;<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly one line for each test case. The line should contain the ID number of the k-th falling ant from the stick among all N ants. You should not write &lsquo;+&rsquo; symbol if the ant ID is positive.&nbsp;<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Asia Pacific > Korea > Nationwide Internet Competition > Daejeon Nationalwide Internet Competition 2013 E번