시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB231888342.347%

문제

이번 주에 알고스팟 회의가 암스테르담에서 열린다. 전국 대학생 프로그래밍 대회 동아리 연합(이하 전대프연) 회장 성진이는 알고스팟 회의를 도청하려고 한다. 성진이는 도청장치를 회의 장소 근처에 숨겨놓았다. 도청장치는 계속해서 녹음하며, 무선 전파를 이용해서 전송한다.

성진이는 전대프연 회원들에게 도청장치의 수신기를 나누어주었고, 여러 장소에 흩어 보냈다. 전파는 서로 간섭을 일으킨다. 따라서, 전혀 듣지 못하는 장소가 있을 수 있다. 수신기를 가진 한 회원의 위치가 주어졌을 때, 그 사람이 들을 수 있는 도청장치를 구하는 프로그램을 작성하시오.

어떤 장소에서 들을 수 있는 도청장치는 다음과 같은 식을 만족하는 \(i\)번째 도청장치이다.

\[r_i > 6(B+\sum_{j \ne i} {r_j})\]

  • \(r_i = \frac{s_i} {\left| P_i - P_{listen} \right| ^2}\)는 \(i\)번째 도청장치의 신호 수신 세기이다.
  • \(s_i\)는 \(i\)번째 도청장치가 보낸 신호의 세기이다.
  • \(P_i\)는 \(i\)번째 도청장치의 위치이다.
  • \(P_{listen}\)는 수신기를 들고있는 사람의 위치이다.
  • \(\left| P_i - P_{j} \right|\) \(P_i\)와 \(P_j\) 사이의 유클리드 거리이다.
  • \(B\)는 백그라운드 노이즈의 레벨이다.

입력

첫째 줄에 테스트 케이스의 수가 주어지며, 100을 넘지 않는다. 각 테스트 케이스의 첫째 줄에는 도청장치의 수 \(n\) (0 ≤ \(n\) ≤ 100,000)이 주어진다. 둘째 줄에는 백그라운드 노이즈의 레벨 \(B\) (0 ≤ \(B\) ≤ 1,000,000)가 주어진다. 셋째 줄에는 수신기를 들고있는 사람의 위치 x좌표와 y좌표 \(x\)와 \(y\)가 주어진다. 다음 \(n\)개 줄에는 \(i\)번째 도청장치의 위치 \(x_i\), \(y_i\)와 신호의 세기 \(s_i\)가 주어진다. (0 ≤ \(s_i\) ≤ 1,000,000)

모든 좌표는 구간 [0, 10000]에 포함되며, 모든 도청장치의 위치 \(P_i\)와 수신기의 위치 \(P_{listen}\)는 다르다. 테스트 케이스는 소수점 오차가 정답에 영향을 주지 않게 설계되어져 있다.

출력

첫째 줄에 들을 수 있는 도청장치의 번호를 출력한다. 만약, 들을 수 있는 도청장치가 없다면 "NOISE"를 출력한다.

도청장치의 번호는 1부터 시작한다.

예제 입력 1

3
4
10
100 100
90 90 20000
110 90 50
90 110 1000
110 110 50
4
100
100 100
90 90 20000
110 90 50
90 110 1000
110 110 50
2
0
0 10
0 0 1000
0 8 1

예제 출력 1

1
NOISE
1
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(0 &le; \\(s_i\\) &le; 1,000,000)<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \uc88c\ud45c\ub294 \uad6c\uac04 [0, 10000]\uc5d0 \ud3ec\ud568\ub418\uba70, \ubaa8\ub4e0 \ub3c4\uccad\uc7a5\uce58\uc758 \uc704\uce58 \\(P_i\\)\uc640 \uc218\uc2e0\uae30\uc758 \uc704\uce58 \\(P_{listen}\\)\ub294 \ub2e4\ub974\ub2e4. \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \uc18c\uc218\uc810 \uc624\ucc28\uac00 \uc815\ub2f5\uc5d0 \uc601\ud5a5\uc744 \uc8fc\uc9c0 \uc54a\uac8c \uc124\uacc4\ub418\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub4e4\uc744 \uc218 \uc788\ub294 \ub3c4\uccad\uc7a5\uce58\uc758 \ubc88\ud638\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub9cc\uc57d, \ub4e4\uc744 \uc218 \uc788\ub294 \ub3c4\uccad\uc7a5\uce58\uac00 \uc5c6\ub2e4\uba74 &quot;NOISE&quot;\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub3c4\uccad\uc7a5\uce58\uc758 \ubc88\ud638\ub294 1\ubd80\ud130 \uc2dc\uc791\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"9319","problem_lang":"1","title":"Bad Signal","description":"<p>There is an important UN meeting in town. Any self-respecting espionage agency will try to eavesdrop on the delegations to gain some advantage in the negotiations. They do this by planting hidden microphones in and around the meeting places. Those microphones continuously capture sound waves and transmit them via radio.<\/p>\r\n\r\n<p>In fact, \ufb01erce competition between espionage agencies has left the whole city scattered with hidden microphones, so much so that the radio waves interfere with each other and it is often not even possible to make out any signal in the mess of radio waves &ndash; depending on your position and proximity to the different transmitters obviously.<\/p>\r\n\r\n<p>Speci\ufb01cally, it is possible to make out a signal i if and only if:<\/p>\r\n\r\n<p>\\[r_i &gt; 6(B+\\sum_{j \\ne i} {r_j})\\]<\/p>\r\n\r\n<p>Where<\/p>\r\n\r\n<ul>\r\n\t<li>\\(r_i = \\frac{s_i} {\\left| P_i - P_{listen} \\right| ^2}\\) is the strength of the received signal of microphone \\(i\\),<\/li>\r\n\t<li>\\(s_i\\) is the strength of the signal sent from microphone \\(i\\),<\/li>\r\n\t<li>\\(P_i\\) is the position of microphone \\(i\\),<\/li>\r\n\t<li>\\(P_{listen}\\) is the position where you are listening to the signals,<\/li>\r\n\t<li>\\(\\left| P_i - P_{j} \\right|\\) is the Euclidean distance between points \\(P_i\\) and \\(P_j\\) and<\/li>\r\n\t<li>\\(B\\) is the level of background noise.<\/li>\r\n<\/ul>\r\n","input":"<p>On the \ufb01rst line one positive number: the number of test cases, at most 100. After that per test case:<\/p>\r\n\r\n<ul>\r\n\t<li>one line with an integer \\(n\\) (0 &le; \\(n\\) &le; 100 000): the number of planted microphones.<\/li>\r\n\t<li>one line with the integer \\(B\\) (0 &le; \\(B\\) &le; 1 000 000): the level of background noise.<\/li>\r\n\t<li>one line with two space-separated integers \\(x\\) and \\(y\\): the x and y coordinates of the location \\(P_{listen}\\) where you receive the signals<\/li>\r\n\t<li>\\(n\\) lines with three space-separated integers \\(x_i\\), \\(y_i\\) and \\(s_i\\) (0 &lt; \\(s_i\\) &le; 1 000 000): the x and y coordinates of the location \\(P_i\\) of microphone \\(i\\) and its signal strength, respectively.<\/li>\r\n<\/ul>\r\n\r\n<p>All coordinates are in the range [0; 10 000]. The locations Pi all differ from Plisten. The test data is constructed so that small \ufb02oating point rounding errors will not in\ufb02uence the outcome of any solution.<\/p>\r\n","output":"<p>Per test case:<\/p>\r\n\r\n<ul>\r\n\t<li>one line with an integer: the (one-based) index of a microphone, the signal of which can be made out, or the string &ldquo;NOISE&rdquo; if there is no such microphone.<\/li>\r\n<\/ul>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]