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문제

상근이는 매일 아침 실험실로 출근해서 샘플의 무게를 재는 일을 하고 있다. 상근이는 두 샘플을 고른 뒤, 저울을 이용해서 무게의 차이를 잰다.

교수님의 마음에 들기 위해서 매일 아침부터 무게를 재고 있지만, 가끔 교수님이 실험실에 들어와서 상근이에게 어떤 두 샘플의 무게의 차이를 물어보기도 한다. 이때, 상근이는 지금까지 잰 결과를 바탕으로 대답을 할 수도 있고, 못 할 수도 있다.

상근이는 결과를 출근한 첫 날부터 공책에 적어 두었다. 하지만, 엄청난 양의 무게가 적혀있기 때문에, 교수님의 질문에 재빨리 대답할 수가 없었다. 이런 상근이를 위해서 프로그램을 만들려고 한다.

상근이가 실험실에서 한 일이 순서대로 주어진다. 어떤 두 샘플의 무게의 차이를 구할 수 있는지 없는지를 알아내는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다.

각 테스트 케이스의 첫째 줄에는 샘플의 종류의 개수 N (2 ≤ N ≤ 100,000)과 상근이가 실험실에서 한 일의 수 M (1 ≤ M ≤ 100,000)이 주어진다. 샘플은 1번부터 N번까지 번호가 매겨져 있다. 다음 M개 줄에는 상근이가 실험실에서 한 일이 주어진다.

상근이가 무게를 쟀다면, ! a b w와 같은 형식으로 주어진다. 이 뜻은 b가 a보다 w그램 무겁다는 뜻이다. (a ≠ b) w는 1,000,000을 넘지 않는 음이 아닌 정수이다. 모든 측정은 정확하고, 일관성을 유지한다.

교수님의 질문은 ? a b와 같은 형식으로 주어진다. 이 뜻은 b가 a보다 얼마나 무거운지를 출력하라는 뜻이다.

마지막 줄에는 0이 두 개 주어진다.

출력

교수님의 질문 (? a b)이 입력으로 들어올 때 마다, 지금까지 측정한 결과를 바탕으로 a와 b의 무게 차이를 계산할 수 있다면, b가 a보다 얼마나 무거운지를 출력한다. 무게의 차이의 절댓값이 1,000,000을 넘지 않는다. 만약, 측정한 결과를 바탕으로 무게의 차이를 계산할 수 없다면, "UNKNOWN"을 출력한다.

예제 입력 1

2 2
! 1 2 1
? 1 2
2 2
! 1 2 1
? 2 1
4 7
! 1 2 100
? 2 3
! 2 3 100
? 2 3
? 1 3
! 4 3 150
? 4 1
0 0

예제 출력 1

1
-1
UNKNOWN
100
200
-50
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(a &ne; b) w\ub294 1,000,000\uc744 \ub118\uc9c0 \uc54a\ub294 \uc74c\uc774 \uc544\ub2cc \uc815\uc218\uc774\ub2e4. \ubaa8\ub4e0 \uce21\uc815\uc740 \uc815\ud655\ud558\uace0, \uc77c\uad00\uc131\uc744 \uc720\uc9c0\ud55c\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uad50\uc218\ub2d8\uc758 \uc9c8\ubb38\uc740 ? a b\uc640 \uac19\uc740 \ud615\uc2dd\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \ub73b\uc740 b\uac00 a\ubcf4\ub2e4 \uc5bc\ub9c8\ub098 \ubb34\uac70\uc6b4\uc9c0\ub97c \ucd9c\ub825\ud558\ub77c\ub294 \ub73b\uc774\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ub450 \uac1c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\r\n\t\uad50\uc218\ub2d8\uc758 \uc9c8\ubb38 (? a b)\uc774 \uc785\ub825\uc73c\ub85c \ub4e4\uc5b4\uc62c \ub54c \ub9c8\ub2e4, \uc9c0\uae08\uae4c\uc9c0 \uce21\uc815\ud55c \uacb0\uacfc\ub97c \ubc14\ud0d5\uc73c\ub85c a\uc640 b\uc758 \ubb34\uac8c \ucc28\uc774\ub97c \uacc4\uc0b0\ud560 \uc218 \uc788\ub2e4\uba74, b\uac00 a\ubcf4\ub2e4 \uc5bc\ub9c8\ub098 \ubb34\uac70\uc6b4\uc9c0\ub97c \ucd9c\ub825\ud55c\ub2e4. \ubb34\uac8c\uc758 \ucc28\uc774\uc758 \uc808\ub313\uac12\uc774 1,000,000\uc744 \ub118\uc9c0 \uc54a\ub294\ub2e4. \ub9cc\uc57d, \uce21\uc815\ud55c \uacb0\uacfc\ub97c \ubc14\ud0d5\uc73c\ub85c \ubb34\uac8c\uc758 \ucc28\uc774\ub97c \uacc4\uc0b0\ud560 \uc218 \uc5c6\ub2e4\uba74, &quot;UNKNOWN&quot;\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"3830","problem_lang":"1","title":"Never Wait for Weights","description":"<p>In a laboratory, an assistant, Nathan Wada, is measuring weight di\ufb00erences between sample pieces pair by pair. He is using a balance because it can more precisely measure the weight difference between two samples than a spring scale when the samples have nearly the same weight.<\/p>\r\n\r\n<p>He is occasionally asked the weight differences between pairs of samples. He can or cannot answer based on measurement results already obtained.<\/p>\r\n\r\n<p>Since he is accumulating a massive amount of measurement data, it is now not easy for him to promptly tell the weight differences. Nathan asks you to develop a program that records measurement results and automatically tells the weight differences.<\/p>\r\n","input":"<p>The input consists of multiple datasets. The fi rst line of a dataset contains two integers N and M. N denotes the number of sample pieces (2 &le; N &le; 100, 000). Each sample is assigned a unique number from 1 to N as an identifi er. The rest of the dataset consists of M lines (1 &le; M &le; 100, 000), each of which corresponds to either a measurement result or an inquiry. They are given in chronological order.<\/p>\r\n\r\n<p>A measurement result has the format,<\/p>\r\n\r\n<pre>! a b w<\/pre>\r\n\r\n<p>which represents the sample piece numbered b is heavier than one numbered a by w micrograms (a &ne; b). That is, w = w<sub>b<\/sub> - w<sub>a<\/sub>, where w<sub>a<\/sub> and w<sub>b<\/sub> are the weights of a and b, respectively. Here, w is a non-negative integer not exceeding 1,000,000.<\/p>\r\n\r\n<p>You may assume that all measurements are exact and consistent.<\/p>\r\n\r\n<p>An inquiry has the format,<\/p>\r\n\r\n<pre>? a b<\/pre>\r\n\r\n<p>which asks the weight difference between the sample pieces numbered a and b (a &ne; b).<\/p>\r\n\r\n<p>The last dataset is followed by a line consisting of two zeros separated by a space.<\/p>","output":"<p>For each inquiry, <code>? a b<\/code>, print the weight difference in micrograms between the sample pieces numbered a and b, w<sub>b<\/sub> - w<sub>a<\/sub>, followed by a newline if the weight difference can be computed based on the measurement results prior to the inquiry. The difference can be zero, or negative as well as positive. You can assume that its absolute value is at most 1,000,000. If the difference cannot be computed based on the measurement results prior to the inquiry, print UNKNOWN followed by a newline.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Asia Pacific > Japan > Asia Regional Contest 2012 in Tokyo F번