시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

상근이는 테러리스트의 전화를 도청하던 중에 큰 공격이 예고되다는 사실을 알게되었다. 테러리스트는 인코딩된 좌표를 서로에게 보내고 있다. 상근이는 이 좌표 중 한 군데에서 공격이 일어날 것이라고 예상하고 있다. 상근이는 좌표를 가로채는데 성공했다.

모든 좌표는 x와 y 좌표로 나누어져 있으며, 두 좌표는 모두 소수 P보다 작은 음이 아닌 정수이다. x좌표와 y좌표는 각각 인코딩되며, 인코딩 되는 과정은 동일하다. 

좌표 하나를 인코딩하려면 A, B, C, K, N이 필요하고, 다음과 같은 과정이 필요하다.

인코딩 과정은 세 함수로 나타낼 수 있고, 다음과 같다.

  • F(n+1) = G(n) + H(n)
  • G(n+1) = K*F(n) + H(n-1)
  • H(n+1) = F(n) + K*G(n)

A, B, C는 함수의 초기값이다.

  • F(1) = A
  • G(1) = B
  • H(1) = C

좌표는 F(N) mod P가 된다.

사실 위의 과정에는 매우 중요한 정보가 하나 빠져있다. G(2)를 계산하려면, H(0)이 필요하다. 하지만, H(0)을 알아낼 수 있는 방법은 없다. H(0)에 대한 유일한 정보는 x와 y를 계산할 때, 동일한 H(0)을 사용한다는 점이다.

상근이는 우연히 x좌표를 디코딩하지 않고 얻게 되었다. 이제, x를 이용해 H(0)을 구한 다음, y를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 테스트 케이스의 개수가 주어진다. 테스트 케이스의 개수는 100개보다 작거나 같다. 각 테스트 케이스의 첫째 줄에는 소수 P (2 ≤ P ≤ 19997)가 주어진다. 둘째 줄에는 x좌표를 인코딩하는데 사용하는 Ax, Bx, Cx, Kx, Nx가 주어진다. (0 ≤ Ax, Bx, Cx, Kx < P, 1 ≤ Nx ≤ 109) 셋째 줄에는 y좌표를 인코딩하는데 사용한 Ay, By, Cy, Ky, Ny가 주어진다. (0 ≤ Ay, By, Cy, Ky < P, 1 ≤ Ny ≤ 109) 넷째 줄에는 x좌표 (0 ≤ x < P)가 주어진다. 

출력

각 테스트 케이스마다 y좌표를 출력한다. 만약, 가능한 y좌표가 여러 개인 경우에는 “UNKNOWN”를 출력한다.

예제 입력 1

2
11
2 3 5 7 4
4 6 8 9 7
5
7
1 6 2 5 1
3 4 2 5 3
1

예제 출력 1

7
UNKNOWN
[{"problem_id":"9371","problem_lang":"0","title":"\uc778\ucf54\ub529 \uc88c\ud45c","description":"<p>\uc0c1\uadfc\uc774\ub294 \ud14c\ub7ec\ub9ac\uc2a4\ud2b8\uc758 \uc804\ud654\ub97c \ub3c4\uccad\ud558\ub358 \uc911\uc5d0 \ud070 \uacf5\uaca9\uc774 \uc608\uace0\ub418\ub2e4\ub294 \uc0ac\uc2e4\uc744 \uc54c\uac8c\ub418\uc5c8\ub2e4. \ud14c\ub7ec\ub9ac\uc2a4\ud2b8\ub294 \uc778\ucf54\ub529\ub41c \uc88c\ud45c\ub97c \uc11c\ub85c\uc5d0\uac8c \ubcf4\ub0b4\uace0 \uc788\ub2e4. \uc0c1\uadfc\uc774\ub294 \uc774 \uc88c\ud45c \uc911 \ud55c \uad70\ub370\uc5d0\uc11c \uacf5\uaca9\uc774 \uc77c\uc5b4\ub0a0 \uac83\uc774\ub77c\uace0 \uc608\uc0c1\ud558\uace0 \uc788\ub2e4. \uc0c1\uadfc\uc774\ub294 \uc88c\ud45c\ub97c \uac00\ub85c\ucc44\ub294\ub370 \uc131\uacf5\ud588\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \uc88c\ud45c\ub294 x\uc640 y \uc88c\ud45c\ub85c \ub098\ub204\uc5b4\uc838 \uc788\uc73c\uba70, \ub450 \uc88c\ud45c\ub294 \ubaa8\ub450 \uc18c\uc218 P\ubcf4\ub2e4 \uc791\uc740 \uc74c\uc774 \uc544\ub2cc \uc815\uc218\uc774\ub2e4. x\uc88c\ud45c\uc640 y\uc88c\ud45c\ub294 \uac01\uac01 \uc778\ucf54\ub529\ub418\uba70, \uc778\ucf54\ub529 \ub418\ub294 \uacfc\uc815\uc740 \ub3d9\uc77c\ud558\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uc88c\ud45c \ud558\ub098\ub97c \uc778\ucf54\ub529\ud558\ub824\uba74 A, B, C, K, N\uc774 \ud544\uc694\ud558\uace0, \ub2e4\uc74c\uacfc \uac19\uc740 \uacfc\uc815\uc774 \ud544\uc694\ud558\ub2e4.<\/p>\r\n\r\n<p>\uc778\ucf54\ub529 \uacfc\uc815\uc740 \uc138 \ud568\uc218\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\uace0, \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>F(n+1) = G(n) + H(n)<\/li>\r\n\t<li>G(n+1) = K*F(n) + H(n-1)<\/li>\r\n\t<li>H(n+1) = F(n) + K*G(n)<\/li>\r\n<\/ul>\r\n\r\n<p>A, B, C\ub294 \ud568\uc218\uc758 \ucd08\uae30\uac12\uc774\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>F(1) = A<\/li>\r\n\t<li>G(1) = B<\/li>\r\n\t<li>H(1) = C<\/li>\r\n<\/ul>\r\n\r\n<p>\uc88c\ud45c\ub294 F(N) mod P\uac00 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc0ac\uc2e4 \uc704\uc758 \uacfc\uc815\uc5d0\ub294 \ub9e4\uc6b0 \uc911\uc694\ud55c \uc815\ubcf4\uac00 \ud558\ub098 \ube60\uc838\uc788\ub2e4. G(2)\ub97c \uacc4\uc0b0\ud558\ub824\uba74, H(0)\uc774 \ud544\uc694\ud558\ub2e4. \ud558\uc9c0\ub9cc, H(0)\uc744 \uc54c\uc544\ub0bc \uc218 \uc788\ub294 \ubc29\ubc95\uc740 \uc5c6\ub2e4. H(0)\uc5d0 \ub300\ud55c \uc720\uc77c\ud55c \uc815\ubcf4\ub294 x\uc640 y\ub97c \uacc4\uc0b0\ud560 \ub54c, \ub3d9\uc77c\ud55c H(0)\uc744 \uc0ac\uc6a9\ud55c\ub2e4\ub294 \uc810\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \uc6b0\uc5f0\ud788 x\uc88c\ud45c\ub97c \ub514\ucf54\ub529\ud558\uc9c0 \uc54a\uace0 \uc5bb\uac8c \ub418\uc5c8\ub2e4. \uc774\uc81c, x\ub97c \uc774\uc6a9\ud574 H(0)\uc744 \uad6c\ud55c \ub2e4\uc74c, y\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\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218\ub294 100\uac1c\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \uc18c\uc218 P (2 &le; P &le; 19997)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 x\uc88c\ud45c\ub97c \uc778\ucf54\ub529\ud558\ub294\ub370 \uc0ac\uc6a9\ud558\ub294&nbsp;A<sub>x<\/sub>, B<sub>x<\/sub>, C<sub>x<\/sub>, K<sub>x<\/sub>,&nbsp;N<sub>x<\/sub>\uac00&nbsp;\uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;(0 &le; A<sub>x<\/sub>, B<sub>x<\/sub>, C<sub>x<\/sub>, K<sub>x<\/sub>&nbsp;&lt; P,&nbsp;1 &le; N<sub>x<\/sub>&nbsp;&le; 10<sup>9<\/sup>) \uc14b\uc9f8 \uc904\uc5d0\ub294 y\uc88c\ud45c\ub97c \uc778\ucf54\ub529\ud558\ub294\ub370 \uc0ac\uc6a9\ud55c&nbsp;A<sub>y<\/sub>, B<sub>y<\/sub>, C<sub>y<\/sub>, K<sub>y<\/sub>, N<sub>y<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (0 &le; A<sub>y<\/sub>, B<sub>y<\/sub>, C<sub>y<\/sub>, K<sub>y<\/sub>&nbsp;&lt; P, 1 &le; N<sub>y<\/sub>&nbsp;&le; 10<sup>9<\/sup>) \ub137\uc9f8 \uc904\uc5d0\ub294 x\uc88c\ud45c (0 &le; x &lt; P)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 y\uc88c\ud45c\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub9cc\uc57d, \uac00\ub2a5\ud55c y\uc88c\ud45c\uac00 \uc5ec\ub7ec \uac1c\uc778 \uacbd\uc6b0\uc5d0\ub294&nbsp;&ldquo;UNKNOWN&rdquo;\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9371","problem_lang":"1","title":"Encoded Coordinates","description":"<p>You have been monitoring a terrorist cell that is planning a big attack somewhere close. The terrorists have been sending encoded coordinates to each other, and you suspect that the attack will happen at one of the locations described by these coordinates. You have intercepted the relevant communications for a series of locations you want to investigate.<\/p>\r\n\r\n<p>Every location consists of a separate x and y coordinate, each being a non-negative integer smaller than some prime number P. Both coordinates are encoded separately using the same process. A source has given you information on the process of decoding a single coordinate. The input of this process consists of \ufb01ve values: A, B, C, K and N.<\/p>\r\n\r\n<p>Central to the decoding process is a collection of three functions, de\ufb01ned in terms of each other and the input value K:<\/p>\r\n\r\n<ul>\r\n\t<li>F(n+1) = G(n) + H(n)<\/li>\r\n\t<li>G(n+1) = K*F(n) + H(n-1)<\/li>\r\n\t<li>H(n+1) = F(n) + K*G(n)<\/li>\r\n<\/ul>\r\n\r\n<p>The values A, B and C are used to initialize these functions as follows:<\/p>\r\n\r\n<ul>\r\n\t<li>F(1) = A<\/li>\r\n\t<li>G(1) = B<\/li>\r\n\t<li>H(1) = C<\/li>\r\n<\/ul>\r\n\r\n<p>The decoded coordinate is the value of F(N) mod P.<\/p>\r\n\r\n<p>As you might have noticed, there is some crucial information missing: you need the value of H(0) to calculate G(2). While you do not have this value, you do know that the x and y coordinate use the same value for H(0). Luckily, you have managed to already obtain the x coordinates for the locations. Your colleagues have suggested that this does not give you enough information to calculate the y coordinates, but you want to prove them wrong.<\/p>\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 the prime number P (2 &le; P &le; 19 997).<\/li>\r\n\t<li>one line with \ufb01ve space-separated integers A<sub>x<\/sub>, B<sub>x<\/sub>, C<sub>x<\/sub>, K<sub>x<\/sub> and N<sub>x<\/sub> (0 &le; A<sub>x<\/sub>, B<sub>x<\/sub>, C<sub>x<\/sub>, K<sub>x<\/sub> &lt; P and 1 &le; N<sub>x<\/sub> &le; 10<sup>9<\/sup>): the parameters for the x coordinate.<\/li>\r\n\t<li>one line with \ufb01ve space-separated integers A<sub>y<\/sub>, B<sub>y<\/sub>, C<sub>y<\/sub>, K<sub>y<\/sub> and N<sub>y<\/sub> (0 &le; A<sub>y<\/sub>, B<sub>y<\/sub>, C<sub>y<\/sub>, K<sub>y<\/sub> &lt; P and 1 &le; N<sub>y<\/sub> &le; 10<sup>9<\/sup>): the parameters for the y coordinate.<\/li>\r\n\t<li>one line with one integer x (0 &le; x &lt; P): the x coordinate.<\/li>\r\n<\/ul>\r\n","output":"<p>Per test case:<\/p>\r\n\r\n<ul>\r\n\t<li>one line with one integer: the calculated y coordinate. If your colleagues are right, and there is not exactly one valid y coordinate, print &ldquo;UNKNOWN&rdquo; on a single line instead.<\/li>\r\n<\/ul>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]