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문제

N개의 도시로 이루어진 나라가 있고, 도시는 1번부터 N번까지 번호가 붙어있다. 그리고 서로 다른 두 도시를 이어주는 양방향 도로 M개가 있고, 도로도 1번부터 M번까지 번호가 매겨져 있다. 두 도시 사이에 도로가 여러 개 있을 수 있다.

최근에 예산이 모자라는 상황이 발생해 도로 청소차를 두 대만 운영하기로 했다. 이 청소차를 이용해 모든 도로를 한 번씩만 청소하려고 한다.

두 청소차는 각각 임의의 도시에서 출발한다. 같은 도시에서 출발할 수도 있고, 다른 도시에서 출발할 수도 있다. 모든 도로를 정확히 한 번씩만 청소하기 위해, 각 도로는 둘 중 딱 한 대의 청소차만 지나가야 한다 (청소차가 청소를 하지 않고 도로를 그냥 지나갈 수는 없다). 마지막으로, 각 청소차는 하나 이상의 도로를 청소해야 한다 (그렇지 않으면 청소차를 두 대 운영할 이유가 없다).

도시의 도로 정보가 주어졌을 때, 두 대의 청소차를 이용해 모든 도시를 청소할 수 있는지 없는지, 있는 경우 어떻게 청소차가 방문해야 하는지 구해보자.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다.

각 테스트 케이스의 첫째 줄에는 도시의 수 N, 도로의 수 M이 주어진다. 둘째 줄과 셋째 줄에 각각 M개의 정수가 주어지며, i번째 정수 쌍이 i번 도로로 이어진 두 도시를 의미한다.

임의의 한 도시에서 다른 모든 도시로 갈 수 있는 경우만 입력으로 주어진다.

출력

각각의 테스트 케이스마다 두 줄을 출력해야 한다.

각 줄에 출력하는 첫 번째 정수는 각 청소차가 청소해야 하는 도로의 수이며, 이후 청소해야 하는 도로의 번호를 순서대로 출력한다. i번 도로가 입력으로 주어진 순서의 반대로 이동하는 경우에는 -i로 출력한다.

모든 도로를 청소하는 것이 불가능한 경우에는 각 줄에 0을 출력한다 (즉 두 줄에 걸쳐 각 줄에 0을 출력한다).

제한

  • 1 ≤ N ≤ 1,000
  • 1 ≤ M ≤ 50,000

예제 입력 1

5
4 5
1 1 1 2 3
2 2 3 4 4
4 5
1 1 1 2 3
2 2 3 4 4
4 3
1 1 1
2 3 4
6 5
1 1 1 1 1
2 3 4 5 6
2 1
2
1

예제 출력 1

1 1
4 2 4 -5 -3
2 3 5
3 -1 2 4
2 -1 3
1 -2
0
0
0
0
[{"problem_id":"17434","problem_lang":"0","title":"\ub3c4\ub85c \uccad\uc18c","description":"<p>N\uac1c\uc758 \ub3c4\uc2dc\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ub098\ub77c\uac00 \uc788\uace0, \ub3c4\uc2dc\ub294 1\ubc88\ubd80\ud130 N\ubc88\uae4c\uc9c0 \ubc88\ud638\uac00 \ubd99\uc5b4\uc788\ub2e4. \uadf8\ub9ac\uace0 \uc11c\ub85c \ub2e4\ub978 \ub450 \ub3c4\uc2dc\ub97c \uc774\uc5b4\uc8fc\ub294 \uc591\ubc29\ud5a5 \ub3c4\ub85c M\uac1c\uac00 \uc788\uace0, \ub3c4\ub85c\ub3c4 1\ubc88\ubd80\ud130&nbsp;M\ubc88\uae4c\uc9c0 \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4. \ub450 \ub3c4\uc2dc \uc0ac\uc774\uc5d0 \ub3c4\ub85c\uac00 \uc5ec\ub7ec \uac1c \uc788\uc744 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ucd5c\uadfc\uc5d0 \uc608\uc0b0\uc774 \ubaa8\uc790\ub77c\ub294 \uc0c1\ud669\uc774 \ubc1c\uc0dd\ud574 \ub3c4\ub85c \uccad\uc18c\ucc28\ub97c \ub450 \ub300\ub9cc \uc6b4\uc601\ud558\uae30\ub85c \ud588\ub2e4. \uc774 \uccad\uc18c\ucc28\ub97c \uc774\uc6a9\ud574 \ubaa8\ub4e0 \ub3c4\ub85c\ub97c \ud55c \ubc88\uc529\ub9cc \uccad\uc18c\ud558\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub450 \uccad\uc18c\ucc28\ub294 \uac01\uac01 \uc784\uc758\uc758 \ub3c4\uc2dc\uc5d0\uc11c \ucd9c\ubc1c\ud55c\ub2e4. \uac19\uc740 \ub3c4\uc2dc\uc5d0\uc11c \ucd9c\ubc1c\ud560 \uc218\ub3c4 \uc788\uace0, \ub2e4\ub978 \ub3c4\uc2dc\uc5d0\uc11c \ucd9c\ubc1c\ud560 \uc218\ub3c4 \uc788\ub2e4. \ubaa8\ub4e0 \ub3c4\ub85c\ub97c \uc815\ud655\ud788 \ud55c \ubc88\uc529\ub9cc \uccad\uc18c\ud558\uae30 \uc704\ud574, \uac01 \ub3c4\ub85c\ub294&nbsp;\ub458 \uc911 \ub531 \ud55c \ub300\uc758 \uccad\uc18c\ucc28\ub9cc \uc9c0\ub098\uac00\uc57c \ud55c\ub2e4 (\uccad\uc18c\ucc28\uac00 \uccad\uc18c\ub97c \ud558\uc9c0 \uc54a\uace0 \ub3c4\ub85c\ub97c \uadf8\ub0e5 \uc9c0\ub098\uac08 \uc218\ub294 \uc5c6\ub2e4). \ub9c8\uc9c0\ub9c9\uc73c\ub85c, \uac01 \uccad\uc18c\ucc28\ub294 \ud558\ub098 \uc774\uc0c1\uc758 \ub3c4\ub85c\ub97c \uccad\uc18c\ud574\uc57c \ud55c\ub2e4 (\uadf8\ub807\uc9c0 \uc54a\uc73c\uba74 \uccad\uc18c\ucc28\ub97c \ub450 \ub300 \uc6b4\uc601\ud560 \uc774\uc720\uac00 \uc5c6\ub2e4).<\/p>\r\n\r\n<p>\ub3c4\uc2dc\uc758 \ub3c4\ub85c \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ub450 \ub300\uc758 \uccad\uc18c\ucc28\ub97c \uc774\uc6a9\ud574 \ubaa8\ub4e0 \ub3c4\uc2dc\ub97c \uccad\uc18c\ud560 \uc218 \uc788\ub294\uc9c0 \uc5c6\ub294\uc9c0, \uc788\ub294 \uacbd\uc6b0 \uc5b4\ub5bb\uac8c \uccad\uc18c\ucc28\uac00 \ubc29\ubb38\ud574\uc57c \ud558\ub294\uc9c0 \uad6c\ud574\ubcf4\uc790.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \ub3c4\uc2dc\uc758 \uc218 N, \ub3c4\ub85c\uc758 \uc218 M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\uacfc \uc14b\uc9f8 \uc904\uc5d0 \uac01\uac01 M\uac1c\uc758 \uc815\uc218\uac00 \uc8fc\uc5b4\uc9c0\uba70, i\ubc88\uc9f8 \uc815\uc218 \uc30d\uc774 i\ubc88 \ub3c4\ub85c\ub85c \uc774\uc5b4\uc9c4 \ub450 \ub3c4\uc2dc\ub97c \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc784\uc758\uc758 \ud55c \ub3c4\uc2dc\uc5d0\uc11c \ub2e4\ub978 \ubaa8\ub4e0&nbsp;\ub3c4\uc2dc\ub85c \uac08 \uc218 \uc788\ub294 \uacbd\uc6b0\ub9cc \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \ub450 \uc904\uc744 \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uac01 \uc904\uc5d0 \ucd9c\ub825\ud558\ub294 \uccab \ubc88\uc9f8 \uc815\uc218\ub294&nbsp;\uac01 \uccad\uc18c\ucc28\uac00 \uccad\uc18c\ud574\uc57c \ud558\ub294 \ub3c4\ub85c\uc758 \uc218\uc774\uba70, \uc774\ud6c4 \uccad\uc18c\ud574\uc57c \ud558\ub294 \ub3c4\ub85c\uc758 \ubc88\ud638\ub97c \uc21c\uc11c\ub300\ub85c \ucd9c\ub825\ud55c\ub2e4. i\ubc88 \ub3c4\ub85c\uac00 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \uc21c\uc11c\uc758 \ubc18\ub300\ub85c \uc774\ub3d9\ud558\ub294 \uacbd\uc6b0\uc5d0\ub294 -i\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ub3c4\ub85c\ub97c \uccad\uc18c\ud558\ub294 \uac83\uc774 \ubd88\uac00\ub2a5\ud55c \uacbd\uc6b0\uc5d0\ub294 \uac01 \uc904\uc5d0 0\uc744 \ucd9c\ub825\ud55c\ub2e4 (\uc989 \ub450 \uc904\uc5d0 \uac78\uccd0 \uac01 \uc904\uc5d0 0\uc744 \ucd9c\ub825\ud55c\ub2e4).<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\ud55c\uad6d\uc5b4","limit":"<ul>\r\n\t<li>1 &le; N &le; 1,000<\/li>\r\n\t<li>1 &le; M &le; 50,000<\/li>\r\n<\/ul>\r\n"},{"problem_id":"17434","problem_lang":"1","title":"Street Cleaning","description":"<p>There is a country that has N cities and the cities are numbered from 1 to N. There are M bi-directional streets each of which connects two distinct cities, the streets are numbered from 1 to M. There may exist multiple streets between the same pair of cities.<\/p>\r\n\r\n<p>Due to a recent budget constraint, the government has decided to operate only two street cleaning vehicles. Using these two vehicles, you wish to clean each street exactly once.<\/p>\r\n\r\n<p>Each vehicle can start cleaning from any city you like. The two vehicles may start from the same city or different cities. In order to clean each street exactly once, every street must be traversed by exactly one vehicle because&nbsp;a&nbsp;cleaning vehicle cannot traverse the street without cleaning it. Finally, each vehicle must clean at least one road (otherwise we have no reason to keep both vehicles).<\/p>\r\n\r\n<p>Given the city and street information, determine whether we can clean each street exactly once using two cleaning vehicles. If possible, we should also find a way to do so.<\/p>\r\n","input":"<p>The first line will contain one integer T.<\/p>\r\n\r\n<p>For each test case, the first line will contain two integers N (the number of cities) and M (the number of streets). The next two lines will contain M integers each so that the i-th pair of integers represent the two cities connected by the i-th street.<\/p>\r\n\r\n<p>Each test case will always satisfy the following: From any city you can reach any other city using the given streets.<\/p>\r\n","output":"<p>For each test case, you must output two lines.<\/p>\r\n\r\n<p>The first integer in each of the two lines is the number of streets a vehicle must clean, followed by the street numbers. If the vehicle must traverse the ith street in the reversed order (compared to the original input), then output -i.<\/p>\r\n\r\n<p>If it is impossible to clean every street exactly once, then you must output 0 in each line (hence, two lines with 0 in each line).<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\uc601\uc5b4","limit":"<ul>\r\n\t<li>1 &le; N &le; 1,000<\/li>\r\n\t<li>1 &le; M &le; 50,000<\/li>\r\n<\/ul>\r\n"}]