시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
10 초 128 MB 24 5 5 23.810%

문제

강원도 횡성에는 엄청나게 큰 나무 두 개가 마주보고 있다. 이 나무의 기둥에는 수많은 구멍들이 있고, 수많은 딱따구리들이 이 구멍에서 서식하기 위해 몰려들었다. 하나의 구멍에는 한 마리의 딱따구리만이 서식할 수 있고 비어있는 구멍도 있을 수 있다. 이들 중 몇몇 두 딱따구리는 친밀한 관계를 유지하여 이들의 서식지를 왔다 갔다 한다. 하지만 딱따구리는 워낙 빨리 이동하기 때문에 충돌의 위험을 줄이기 위해 몇몇 규칙으로 딱따구리의 서식지를 배정하려 한다.

⑴ 딱따구리의 이동경로는 직선이다.
⑵ 친밀한 관계를 가지는 두 딱따구리는 서로 다른 나무에 서식하고 있어야한다.
⑶ 친밀한 관계를 가지는 딱따구리의 서식지를 연결하는 선분끼리 교차하면 안 된다. (단, 끝점 즉 서식지는 공유해도 상관없다)

딱따구리는 가능한 한 낮은 곳에 위치한 구멍에서 서식하기를 원한다. 또한 각각의 나무에 있는 구멍의 수는 딱따구리의 수보다 크다. 문제는 이러한 조건을 만족하는 서식지 배정의 가짓수를 구하는 것이다.

입력

첫째 줄에 새들의 숫자를 나타내는 N(1≤N≤1,000,000), 친밀한 관계를 유지하는 딱따구리 쌍의 수를 나타내는 M(1≤M≤10,000,000), 결과를 나눌 제수 K(1≤K≤2000,000)가 공백으로 구분되어 주어진다. 새들은 1번부터 N번까지 번호가 붙여져 있고 두 번째 줄부터 M+1번째 줄까지 각 줄에 친밀한 관계를 가지는 딱따구리의 번호가 공백으로 구분되어 주어진다.

출력

첫째 줄에 서식지 배정의 가짓수 R을 K로 나눈 나머지를 출력한다. 서식지를 배정할 수 없는 경우는 0을 출력한다.

예제 입력 1

3 2 10
1 2
1 3

예제 출력 1

4

힌트

[{"problem_id":"1642","problem_lang":"0","title":"\ub531\ub530\uad6c\ub9ac","description":"<p>\uac15\uc6d0\ub3c4 \ud6a1\uc131\uc5d0\ub294 \uc5c4\uccad\ub098\uac8c \ud070 \ub098\ubb34 \ub450 \uac1c\uac00 \ub9c8\uc8fc\ubcf4\uace0 \uc788\ub2e4. \uc774 \ub098\ubb34\uc758 \uae30\ub465\uc5d0\ub294 \uc218\ub9ce\uc740 \uad6c\uba4d\ub4e4\uc774 \uc788\uace0, \uc218\ub9ce\uc740 \ub531\ub530\uad6c\ub9ac\ub4e4\uc774 \uc774 \uad6c\uba4d\uc5d0\uc11c \uc11c\uc2dd\ud558\uae30 \uc704\ud574 \ubab0\ub824\ub4e4\uc5c8\ub2e4. \ud558\ub098\uc758 \uad6c\uba4d\uc5d0\ub294 \ud55c \ub9c8\ub9ac\uc758 \ub531\ub530\uad6c\ub9ac\ub9cc\uc774 \uc11c\uc2dd\ud560 \uc218 \uc788\uace0 \ube44\uc5b4\uc788\ub294 \uad6c\uba4d\ub3c4 \uc788\uc744 \uc218 \uc788\ub2e4. \uc774\ub4e4 \uc911 \uba87\uba87 \ub450 \ub531\ub530\uad6c\ub9ac\ub294 \uce5c\ubc00\ud55c \uad00\uacc4\ub97c \uc720\uc9c0\ud558\uc5ec \uc774\ub4e4\uc758 \uc11c\uc2dd\uc9c0\ub97c \uc654\ub2e4 \uac14\ub2e4 \ud55c\ub2e4. \ud558\uc9c0\ub9cc \ub531\ub530\uad6c\ub9ac\ub294 \uc6cc\ub099 \ube68\ub9ac \uc774\ub3d9\ud558\uae30 \ub54c\ubb38\uc5d0 \ucda9\ub3cc\uc758 \uc704\ud5d8\uc744 \uc904\uc774\uae30 \uc704\ud574 \uba87\uba87 \uaddc\uce59\uc73c\ub85c \ub531\ub530\uad6c\ub9ac\uc758 \uc11c\uc2dd\uc9c0\ub97c \ubc30\uc815\ud558\ub824 \ud55c\ub2e4.<\/p><p>\u2474 \ub531\ub530\uad6c\ub9ac\uc758 \uc774\ub3d9\uacbd\ub85c\ub294 \uc9c1\uc120\uc774\ub2e4.<br \/>\r\n\u2475 \uce5c\ubc00\ud55c \uad00\uacc4\ub97c \uac00\uc9c0\ub294 \ub450 \ub531\ub530\uad6c\ub9ac\ub294 \uc11c\ub85c \ub2e4\ub978 \ub098\ubb34\uc5d0 \uc11c\uc2dd\ud558\uace0 \uc788\uc5b4\uc57c\ud55c\ub2e4.<br \/>\r\n\u2476 \uce5c\ubc00\ud55c \uad00\uacc4\ub97c \uac00\uc9c0\ub294 \ub531\ub530\uad6c\ub9ac\uc758 \uc11c\uc2dd\uc9c0\ub97c \uc5f0\uacb0\ud558\ub294 \uc120\ubd84\ub07c\ub9ac \uad50\ucc28\ud558\uba74 \uc548 \ub41c\ub2e4. (\ub2e8, \ub05d\uc810 \uc989 \uc11c\uc2dd\uc9c0\ub294 \uacf5\uc720\ud574\ub3c4 \uc0c1\uad00\uc5c6\ub2e4)<\/p>\r\n<p>\ub531\ub530\uad6c\ub9ac\ub294 \uac00\ub2a5\ud55c \ud55c \ub0ae\uc740 \uacf3\uc5d0 \uc704\uce58\ud55c \uad6c\uba4d\uc5d0\uc11c \uc11c\uc2dd\ud558\uae30\ub97c \uc6d0\ud55c\ub2e4. \ub610\ud55c \uac01\uac01\uc758 \ub098\ubb34\uc5d0 \uc788\ub294 \uad6c\uba4d\uc758 \uc218\ub294 \ub531\ub530\uad6c\ub9ac\uc758 \uc218\ubcf4\ub2e4 \ud06c\ub2e4. \ubb38\uc81c\ub294 \uc774\ub7ec\ud55c \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \uc11c\uc2dd\uc9c0 \ubc30\uc815\uc758 \uac00\uc9d3\uc218\ub97c \uad6c\ud558\ub294 \uac83\uc774\ub2e4.<\/p>","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc0c8\ub4e4\uc758 \uc22b\uc790\ub97c \ub098\ud0c0\ub0b4\ub294 N(1&le;N&le;1,000,000), \uce5c\ubc00\ud55c \uad00\uacc4\ub97c \uc720\uc9c0\ud558\ub294 \ub531\ub530\uad6c\ub9ac \uc30d\uc758 \uc218\ub97c \ub098\ud0c0\ub0b4\ub294 M(1&le;M&le;10,000,000), \uacb0\uacfc\ub97c \ub098\ub20c \uc81c\uc218 K(1&le;K&le;2000,000)\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \uc0c8\ub4e4\uc740 1\ubc88\ubd80\ud130 N\ubc88\uae4c\uc9c0 \ubc88\ud638\uac00 \ubd99\uc5ec\uc838 \uc788\uace0 \ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 M+1\ubc88\uc9f8 \uc904\uae4c\uc9c0 \uac01 \uc904\uc5d0 \uce5c\ubc00\ud55c \uad00\uacc4\ub97c \uac00\uc9c0\ub294 \ub531\ub530\uad6c\ub9ac\uc758 \ubc88\ud638\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc11c\uc2dd\uc9c0 \ubc30\uc815\uc758 \uac00\uc9d3\uc218 R\uc744 K\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud55c\ub2e4. \uc11c\uc2dd\uc9c0\ub97c \ubc30\uc815\ud560 \uc218 \uc5c6\ub294 \uacbd\uc6b0\ub294 0\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>","hint":"<p><img alt=\"\" width=\"422\" height=\"392\" src=\"\/JudgeOnline\/upload\/201005\/ekrekrnfl.PNG\" \/><\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"1642","problem_lang":"1","title":"Hollows","description":"<p>There are two extremely high trees in Byteotia, and each of them has many hollows scooped out in its trunk, one under another. Once upon a time &nbsp;very fast birds decided to inhabit the hollows. Some of them know each other and therefore would like to be able to pay one another visits in their hollows. The birds fly very fast and always along a straight line. In order to avoid the danger of collision they decided to quarter in a way that:<\/p>\r\n\r\n<ul>\r\n\t<li>each two birds that would like to pay themselves visits live in different trees, and<\/li>\r\n\t<li>for each two pairs of familiar birds, the segments connecting the hollows of the familiar birds do not intersect (they may, however, have a common endpoint).<\/li>\r\n<\/ul>\r\n\r\n<p>In addition, the birds would like to live as low as possible. So in each tree they inhabit a certain number of lower hollows. There are more hollows in each tree than there are birds in whole.<\/p>\r\n\r\n<p>It is well-known that birds have very small brains. That&#39;s why they have asked you - a respected ornithologist - to help them find out in how many ways they can quarter in the hollows.<\/p>\r\n\r\n<p>Write a programme that:<\/p>\r\n\r\n<ul>\r\n\t<li>reads from the standard input the description of acquaintanceship between the birds,<\/li>\r\n\t<li>calculates in how many ways can the birds be quartered in the trees, satisfying the above constraints,<\/li>\r\n\t<li>writes the result to the standard output.<\/li>\r\n<\/ul>\r\n","input":"<p>In the first line of the standard input there are three integers written n, m and k, denoting respectively: the number of birds, the number of distinct pairs of birds knowing each other and the number that is to be used when giving result (see: Output), 2 &le; n &le; 1 000 000, 1 &le; m &le; 10 000 000, 2 &le; k &le; 2 000 000. The birds are numbered from 1 to n. In the following m lines the pairs of birds knowing each other are given, one per line. In the line no. i+1 two integers a<sub>i<\/sub> and b<sub>i<\/sub>, separated by a single space, are written (1 &le; a<sub>i<\/sub>, b<sub>i<\/sub> &le; n, a<sub>i<\/sub> &ne; b<sub>i<\/sub>). These are the numbers of the familiar birds. Each (unordered) pair of familiar birds is given exactly once.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","output":"<p>Let r denote the number of distinct quarterings of birds satisfying the given constraints. Your programme should write one integer in the first line of the standard output: the remainder of division of r by k. If no quartering exists the correct result is 0.<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/dzizad-img3.gif\" style=\"height:376px; width:403px\" \/><\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]