문제
NLCS Jeju에서는 학생회(Student Council) 회장 강준석이 다른 학생 단체에 예산을 분배한다.
준석이는 학생회를 제외한 $N$개의 단체에 올해 예산 $M$을 분배해야 한다. $N$개의 단체에 예산을 분배하고 남은 금액을 학생회 예산으로 사용할 수 있다. 준석이는 학생회 예산으로 최대한 많은 예산을 가져오고 싶어 어떻게 예산을 분배할지 깊은 고민에 빠졌다.
매년 예산 분배가 끝난 직후 학생 단체들은 학생회장을 탄핵할지 투표를 진행한다. $i$번째 학생단체는 $V_i$표를 투표할 수 있다. 투표 결과 탄핵에 찬성하는 표가 과반인 경우 학생회장이 탄핵된다.
각 학생단체는 학생회보다 더 많은 예산을 받기를 원한다. 학생회보다 많거나 같은 예산을 받은 학생단체는 학생회장을 탄핵하는데 반대로 투표하며, 학생회보다 적은 예산을 받은 학생단체는 학생회장을 탄핵하는 데 투표할 것이다.
준석이가 학생회로 예산을 아무리 많이 가져온다고 한들 탄핵되면 아무 의미가 없어진다. 준석이는 탄핵되지 않으면서 학생회로 최대한 예산을 가져오려고 한다.
모든 학생 단체에 0ドル$ 이상의 예산을 분배하고 남은 예산이 학생회의 예산이 된다. 준석이가 탄핵되지 않으면서 가져올 수 있는 최대 예산을 구해보자.
출력
준석이가 탄핵되지 않으면서 학생회가 가져갈 수 있는 최대 예산을 정수로 출력한다.
제한
- 1ドル \le N \le 100,000円$
- 1ドル \le M \le 10^9$
- 1ドル \le V_i \le 10^9$
[{"problem_id":"31673","problem_lang":"0","title":"\ud2b9\ubcc4\ud55c \ud559\uc0dd\ud68c\uc7a5 \uad50\uccb4","description":"<p>NLCS Jeju\uc5d0\uc11c\ub294 \ud559\uc0dd\ud68c(Student Council) \ud68c\uc7a5 \uac15\uc900\uc11d\uc774 \ub2e4\ub978 \ud559\uc0dd \ub2e8\uccb4\uc5d0 \uc608\uc0b0\uc744 \ubd84\ubc30\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc900\uc11d\uc774\ub294 \ud559\uc0dd\ud68c\ub97c \uc81c\uc678\ud55c $N$\uac1c\uc758 \ub2e8\uccb4\uc5d0 \uc62c\ud574 \uc608\uc0b0 $M$\uc744 \ubd84\ubc30\ud574\uc57c \ud55c\ub2e4. $N$\uac1c\uc758 \ub2e8\uccb4\uc5d0 \uc608\uc0b0\uc744 \ubd84\ubc30\ud558\uace0 \ub0a8\uc740 \uae08\uc561\uc744 \ud559\uc0dd\ud68c \uc608\uc0b0\uc73c\ub85c \uc0ac\uc6a9\ud560 \uc218 \uc788\ub2e4. \uc900\uc11d\uc774\ub294 \ud559\uc0dd\ud68c \uc608\uc0b0\uc73c\ub85c \ucd5c\ub300\ud55c \ub9ce\uc740 \uc608\uc0b0\uc744 \uac00\uc838\uc624\uace0 \uc2f6\uc5b4 \uc5b4\ub5bb\uac8c \uc608\uc0b0\uc744 \ubd84\ubc30\ud560\uc9c0 \uae4a\uc740 \uace0\ubbfc\uc5d0 \ube60\uc84c\ub2e4.<\/p>\r\n\r\n<p>\ub9e4\ub144 \uc608\uc0b0 \ubd84\ubc30\uac00 \ub05d\ub09c \uc9c1\ud6c4 \ud559\uc0dd \ub2e8\uccb4\ub4e4\uc740 \ud559\uc0dd\ud68c\uc7a5\uc744 \ud0c4\ud575\ud560\uc9c0 \ud22c\ud45c\ub97c \uc9c4\ud589\ud55c\ub2e4. $i$\ubc88\uc9f8 \ud559\uc0dd\ub2e8\uccb4\ub294 $V_i$\ud45c\ub97c \ud22c\ud45c\ud560 \uc218 \uc788\ub2e4. \ud22c\ud45c \uacb0\uacfc \ud0c4\ud575\uc5d0 \ucc2c\uc131\ud558\ub294 \ud45c\uac00 \uacfc\ubc18\uc778 \uacbd\uc6b0 \ud559\uc0dd\ud68c\uc7a5\uc774 \ud0c4\ud575\ub41c\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud559\uc0dd\ub2e8\uccb4\ub294 \ud559\uc0dd\ud68c\ubcf4\ub2e4 \ub354 \ub9ce\uc740 \uc608\uc0b0\uc744 \ubc1b\uae30\ub97c \uc6d0\ud55c\ub2e4. \ud559\uc0dd\ud68c\ubcf4\ub2e4 \ub9ce\uac70\ub098 \uac19\uc740 \uc608\uc0b0\uc744 \ubc1b\uc740 \ud559\uc0dd\ub2e8\uccb4\ub294 \ud559\uc0dd\ud68c\uc7a5\uc744 \ud0c4\ud575\ud558\ub294\ub370 \ubc18\ub300\ub85c \ud22c\ud45c\ud558\uba70, \ud559\uc0dd\ud68c\ubcf4\ub2e4 \uc801\uc740 \uc608\uc0b0\uc744 \ubc1b\uc740 \ud559\uc0dd\ub2e8\uccb4\ub294 \ud559\uc0dd\ud68c\uc7a5\uc744 \ud0c4\ud575\ud558\ub294 \ub370 \ud22c\ud45c\ud560 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc900\uc11d\uc774\uac00 \ud559\uc0dd\ud68c\ub85c \uc608\uc0b0\uc744 \uc544\ubb34\ub9ac \ub9ce\uc774 \uac00\uc838\uc628\ub2e4\uace0 \ud55c\ub4e4 \ud0c4\ud575\ub418\uba74 \uc544\ubb34 \uc758\ubbf8\uac00 \uc5c6\uc5b4\uc9c4\ub2e4. \uc900\uc11d\uc774\ub294 \ud0c4\ud575\ub418\uc9c0 \uc54a\uc73c\uba74\uc11c \ud559\uc0dd\ud68c\ub85c \ucd5c\ub300\ud55c \uc608\uc0b0\uc744 \uac00\uc838\uc624\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ud559\uc0dd \ub2e8\uccb4\uc5d0 $0$ \uc774\uc0c1\uc758 \uc608\uc0b0\uc744 \ubd84\ubc30\ud558\uace0 \ub0a8\uc740 \uc608\uc0b0\uc774 \ud559\uc0dd\ud68c\uc758 \uc608\uc0b0\uc774 \ub41c\ub2e4. \uc900\uc11d\uc774\uac00 \ud0c4\ud575\ub418\uc9c0 \uc54a\uc73c\uba74\uc11c \uac00\uc838\uc62c \uc218 \uc788\ub294 \ucd5c\ub300 \uc608\uc0b0\uc744 \uad6c\ud574\ubcf4\uc790.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ud559\uc0dd\ub2e8\uccb4\uc758 \uc218 $N$\uacfc \ucd1d\uc608\uc0b0\uc744 \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 $M$\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0 \uac01 \ud559\uc0dd\ub2e8\uccb4\uac00 \uc0ac\uc6a9\ud560 \uc218 \uc788\ub294 \ud45c\uc758 \uc218\ub97c \ub098\ud0c0\ub0b4\ub294 $N$\uac1c\uc758 \uc815\uc218 $V_i$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uc900\uc11d\uc774\uac00 \ud0c4\ud575\ub418\uc9c0 \uc54a\uc73c\uba74\uc11c \ud559\uc0dd\ud68c\uac00 \uac00\uc838\uac08 \uc218 \uc788\ub294 \ucd5c\ub300 \uc608\uc0b0\uc744 \uc815\uc218\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$1 \\le N \\le 100\\,000$<\/li>\r\n\t<li>$1 \\le M \\le 10^9$<\/li>\r\n\t<li>$1 \\le V_i \\le 10^9$<\/li>\r\n<\/ul>\r\n"},{"problem_id":"31673","problem_lang":"1","title":"Exceptional Student Council","description":"<p>In NLCS Jeju, the Head of the Student Council&nbsp;Aaren Kang distributes the budget to other student organisations.<\/p>\r\n\r\n<p>Aaren must distribute the total budget $M$ to $N$ other organisations, excluding the Student Council. The remaining amount after distribution to $N$ organisations can be used as the Student Council&#39;s budget. Aaren wants to bring as much budget as possible to the Student Council and is finding a way to distribute the budget.<\/p>\r\n\r\n<p>Every year, right after the budget distribution is completed, the student organisations vote on whether to impeach the Student Council President. The $i$-th student organisation can cast&nbsp;$V_i$ votes. If the majority votes in favour, the Student Council President will be impeached.<\/p>\r\n\r\n<p>Each student organisation wants to receive more budget than the Student Council. Organisations that receive the same or more budget than the Student Council will vote against impeaching the President, while those that receive less will vote for impeachment.<\/p>\r\n\r\n<p>Even if Aaren brings as much budget as possible to the Student Council, it will be meaningless if he is impeached. He wants to bring the maximum budget to the Student Council without being impeached.<\/p>\r\n\r\n<p>The budget can be distributed as non-negative integers including $0$ to all student organisations, and the remaining budget after distribution becomes the Student Council&#39;s budget. Find the maximum budget Aaren can bring to the Student Council without being impeached.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","input":"<p>The first line contains two integers&nbsp;$N$ and&nbsp;$M$ $-$ the number of student organisations&nbsp;and the total budget, respectively.<\/p>\r\n\r\n<p>The second line contains $N$ integers $V_i$ $-$ the number of votes each student organisation can cast.<\/p>\r\n","output":"<p>Print a single integer $-$ the maximum budget that the Student Council can keep without Aaren getting impeached.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$1 \\le N \\le 100\\,000$<\/li>\r\n\t<li>$1 \\le M \\le 10^9$<\/li>\r\n\t<li>$1 \\le V_i \\le 10^9$<\/li>\r\n<\/ul>\r\n"}]