Shubham walks up out to Arun to join him for a midnight quest of lighting up n bulbs along some path of length len, consisting of n bulbs. Consider the path to be a straight line starting from 0, and it ends at len. The position of j-th bulb is at the point aj. Each bulb has a luminance power of p units, where p denotes the total distance till which the bulb can emit light. Help Shubham and Arun in determining the minimum luminance power p which bulbs must have to enlighten the path.
Input Format
The first line contains two integers n, len (1<=n<=1000, 1<=len<=109) the number of bulbs and the length of the path respectively. The next line contains n integers aj (0<=aj<=len). Multiple bulbs can be located at the same point. The bulbs can be located at the ends of the path.
Output Format
Print the minimum luminance power p, needed to light the whole path. The answer will be considered correct if its absolute or relative error doesn't exceed 10 raised to power -9.
Constraints
NA
Notice
NA
Example
Input
800 1065478 82305280 27559819 91416808 96791118 21993849 5454468 25472723 495861 11333302 73953863 51687990 27547125 77963079 72809590 96445936 68088468 77548094 17734805 72712984 3686839 92450719 30001312 75045917 70418921 75655852 65511092 73955300 6162478 914052 14976185 13998263 36587881 48915333 25844690 65383934 72411472 6278913 78739686 52410035 61663847 79241862 36431653 83709266 65042469 27152209 71743933 39069257 99859519 2219792 72294685 25500071 28662222 41450719 14607689 1258333 52294346 94289029 97878237 80697259 3983949 85211752 28559275 75097014 30983870 4371251 50936875 95039958 93357836 91351346 25992997 38430522 5696525 27201465 71107439 14919591 96864260 78135575 86529728 12278463 65318470 40630491 11055691 93177542 63110409 22130623 68972259 21860168 50367110 54164037 93088042 59362059 23870855 75397258 34546067 33212059 38293932 41003957 99119000 82960008 6712802 11695291 81816089 6412699 88217264 50857337 6884937 83119104 44746524 11463693 18670158 31431111 76725590 25779028 10294844 63376256 27641708 20341950 21759708 37614041 81392058 66313261 86808648 74907618 63050272 40998327 58788385 92827732 93640772 20199932 99733769 36816020 42576313 43030615 74039183 33269886 67605546 90911239 48330493 66971354 31433798 705039 62530727 89967412 36621688 88284255 3616815 1919587 25932610 93298900 83193330 2975578 53991478 68515064 92763376 9375976 47933613 27812632 86455450 39294225 39663959 35780115 19969107 21818163 70413318 68816830 56631190 55516623 39469632 2750371 36708204 44694724 93278785 85199956 94499417 71226643 28550754 32263929 99239083 17764843 13573434 48582269 90465184 44159825 15627768 7422709 76265908 33084702 59214294 43161660 63694037 63143996 29742573 2378820 94643335 38156229 80401421 71756989 67609856 99835059 96119214 51076277 36015108 77753819 17840026 67814559 87146835 85263547 32782630 36213642 22277094 52944659 91915992 48143349 78146254 2207642 24576077 45693253 52755416 818299 81965381 66144630 24288635 9408183 56217876 68822639 80990313 23441053 89778551 50301601 11951936 38641366 11038072 29533761 44016318 19550886 6479529 37694639 48386385 30664746 67035654 78885713 82029408 97508409 26921240 37307835 73596599 1052120 46896975 94116464 11331738 73019608 80737252 82892387 41321594 51932988 3615954 56509339 38444596 80145903 74190612 60152529 69503332 70652156 48356723 5339779 28280184 49117216 61960452 18019578 85634408 81365141 52199325 90168088 64262872 29463618 93006939 98779739 17375509 40584984 78409101 68743719 63290533 61981218 99655250 46821317 3833293 92696113 26870381 22786780 33426602 28047901 24039134 80766905 27889270 26450870 97325093 88912355 87213450 29804551 1044739 38756239 94970355 98464322 3056956 26963263 48497756 79717353 41895306 31645290 8651671 14722992 91661825 73016913 15658423 3036871 87517342 63887248 18482284 86123142 54544869 49331818 69127752 81669424 25828935 6861031 40424432 99054192 31785161 28499481 36096416 92976483 92090796 34412894 75296926 67042976 44008328 74067184 50292927 22017649 96460675 55376835 75613316 54474361 7907900 4897364 69728164 50752870 47891773 2839362 36205461 88403958 17055936 55529209 40295639 52719506 68515777 64914279 9023132 99478457 94643615 29808033 18118081 46699873 17651123 66793106 67500240 57979284 49792352 70048139 88530993 87894894 69577147 38836752 70878371 96005148 94076115 88994726 44593797 119479 14214726 30474089 3878208 31809153 99895549 36850510 13019182 77535248 74854021 54673013 92109462 37306059 7344519 632663 40411311 9436247 62069991 72749655 18609984 14765343 11209719 58125688 77703467 6603257 7966258 54281362 91904635 73705673 84743966 33695885 25685799 32742341 49887968 71889030 40974554 24006421 21853788 28233004 29513776 69523231 57744281 15654476 37527451 26251844 4341955 20484719 35087993 68733208 24081088 36938437 70959575 65323557 25845563 62049553 45195920 70062075 61044620 56364821 26399912 38256923 29110294 13293871 38306249 88033869 73376525 95736852 41227333 72376978 38241500 92458582 37906452 96600907 1581088 18650719 40451225 14729532 92572690 35221141 45274185 64915837 54405183 89572368 76346303 58823050 13792106 86978529 73573135 22797273 74771589 86143038 22732180 99696949 62967954 75116767 46163979 59404664 8306318 24479197 99288343 33331962 69112954 33532667 47021040 83638019 68600537 82232488 26295156 41418119 35928829 76673378 36145278 99778106 18347768 29175292 35191508 27496070 58371329 45359391 67864267 76882760 10496916 77572 85339746 95487289 5676461 71656606 74909730 15454919 58561828 69640590 62388497 86628835 52488502 35063114 6163309 39897999 30227949 14253136 58624020 15828278 64730467 7276281 30961153 70274276 83396729 70335889 60700717 73454402 71857618 7805798 47848000 51881846 88808405 24039549 95141401 83579356 82134657 17698287 60671312 46165818 8383759 92062341 6997979 34687800 22577228 23639112 9906140 11479382 23425521 78352529 72063163 23868765 10198354 89697018 72101335 27210315 31819996 16461579 68023813 80505766 86200424 78977204 65337699 39788635 58379566 32313560 54946573 60480855 69753361 72448475 23588749 34090958 47466682 87156456 40486405 26908199 12999612 57210103 27874675 58757199 32039996 85460961 30208640 58412838 63926543 81463981 7100145 58935287 98263202 57532428 88415182 50970226 68746914 98457755 46466568 94969449 89817276 51601569 59865492 4322189 70428027 46664515 66349452 50547735 21056702 95159542 27782978 8984919 85010179 38464672 59531473 58824402 93150299 10303047 8537388 74864649 62355049 54595686 99681867 32780 32347329 92855058 8393877 67496600 62964638 66635207 58972810 49104212 94509436 90026818 92719339 42922862 7511399 34783321 97723366 76808763 5049101 36386707 43036639 97224805 80720163 53209464 13961663 32933256 28415214 32901632 2317371 71725650 96242509 40229682 65795891 65012290 86266384 78816550 33903770 79878855 54164175 95579822 4484774 51127876 68472619 91137741 44450399 46857886 47786164 72050307 81098122 50293282 6086012 71485480 46276226 77863058 1320154 33748091 14658112 98936742 421024 5081711 59517740 96161015 45138832 98251466 34651885 7000644 27385032 1638349 79473713 16872531 60221792 84923284 35806122 32171819 61199735 12911859 59532230 47524189 48437619 16648270 8014200 35758556 86654060 86689705 85070637 31379648 10302761 47260030 29306564 48729982 94029176 41974313 38718991 74566029 36857859 11923373 34754934 1433399 75836272 75130173 82377680 23011127 47302108 22737593 99200982 95505249 69507682 31759695 6379804 80207017 29026316 56826315 96700088 21491286 15182022 4073448 21188977 81815716 61685270 9179534 24570813 50691627 22723936 38520425 92023120 68132502 31950021 7513491 4940710 54746248 67119082 63443921 41794945 20422528 70580733 11413983 1679099 31476612 56385006 71528671 72759678 52146345 68460724 43028745 15607429 40499011 41138494 16804913 82260717 71089984 53232291 21574543 45877848 77125273 59960041 10974893 72963776 53415176 33174988 98924575 30410618 38066429 39696077 28827569 82970218 95645393 39966946 18541823 3280994 57455001 94839556 57507033 86200138 35603284 26969885 45023980 31946183 16701517 95129529 49400336 38435853 58315155 4678425
Output
517350.0000000000