---{"category_name":"medium","problem_code":"CLIMBINGRANK","problem_name":"The Strange Ranking of Sport Climbing","problemComponents":{"constraints":"- $1\\le t\\le 5000$\n- $1\\le m\\le n\\le 5000$\n- The sum of $n$ over all test cases is at most $5000$.\n- The array $s_1, s_2,\\dots, s_n$ is a permutation of $1,2,\\dots, n$.\n- The array $b_1, b_2,\\dots, b_n$ is a permutation of $1,2,\\dots, n$.\n- $1\\le l_i\\le n$ for all $i=1,2,\\dots, m$.\n- $l_i\\neq l_j$ for all $1\\le i\\lt j\\le m$.","constraintsState":true,"subtasks":"- 30 points : $1 \\leq R \\leq 10000$\n- 70 points : $1 \\leq R \\leq 10^9$\n","subtasksState":false,"inputFormat":"- First line contains $t$ — the number of test cases. Then the test cases follow.\n- The first line of each test case contains the two integers $n, m$ — the number of climbers and the number of climbers who have already taken part in the lead contest.\n- The second line contains $n$ integers $s_1, s_2,\\dots, s_n$ — the ranking of the speed contest. In particular $s_i$ is the athlete who ranked $i$-th in the speed contest.\n- The third line contains $n$ integers $b_1, b_2,\\dots, b_n$ — the ranking of the bouldering contest. In particular $b_i$ is the athlete who ranked $i$-th in the bouldering contest. \n- The fourth line contains $m$ integers $l_1,l_2,\\dots, l_m$ — the current ranking of the lead contest. In particular $l_i$ is the athlete who is currently ranked $i$-th in the lead contest.","inputFormatState":true,"outputFormat":"For each test case, print the best final ranking that athlete $1$ can have at the end of the competition.","outputFormatState":true,"sampleTestCases":{"0":{"id":1,"input":"8\n1 1\n1\n1\n1\n3 3\n1 2 3\n2 3 1\n3 1 2\n5 1\n3 4 2 1 5\n4 1 5 2 3\n1\n4 2\n2 4 1 3\n2 4 1 3\n3 1\n4 2\n3 2 4 1\n4 2 3 1\n3 2\n4 2\n4 2 3 1\n4 1 2 3\n1 3\n7 4\n7 5 1 3 2 6 4\n3 6 4 1 2 7 5\n6 4 5 1\n7 6\n4 3 6 7 1 2 5\n5 3 7 4 6 2 1\n1 7 4 2 5 3\n","output":"1\n1\n1\n3\n3\n2\n4\n4\n","explanation":"\u003Cp\u003E\n\u003Cb\u003EExplanation of test case 1:\u003C/b\u003E There is only athlete $1$, who has already taken part in the lead contest. His ranking positions in the three contests are $1$, $1$, $1$, hence is final score is $1$ and he gets final ranking position $1$.\n\u003C/p\u003E\n\n\u003Cp\u003E\n\u003Cb\u003EExplanation of test case 2:\u003C/b\u003E There are $3$ athletes and all of them have already taken part in the lead contest. Their scores are:\n\u003C/p\u003E\n\n\u003Cul\u003E\u003Cli\u003E Athlete $1$ has final score of $1\\cdot 3\\cdot 2 = 6$. Indeed his speed ranking is $1$, his bouldering ranking is $3$, and his lead ranking is $2$. \u003C/li\u003E\n\u003Cli\u003E Athlete $2$ has final score of $2\\cdot 1\\cdot 3 = 6$. Indeed his speed ranking is $2$, his bouldering ranking is $1$, and his lead ranking is $3$. \u003C/li\u003E\n\u003Cli\u003E Athlete $3$ has final score of $3\\cdot 2\\cdot 1 = 6$. Indeed his speed ranking is $3$, his bouldering ranking is $2$, and his lead ranking is $1$. \u003C/li\u003E\n\u003C/ul\u003E\u003Cp\u003EAll the athletes have final score equal to $6$, hence all of them (and in particular athlete $1$) get final ranking position $1$. \u003C/p\u003E\n\n\u003Cp\u003E\n\u003Cb\u003EExplanation of test case 3\u003C/b\u003E There are $5$ athletes and only athlete $1$ has already taken part in the lead contest. The best final ranking positions for athlete $1$ is $1$ and can be achieved if the lead ranking in the end is $1, 2, 3, 4, 5$.\nWith this lead ranking, the final scores of the $5$ athletes would be (in order): $8, 24, 15, 8, 65$. Since athlete $1$ has the minimum score (tying with athlete $4$), his final ranking position is $1$.\n\u003C/p\u003E\n\n\u003Cp\u003E\n\u003Cb\u003EExplanation of test case 4:\u003C/b\u003E There are $4$ athletes; athletes $1$ and $3$ have already taken part in the lead contest with $3$ being ranked first and $1$ being ranked second. Let us describe some (not necessarily possible) lead rankings:\n\n\u003C/p\u003E\u003Cul\u003E\u003Cli\u003E The lead ranking $1, 3, 2, 4$ is impossible since it is not consistent with the current lead ranking (athlete $1$ and $3$ appear in a different order in the current ranking). \u003C/li\u003E\n\u003Cli\u003E The lead ranking $3, 1, 2, 4$ is consistent with the current lead ranking. In this case, the final scores of the athletes would be (in order) $18,3,16,16$; hence athlete $1$ would get final ranking equal to $4$ (that is, he would be last). \u003C/li\u003E\n\u003Cli\u003E The lead ranking $2, 4, 3, 1$ is consistent with the current lead ranking. In this case, the final scores of the athletes would be (in order) $36, 1, 48, 8$; hence athlete $1$ would get final ranking equal to $3$ (and this is the best possible final ranking). \u003C/li\u003E\n\u003C/ul\u003E","isDeleted":false}}},"video_editorial_url":"","languages_supported":{"0":"CPP14","1":"C","2":"JAVA","3":"PYTH 3.6","4":"CPP17","5":"PYTH","6":"PYP3","7":"CS2","8":"ADA","9":"PYPY","10":"TEXT","11":"PAS fpc","12":"NODEJS","13":"RUBY","14":"PHP","15":"GO","16":"HASK","17":"TCL","18":"PERL","19":"SCALA","20":"LUA","21":"kotlin","22":"BASH","23":"JS","24":"LISP sbcl","25":"rust","26":"PAS gpc","27":"BF","28":"CLOJ","29":"R","30":"D","31":"CAML","32":"FORT","33":"ASM","34":"swift","35":"FS","36":"WSPC","37":"LISP clisp","38":"SQL","39":"SCM guile","40":"PERL6","41":"ERL","42":"CLPS","43":"ICK","44":"NICE","45":"PRLG","46":"ICON","47":"COB","48":"SCM chicken","49":"PIKE","50":"SCM qobi","51":"ST","52":"SQLQ","53":"NEM"},"max_timelimit":4,"source_sizelimit":50000,"problem_author":"dario2994","problem_tester":"","date_added":"5-01-2022","tags":{"0":"dario2994","1":"medium","2":"snckfl21","3":"snckfp21"},"problem_difficulty_level":"Unavailable","best_tag":"","editorial_url":"https://discuss.codechef.com/problems/CLIMBINGRANK","time":{"view_start_date":1641747600,"submit_start_date":1641747600,"visible_start_date":1641747600,"end_date":1735669800},"is_direct_submittable":false,"problemDiscussURL":"https://discuss.codechef.com/search?q=CLIMBINGRANK","is_proctored":false,"visitedContests":{},"layout":"problem"}---This is an example statement in markdown. This is the statement of the problem [TANDC](https://codechef.com/problems/TANDC) on CodeChef. The main statement starts with the next paragraph. Please make sure to remove this paragraph from your statement before publishing your problem. If your problem doesn't contain Subtasks, you should remove the section subtask too. We are using markdown the syntax of which can be seen [at](https://github.com/showdownjs/showdown/wiki/Showdown's-Markdown-syntax). We request you to not use any HTML tags in the statement, e.g. no p, ul, li, pre, br or b tags. If you face any issue, please contact admins or email us at help@codechef.com.Tracy is teaching Charlie maths via a game called $N$-Cube, which involves three sections involving $N$.Tracy gives Charlie a number $N$, and Charlie makes a list of $N$-th powers of integers in increasing order $1^N, 2^N, 3^N, \dot, \text{so on}$. This teaches him exponentiation.Then Charlie performs the following subtraction game $N$ times: Take all pairs of consecutive numbers in the list and take their difference. These differences then form the new list for the next iteration of the game. Eg, if $N$ was 6, the list proceeds as $[1, 64, 729, 4096 ... ]$ to $[63, 685, 3367 ...]$, and so on $5$ more times.After the subtraction game, Charlie has to correctly tell Tracy the $N$-th element of the list. This number is the *value of the game*.After practice Charlie became an expert in the game. To challenge him more, Tracy will give two numbers $M$ (where $M$ is a prime) and $R$ instead of just a single number $N$, and the game must start from $M_R - 1$ instead of $N$. Since the *value of the game* can now become large, Charlie just have to tell the largest integer $K$ such that $M_K$ divides this number. Since even $K$ can be large, output $K$ modulo 1000000007 ($10^9 + 7$).<aside style='background: #f8f8f8;padding: 10px 15px;'><div>All submissions for this problem are available.</div></aside>