---{"category_name":"medium","problem_code":"FUNARR","problem_name":"Functional Array","problemComponents":{"constraints":"- $1 \\leq T \\leq 10^5$\n- $1 \\leq N \\leq 10^5$\n- $1 \\leq M \\leq 10^5$\n- $0 \\leq B_i \\leq 10^5$\n- $0 \\leq Z_i \\leq 10^5$\n- The sum of $N$ over all test cases does not exceed $10^5$\n- The sum of $M$ over all test cases does not exceed $10^5$","constraintsState":true,"subtasks":"**Subtask #1 (5 points):**\n- $1\\leq M \\leq 10$\n- $1\\leq N \\leq 10^3$\n- $0\\leq B_i \\leq 10^3$\n- $0\\leq Z_i \\leq 10^3$\n- The sum of $M$ over all test cases does not exceed $100$\n\n**Subtask #2 (40 points):**\n- $1\\leq M \\leq 10^3$\n- $1\\leq N \\leq 10^3$\n- $0\\leq B_i \\leq 10^3$\n- $0\\leq Z_i \\leq 10^3$\n- The sum of $M$ over all test cases does not exceed $10^3$\n\n**Subtask #3 (55 points):**\n- Original constraints\n\n","subtasksState":true,"inputFormat":"- The first line of input contains a single integer $T$, denoting the number of test cases. The description of $T$ test cases follows.\n- Each test case contains three lines of input.\n- The first line contains two integers $N$ and $M$ - the lengths of $B$ and $Z$ respectively.\n- The second line contains $N$ space-separated integers $B_1, B_2, \\dots, B_N$; the elements of $B$.\n- The third line contains $M$ space-separated integers $Z_1, Z_2, \\dots, Z_M$; the elements of $Z$.\n","inputFormatState":true,"outputFormat":"For each test case, output a single line containing one word - either \u0022YES\u0022 or \u0022NO\u0022. You may print each character of the string in uppercase or lowercase (for example, the strings \u0022yEs\u0022, \u0022yes\u0022, \u0022Yes\u0022 and \u0022YES\u0022 will all be treated as identical).\n","outputFormatState":true,"sampleTestCases":{"0":{"id":1,"input":"2\n2 2\n2 3\n1 1\n2 2\n2 4\n1 3","output":"YES\nNO","explanation":"**Test case 1:**\n\n$A = [1, 2, 3]$ is one possible array.\n- $B = [2, 3]$ is a subsequence of $A$\n- $fA = [1, 1]$ is a subsequence of $Z = [1, 1]$.\n\n**Test case 2:**\n\nIt can be shown that no array $A$ can both contain $B = [2, 4]$ as a subsequence and also have $fA$ be a subsequence of $Z = [1, 3]$","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":1,"source_sizelimit":50000,"problem_author":"inov_360","problem_tester":"","date_added":"31-10-2021","tags":{"0":"greedy","1":"greedy","2":"inov_360","3":"knapsack","4":"knapsack","5":"medium","6":"medium","7":"nov21","8":"nov21"},"problem_difficulty_level":"Unavailable","best_tag":"","editorial_url":"https://discuss.codechef.com/problems/FUNARR","time":{"view_start_date":1636968600,"submit_start_date":1636968600,"visible_start_date":1636968600,"end_date":1735669800},"is_direct_submittable":false,"problemDiscussURL":"https://discuss.codechef.com/search?q=FUNARR","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>