---{"category_name":"school","problem_code":"CHECKMATE","problem_name":"Check Mate","problemComponents":{"constraints":"- $1 \\leq T \\leq 1.6 \\cdot 10^5$\n- $1 \\leq x_k, y_k, x_1, y_1, x_2, y_2 \\leq 8$\n- Initially the king is not under check, i.e, $x_k \\neq x_1$ and $x_k \\neq x_2$ and $y_k \\neq y_1$ and $y_k \\neq y_2$.\n- No two pieces overlap.\n","constraintsState":true,"subtasks":"**Subtask #1 (100 points):** Original constraints\n","subtasksState":true,"inputFormat":"- The first line of input will contain 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 space-separated integers $x_k$ and $y_k$, the row and column respectively in which white king is placed.\n- The second line contains two space-separated integers $x_1$ and $y_1$, the row and column respectively in which the first black rook is placed.\n- The third line contains two space-separated integers $x_2$ and $y_2$, the row and column respectively in which the second black rook is placed.\n\n","inputFormatState":true,"outputFormat":"For each test case, output a single line containing the answer: `\u0022YES\u0022` if it\u0027s possible to checkmate the king in one move and `\u0022NO\u0022` if not.\n\nYou 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":"4\n1 1\n8 2\n7 3\n1 8\n8 2\n8 3\n1 1\n8 2\n2 3\n1 1\n8 8\n8 2\n","output":"YES\nNO\nNO\nNO","explanation":"**Test Case $1$:** The second rook can be moved to $(7, 1)$, thus checkmating the king.\n \n\n\n\n**Test Case $2$ and $3$:** No possible move exists to checkmate the king. The following images describe why checkmating is impossible in test case $2$:\n\n \n\n\n\n \n \n\n\n\n**Test Case $4$:** The game can end in a stalemate if the first rook is moved to $(2, 8)$, but there exists no move to checkmate the king.","isDeleted":false}}},"video_editorial_url":"https://youtu.be/YP3B5zEAGF8","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":0.5,"source_sizelimit":50000,"problem_author":"daanish_adm","problem_tester":"","date_added":"30-11-2021","tags":{"0":"cakewalk","1":"daanish_adm","2":"dec21"},"problem_difficulty_level":"Cakewalk","best_tag":"","editorial_url":"https://discuss.codechef.com/problems/CHECKMATE","time":{"view_start_date":1639387800,"submit_start_date":1639387800,"visible_start_date":1639387800,"end_date":1735669800},"is_direct_submittable":false,"problemDiscussURL":"https://discuss.codechef.com/search?q=CHECKMATE","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>