github.com/captn3m0/codechef.git

---
{"category_name":"easy","problem_code":"TOW","problem_name":"Tug of War","problemComponents":{"constraints":"- $1 \\leq T \\leq 10^4$\n- $1 \\leq N,M \\leq 10^6$\n- $1 \\leq A_i,B_j \\leq 10^9$ ($1 \\leq i \\leq N$, $1 \\leq j \\leq M$)\n- Sum of $N$ and $M$ across all test cases will not exceed $10^6$\n\n","constraintsState":true,"subtasks":"- 30 points : $1 \\leq R \\leq 10000$\n- 70 points : $1 \\leq R \\leq 10^9$\n","subtasksState":false,"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- The first line of each test case contains two space-separated integers $N$ and $M$ — the sizes of the opponent team and Gi-Hun\u0027s team, respectively.\n- The second line of each test case contains $N$ space-separated integers, $A_1, A_2, \\ldots, A_N$ — the strengths of the opponents, in order.\n- The third line of each test case contains $M$ space-separated integers, $B_1, B_2, \\ldots, B_M$ — the strengths of Gi-Hun\u0027s team.\n","inputFormatState":true,"outputFormat":"- The first line of each test case should contain a single string, either “YES” or “NO”, denoting whether it is possible for Gi-Hun\u0027s team to win or not.\n- If the first line contains \u0022YES\u0022, print a second line containing $M$ space-separated integers — the lexicographically smallest ordering which will allow Gi-Hun\u0027s team to win.\n","outputFormatState":true,"sampleTestCases":{"0":{"id":1,"input":"5\n3 1\n4 3 5\n6\n3 3\n2 4 7\n2 3 7\n3 3\n2 7 4\n2 7 3\n4 4\n2 6 5 1\n4 6 5 2\n2 2\n7 4\n7 4\n","output":"YES\n6\nYES\n2 7 3\nNO\nYES\n2 6 5 4\nNO\n","explanation":"**Test Case 1:** There is only one possible ordering, that being $[6]$. The match will proceed as follows:\n\n- Round 1: $B_1 = 6$ will defeat $A_1 = 4$, $A_1$ is eliminated.\n- Round 2: $B_1 = 6$ will defeat $A_2 = 3$, $A_2$ is eliminated.\n- Round 3: $B_1 = 6$ will defeat $A_3 = 5$, $A_3$ is eliminated.\n\n$B_1$ still remains and all opponents have been defeated, making this a victory for Gi-Hun\u0027s team.\n\n**Test Case 2:** The ordering which result in victory are $[2,7,3],[3,7,2],[7,2,3]$, and $[7,3,2]$. Of these, the lexicographically smallest is $[2, 7, 3]$.\n\nLet $Q = [2, 7, 3]$. The match proceeds as follows:\n- Round 1: $Q_1 = 2$ will draw with $A_1 = 2$, eliminating both.\n- Round 2: $Q_2 = 7$ will defeat $A_2 = 4$, eliminating $A_2$.\n- Round 3: $Q_2 = 7$ will draw with $A_3 = 7$, eliminating both.\n\n$Q_3 = 3$ still remains, so Gi-Hun\u0027s team wins.\n\n**Test Case 3:** It is not possible to win the match.\n","isDeleted":false}}},"video_editorial_url":"https://youtu.be/R6PRY98K7WI","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":"aman1108","problem_tester":"","date_added":"10-12-2021","tags":{"0":"aman1108","1":"binary","2":"constructive","3":"easy","4":"infi2021","5":"two"},"problem_difficulty_level":"Unavailable","best_tag":"Binary Search","editorial_url":"https://discuss.codechef.com/problems/TOW","time":{"view_start_date":1640194200,"submit_start_date":1640194200,"visible_start_date":1640194200,"end_date":1735669800},"is_direct_submittable":false,"problemDiscussURL":"https://discuss.codechef.com/search?q=TOW","is_proctored":false,"visitedContests":{},"layout":"problem"}
---
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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>