---{"category_name":"easy","problem_code":"POWSUM","problem_name":"Power Sum","problemComponents":{"constraints":"- $1 \\leq T \\leq 1000$\n- $1 \\leq N \\leq 100$\n- $1 \\leq A_i \\leq 2^{20} $\n","constraintsState":true,"subtasks":"**Subtask #1 (100 points):** Original constraints\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- The first line of each test case contains a single integer $N$.\n- The second line of each test case contains $N$ space-separated integers $A_1, A_2, \\ldots, A_N$. ","inputFormatState":true,"outputFormat":"For each test case, print the answer in the following format:\n- First, print one line containing an integer $M$, denoting the minimum number of moves required.\n- Then, print $2M$ lines describing $M$ operations.\n - Each operation is described by $2$ lines.\n - On the first line, print two space-separated integers $K$ and $X$, denoting the size of the subsequence and the multiplier for this operation.\n - On the second line, print $K$ distinct space-separated integers denoting the indices of the elements chosen to be multiplied in this operation. These $K$ integers can be printed in any order.","outputFormatState":true,"sampleTestCases":{"0":{"id":1,"input":"2\n4\n4 8 4 32\n3\n2 2 4","output":"1\n3 2\n1 2 3\n0","explanation":"**Test case $1$:** Multiplying the $1^{st}, 2^{nd}$ and $3^{rd}$ elements by $2$ turns the array into $[8, 16, 8, 32]$, whose sum is $64 = 2^6$.\n\n**Test case $2$:** The array is already `good`.","isDeleted":false}}},"video_editorial_url":"https://youtu.be/keF8rG5Ld0o","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":"prasant21","problem_tester":"","date_added":"6-01-2022","tags":{"0":"easy","1":"jan222","2":"prasant21"},"problem_difficulty_level":"Unavailable","best_tag":"","editorial_url":"https://discuss.codechef.com/problems/POWSUM","time":{"view_start_date":1642411800,"submit_start_date":1642411800,"visible_start_date":1642411800,"end_date":1735669800},"is_direct_submittable":false,"problemDiscussURL":"https://discuss.codechef.com/search?q=POWSUM","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>