---{"category_name":"school","problem_code":"MINFD","problem_name":"Chef and Fixed Deposits","problemComponents":{"constraints":"- $1 \\leq T, A_i, N \\leq 100$\n- $1 \\leq X \\leq 10^4$","constraintsState":true,"subtasks":"**Subtask #1 (100 points):** 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- The first line of each test case contains two space-separated integers — $N$ and $X$, as described in the statement.\n- The second line of each test case contains $N$ space-separated integers — the $i^{th}$ of which is $A_i$.\n","inputFormatState":true,"outputFormat":"For each test case, output one line containing the answer — the minimum number of FDs Chef must open to have at least $X$ coins. If it is not possible for him to open FDs such that he has at least $X$ coins, output $-1$. \n","outputFormatState":true,"sampleTestCases":{"0":{"id":1,"input":"4\n4 6\n4 3 5 1\n3 15\n1 5 3\n2 5\n10 3\n4 7\n1 2 3 4","output":"2\n-1\n1\n2","explanation":"**Test case $1$:** Chef can open the first and second FDs to get $4 + 3 = 7$ coins, which is more than the $6$ coins he needs. There are other combinations of two FDs giving at least $6$ coins — for example, the first and third (for $4 + 5 = 9$) and third and fourth (for $5 + 1 = 6$), but there is no way to open only one FD and get $6$ or more coins.\n\n**Test case $2$:** No matter which FDs Chef opens, he cannot have $\\geq 15 $ coins, so the answer is $-1$ — even if he opens all of them, he will have only $1 + 5 + 3 = 9$ coins.\n\n**Test case $3$:** Chef can open the first FD to obtain $10$ coins, which is larger than the $5$ coins he needs.\n\n**Test case $4$:** Chef can open the third and fourth FDs to get $3 + 4 = 7$ coins, which is enough because he needs $7$ coins.","isDeleted":false}}},"video_editorial_url":"https://youtu.be/XCEqFUszeF0","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":"utkarsh_adm","problem_tester":"","date_added":"13-01-2022","tags":{"0":"cakewalk","1":"jan222","2":"utkarsh_adm"},"problem_difficulty_level":"Unavailable","best_tag":"","editorial_url":"https://discuss.codechef.com/problems/MINFD","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=MINFD","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>