---{"category_name":"school","problem_code":"MINPIZZAS","problem_name":"Minimum Number of Pizzas","problemComponents":{"constraints":"- $1 \\leq T \\leq 2 \\cdot 10^5$\n- $1 \\leq N, K \\leq 10^9$\n","constraintsState":true,"subtasks":"- **Subtask 1 (100 points):** Original constraints","subtasksState":true,"inputFormat":"- First line of input contains $T$, the number of test cases. Then the test cases follow.\n- Each test case contains two space-separated integers $N$ and $K$, where $N$ is the number of friends of chef and $K$ is the number of slices in a pizza.\n","inputFormatState":true,"outputFormat":"For each test case, print the minimum number of pizzas chef has to buy to share among his friends so that none of his friends gets sad.\n","outputFormatState":true,"sampleTestCases":{"0":{"id":1,"input":"3\n2 2\n2 3\n4 2\n","output":"1\n2\n2\n","explanation":"- **Test case $1$:** One pizza has $2$ slices. And there are $2$ friends. So chef can just buy one pizza and give one slice to one friend and another slice to another friend.\n- **Test case $2$:** One pizza has $3$ slices. And there are $2$ friends. So chef can\u0027t share one pizza without being left out with a slice. So he needs to buy at least $2$ pizzas. And if he buys $2$ pizzas, he can give $3$ slices to one friend and $3$ to another. So the minimum number of pizzas chef needs to buy is equal to $2$.\n- **Test case $3$:** One pizza has $2$ slices. And there are $4$ friends. So chef can\u0027t share one pizza among the $4$ friends. So he needs to buy at least $2$ pizzas. And if he buys $2$ pizzas, he can give $1$ slice to each of his friends. So the minimum number of pizzas chef needs to buy is equal to $2$.","isDeleted":false}}},"video_editorial_url":"https://youtu.be/YypNoP9LzIE","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":"suryaprak_adm","problem_tester":"aryanc403","date_added":"22-11-2021","tags":{"0":"cakewalk","1":"ltime102","2":"math","3":"suryaprak_adm"},"problem_difficulty_level":"Unavailable","best_tag":"","editorial_url":"https://discuss.codechef.com/problems/MINPIZZAS","time":{"view_start_date":1638032400,"submit_start_date":1638032400,"visible_start_date":1638032400,"end_date":1735669800},"is_direct_submittable":false,"problemDiscussURL":"https://discuss.codechef.com/search?q=MINPIZZAS","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>