---{"category_name":"medium","problem_code":"CHASE","problem_name":"Ghost Chase","problemComponents":{"constraints":"- $2 \\le N \\le 2 \\cdot 10^5$\n- $1 \\le Q \\le 2 \\cdot 10^5$\n- $1 \\le U_i, V_i \\le N$\n- The chambers and passageways form a tree.\n- $1 \\le A_j, B_j \\le N$\n- $1 \\le K_j \\le 10^9$\n","constraintsState":true,"subtasks":"- **Subtask 1** (10 points): Each chamber is connected by at most two passageways.\n- **Subtask 2** (20 points): $K = 1$ for all queries.\n- **Subtask 3** (30 points): $2 \\le N \\le 5000$, $1 \\le Q \\le 5000$\n- **Subtask 4** (40 points): Original constraints.","subtasksState":true,"inputFormat":"- The first line contains two space-separated integers $N$ and $Q$, representing the number of chambers and queries respectively.\n\n- Each of the next $N-1$ lines contains two space-separated integers $U_i$ and $V_i$, representing the two endpoints of a passageway.\n\n- Each of the next $q$ lines contains three space-separated integers $A_j$, $B_j$ and $K_j$, representing the start chamber, end chamber and ghost\u0027s movement delay for a query respectively.","inputFormatState":true,"outputFormat":"For each query, output on a single line the maximum number of distinct chambers that Chef can visit.","outputFormatState":true,"sampleTestCases":{"0":{"id":1,"input":"10 4\n1 2\n2 3\n3 4\n5 1\n6 1\n6 7\n8 7\n8 9\n10 7\n2 7 4\n10 5 1\n6 6 3\n9 8 765\n","output":"8\n5\n7\n10\n","explanation":"The graph in the sample test case looks like this:\n\n\u003Cimg src=\u0022https://media.discordapp.net/attachments/906231756745764884/913773576463732746/sample-graph.png\u0022 alt=\u0022Sample Graph\u0022, height=\u0022300\u0022\u003E\n\nFor the first query, the following table describes one way to move to visit $8$ chambers. Notice that Chef can choose to stay in a chamber. It can be shown that there is no way to visit more than $8$ chambers.\n\n\u003Ctable style=\u0022width:51%;text-align:center\u0022\u003E\n \u003Ctr\u003E\n \u003Cth\u003ETime\u003C/th\u003E\n \u003Cth\u003EChef\u0026rsquo;s position\u003C/th\u003E\n \u003Cth\u003EGhost\u0026rsquo;s position\u003C/th\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E0\u003C/td\u003E\n \u003Ctd\u003E2\u003C/td\u003E\n \u003Ctd\u003E\u0026ndash;\u003C/td\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E1\u003C/td\u003E\n \u003Ctd\u003E3\u003C/td\u003E\n \u003Ctd\u003E\u0026ndash;\u003C/td\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E2\u003C/td\u003E\n \u003Ctd\u003E2\u003C/td\u003E\n \u003Ctd\u003E\u0026ndash;\u003C/td\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E3\u003C/td\u003E\n \u003Ctd\u003E1\u003C/td\u003E\n \u003Ctd\u003E\u0026ndash;\u003C/td\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E4\u003C/td\u003E\n \u003Ctd\u003E5\u003C/td\u003E\n \u003Ctd\u003E2\u003C/td\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E5\u003C/td\u003E\n \u003Ctd\u003E1\u003C/td\u003E\n \u003Ctd\u003E3\u003C/td\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E6\u003C/td\u003E\n \u003Ctd\u003E6\u003C/td\u003E\n \u003Ctd\u003E2\u003C/td\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E7\u003C/td\u003E\n \u003Ctd\u003E7\u003C/td\u003E\n \u003Ctd\u003E1\u003C/td\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E8\u003C/td\u003E\n \u003Ctd\u003E10\u003C/td\u003E\n \u003Ctd\u003E5\u003C/td\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E9\u003C/td\u003E\n \u003Ctd\u003E7\u003C/td\u003E\n \u003Ctd\u003E1\u003C/td\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E10\u003C/td\u003E\n \u003Ctd\u003E8\u003C/td\u003E\n \u003Ctd\u003E6\u003C/td\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E11\u003C/td\u003E\n \u003Ctd\u003E8\u003C/td\u003E\n \u003Ctd\u003E7\u003C/td\u003E\n \u003C/tr\u003E\n \u003Ctr\u003E\n \u003Ctd\u003E12\u003C/td\u003E\n \u003Ctd\u003E7\u003C/td\u003E\n \u003Ctd\u003E10\u003C/td\u003E\n \u003C/tr\u003E\n\u003C/table\u003E","isDeleted":false}}},"video_editorial_url":"","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":1.5,"source_sizelimit":50000,"problem_author":"cstuart","problem_tester":"aryanc403","date_added":"25-11-2021","tags":{"0":"cstuart"},"problem_difficulty_level":"Medium","best_tag":"","editorial_url":"","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=CHASE","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>