---{"category_name":"medium","problem_code":"INFDIV","problem_name":"Make it Zero","languages_supported":{"0":"C","1":"CPP14","2":"JAVA","3":"PYTH","4":"PYTH 3.6","5":"PYPY","6":"CS2","7":"PAS fpc","8":"PAS gpc","9":"RUBY","10":"PHP","11":"GO","12":"NODEJS","13":"HASK","14":"rust","15":"SCALA","16":"swift","17":"D","18":"PERL","19":"FORT","20":"WSPC","21":"ADA","22":"CAML","23":"ICK","24":"BF","25":"ASM","26":"CLPS","27":"PRLG","28":"ICON","29":"SCM qobi","30":"PIKE","31":"ST","32":"NICE","33":"LUA","34":"BASH","35":"NEM","36":"LISP sbcl","37":"LISP clisp","38":"SCM guile","39":"JS","40":"ERL","41":"TCL","42":"kotlin","43":"PERL6","44":"TEXT","45":"SCM chicken","46":"PYP3","47":"CLOJ","48":"COB","49":"FS"},"max_timelimit":2,"source_sizelimit":50000,"problem_author":"jtnydv25","problem_tester":null,"date_added":"11-12-2018","tags":{"0":"jtnydv25"},"time":{"view_start_date":1544985000,"submit_start_date":1544985000,"visible_start_date":1544985000,"end_date":1735669800},"is_direct_submittable":false,"layout":"problem"}---<span class="solution-visible-txt">All submissions for this problem are available.</span>You are given two integers, $n$ and $m$. You want to make $m$ equal to $0$. You decide to keep repeating the following operation until $m$ becomes $0$ :- Choose an integer $r$, uniformly at random from the range $[1, n]$. Set $m$ equal to the remainder obtained on dividing it by $r$. That is, replace $m$ with $m \% r$, where $\%$ denotes the modulo operator.Find the expected number of operations after which $m$ becomes $0$. Let the answer be equal to $E = \dfrac{P}{Q}$ for some integers $P$ and $Q$ such that gcd($P$, $Q$) = 1. Output the value of $P Q^{-1} $ modulo $10^9 + 7$, where $Q^{-1}$ denotes the modular inverse of $Q$ modulo $10^9 + 7$.###Input:- The only line of the input contains two integers $n$ and $m$.###Output:- Output one line containing the value of $P Q^{-1}$ modulo $10^9 + 7$ as described above.###Constraints- $1 \leq n \leq 200000$- $1 \leq m \leq 10^{18}$###Sample Input:3 2###Sample Output:500000005###EXPLANATION:$m$ is initially $2$. In each operation, we choose a random number $r$ from {$1, 2, 3$}. If $r = 1$, then $m \% r = 0$, and we stop. If $r = 2$, then $m \% r = 0$, and we stop. If $r = 3$, then $m \% r = 2$, and we continue the process.Hence, we will repeat the procedure until we get a $1$ or $2$. You can check that the expected number of steps needed to get this is $\frac{3}{2}$. Hence, we output $3 \times 2^{-1} = 3 \times 500000004 = 500000005 \mod 10^9 + 7$