Chef and Modulo Game

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###Read problem statements in [Hindi](http://www.codechef.com/download/translated/JAN19/hindi/MGAME.pdf), [Bengali](http://www.codechef.com/download/translated/JAN19/bengali/MGAME.pdf), [Mandarin Chinese](http://www.codechef.com/download/translated/JAN19/mandarin/MGAME.pdf), [Russian](http://www.codechef.com/download/translated/JAN19/russian/MGAME.pdf), and [Vietnamese](http://www.codechef.com/download/translated/JAN19/vietnamese/MGAME.pdf) as well. Chef is playing a game with two of his friends. In this game, each player chooses an integer between $1$ and $P$ inclusive. Let's denote the integers chosen by Chef, friend 1 and friend 2 by $i$, $j$ and $k$ respectively; then, Chef's score is $$(((N\,\mathrm{mod}\,i)\,\mathrm{mod}\,j)\,\mathrm{mod}\,k)\,\mathrm{mod}\,N\,.$$ Chef wants to obtain the maximum possible score. Let's denote this maximum score by $M$. Find the number of ways to choose the triple $(i, j, k)$ so that Chef's score is equal to $M$. ### Input  The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.  The first and only line of each test case contains two spaceseparated integers $N$ and $P$. ### Output For each test case, print a single line containing one integer — the number of ways to obtain the maximum score. ### Constraints  $1 \le T \le 10^6$  $1 \le N \le P \le 10^6$ ### Subtasks **Subtask #1 (10 points):**  $1 \le T \le 100$  $1 \le N \le P \le 100$ **Subtask #2 (90 points):** original constraints ### Example Input ``` 2 4 4 3 4 ``` ### Example Output ``` 9 13 ``` ### Explanation **Example case 1:** Chef's maximum possible score is $M = 1$. All possible values of $(i, j, k)$ such that the score is $1$ are $(3, 2, 2)$, $(3, 2, 3)$, $(3, 2, 4)$, $(3, 3, 2)$, $(3, 3, 3)$, $(3, 3, 4)$, $(3, 4, 2)$, $(3, 4, 3)$, $(3, 4, 4)$.Author:  l_returns 
Editorial  https://discuss.codechef.com/problems/MGAME 
Tags  combinatorics, easy, jan19, l_returns, modulo, taran_1407 
Date Added:  1012019 
Time Limit:  2 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, COB, FS 
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