---{"category_name":"easy","problem_code":"ARMYFGT","problem_name":"Fighting Armies","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":1,"source_sizelimit":50000,"problem_author":"bipin2","problem_tester":null,"date_added":"20-12-2018","tags":{"0":"bipin2"},"time":{"view_start_date":1546074900,"submit_start_date":1546074900,"visible_start_date":1546074900,"end_date":1735669800},"is_direct_submittable":false,"layout":"problem"}---<span class="solution-visible-txt">All submissions for this problem are available.</span>Civil war is brewing in the kingdom of NaturalLand again, and this time, the rebels have adopted guerilla warfare. There are $N$ rebel soldiers and they are represented by the numbers $Rebel_1, Rebel_2, \ldots, Rebel_N$. The king has deployed his soldiers in a long defensive wall, and this is represented by two integers: $lower$ and $upper$. This means that the King's army contains ($upper$ - $lower$ +1) soldiers represented by all the numbers between $lower$ and $upper$ (end points inclusive).The rebels pick individual soldiers from the King's army and ambush them one by one. A soldier $x$ in the King's army will be defeated only if all the $N$ numbers $Rebel_1, Rebel_2, \ldots,$ and $Rebel_N$ divide $x$ without leaving a remainder. Else, $x$ will survive.Your job is to count the number of soldiers in the King's army who will survive at the end,###Input:- First line will contain $T$, the number of test cases. Then the test cases follow.- The first line of each test case will contain $N$, representing the number of soldiers in the rebel army.- The second line of each testcase contains $N$ spaced integers: $Rebel_1, Rebel_2, \ldots, Rebel_N$.- The third line of each testcase contains the 2 integers representing the range $[lower, upper]$ of the King's army.###Output:For each test case, output the answer in a single line.###Constraints- $1 \leq T \leq 1000$- $1 \leq N \leq 500$- $1 \leq Rebel_i \leq 10^9$- $1 \leq lower \leq upper \leq 10^{18}$###Sample Input:```122 44 8```###Sample Output:```3```###EXPLANATION:The rebels' army contains the soldiers {$2,4$}. The King's army contains the soldiers {$4,5,6,7,8$}.The rebels will be able to kill {$4,8$} in the King's army as all the members of rebel army can divide {$4,8$} without leaving a remainder. The other three soldiers, {$5,6,7$} will survive, and hence the answer is 3.