---{"category_name":"easy","problem_code":"LEDIV","problem_name":"Little Elephant and Divisors","languages_supported":{"0":"ADA","1":"ASM","2":"BASH","3":"BF","4":"C","5":"C99 strict","6":"CAML","7":"CLOJ","8":"CLPS","9":"CPP 4.3.2","10":"CPP 4.9.2","11":"CPP14","12":"CS2","13":"D","14":"ERL","15":"FORT","16":"FS","17":"GO","18":"HASK","19":"ICK","20":"ICON","21":"JAVA","22":"JS","23":"LISP clisp","24":"LISP sbcl","25":"LUA","26":"NEM","27":"NICE","28":"NODEJS","29":"PAS fpc","30":"PAS gpc","31":"PERL","32":"PERL6","33":"PHP","34":"PIKE","35":"PRLG","36":"PYTH","37":"PYTH 3.4","38":"RUBY","39":"SCALA","40":"SCM guile","41":"SCM qobi","42":"ST","43":"TCL","44":"TEXT","45":"WSPC"},"max_timelimit":2,"source_sizelimit":50000,"problem_author":"witua","problem_tester":null,"date_added":"20-10-2012","tags":{"0":"cook28","1":"simple","2":"simple","3":"witua"},"editorial_url":"http://discuss.codechef.com/problems/LEDIV","time":{"view_start_date":1353262825,"submit_start_date":1353262825,"visible_start_date":1353263400,"end_date":1735669800},"layout":"problem"}---<span class="solution-visible-txt">All submissions for this problem are available.</span><p style="text-align:justify">The Little Elephant from the Zoo of Lviv has an array <b>A</b> that consists of <b>N</b> positive integers. Let <b>A[i]</b> be the <b>i</b>-th number in this array (<b>i = 1, 2, ..., N</b>).</p><p style="text-align:justify">Find the minimal number <b>x > 1</b> such that <b>x</b> is a divisor of all integers from array <b>A</b>. More formally, this <b>x</b> should satisfy the following relations:</p><p style="text-align:center"><b>A[1] mod x = 0</b>, <b>A[2] mod x = 0</b>, ..., <b>A[N] mod x = 0</b>,</p><p style="text-align:justify">where <b>mod</b> stands for the modulo operation. For example, <b> 8 mod 3 = 2</b>, <b> 2 mod 2 = 0</b>, <b>100 mod 5 = 0</b> and so on. If such number does not exist, output <b>-1</b>.</p><h3>Input</h3><p style="text-align:justify">The first line of the input contains a single integer <b>T</b>, the number of test cases. <b>T</b> test cases follow. The first line of each test case contains a single integer <b>N</b>, the size of the array <b>A</b> for the corresponding test case. The second line contains <b>N</b> space separated integers <b>A[1]</b>, <b>A[2]</b>, ..., <b>A[N]</b>.</p><h3>Output</h3><p style="text-align:justify">For each test case output a single line containing the answer for the corresponding test case.</p><h3>Constraints</h3><p style="text-align:justify"><b>1</b> ≤ <b>T</b> ≤ <b>100000</b><br /><br /><b>1</b> ≤ <b>N</b> ≤ <b>100000</b><br /><br />The sum of values of <b>N</b> in each test file does not exceed <b>100000</b><br /><br /><b>1</b> ≤ <b>A[i]</b> ≤ <b>100000</b></p><h3>Example</h3><pre><b>Input:</b>232 4 834 7 5<b>Output:</b>2-1</pre><h3>Explanation</h3><p style="text-align:justify"><b>Case 1.</b> Clearly 2 is a divisor of each of the numbers 2, 4 and 8. Since 2 is the least number greater than 1 then it is the answer.</p><p style="text-align:justify"><b>Case 2.</b> Let's perform check for several first values of <b>x</b>.</p><p style="text-align:justify"><table width="50%" border=1><tr><td><b>x</b></td><td><b>4 mod x</b></td><td><b>7 mod x</b></td><td><b>5 mod x</b></td></tr><tr><td>2</td><td>0</td><td>1</td><td>1</td></tr><tr><td>3</td><td>1</td><td>1</td><td>2</td></tr><tr><td>4</td><td>0</td><td>3</td><td>1</td></tr><tr><td>5</td><td>4</td><td>2</td><td>0</td></tr><tr><td>6</td><td>4</td><td>1</td><td>5</td></tr><tr><td>7</td><td>4</td><td>0</td><td>5</td></tr><tr><td>8</td><td>4</td><td>7</td><td>5</td></tr><tr><td>9</td><td>4</td><td>7</td><td>5</td></tr></table></p><p style="text-align:justify">As we see each number up to 9 does not divide all of the numbers in the array. Clearly all larger numbers also will fail to do this. So there is no such number <b>x > 1</b> and the answer is <b>-1</b>.</p>