Write a recursive method public int GCD$($int n$,$ int m$)$ that returns thegreatest common divisor of two nonnegative integers and according to the following definition:GCD$(,)=\{$ if and mod $=0$GCD$(,)$ if $<$ GCD$(,$ mod $)$ otherwiseQuestion II $(25$ points$)$: Implement in BinaryTree class the following methods:a$)$ public int longestPathTwoLeaves$()$ to return the length of the longest path between two leaves.$($Hint: use the height method$)$b$)$ public void maxValueInEachLevel$()$ to print the largest value in each level. $($Hint keep track ofnodes level$)$c$)$ public int sizeRightSubtree$($BTNode v$)$ to find the size of the right subtree of a node v$.$d$)$ public void deleteNodes$($int x$)$ to delete all nodes whose keys are larger than x$.$e$)$ public void deleteAllLeaves$()$ to delete all leaves from a binary tree.Question III $(20$ points$)$: Implement the following Boolean methods in BinaryTree class