Create a recursive Java method getProduct to compute the product of two positive integers, m and n$,$ using only addition and subtraction. Implement the Java code. Test the method by calling it in the main method of the relevant class. Hint: You need subtraction to count down from m or n and addition to do the arithmetic needed to get the right answer. The linearSum method may be helpful.

public class ArraySum $\{$

$/**$ Returns the sum of the first n integers of the given array. $*/$

public static int linearSum$($int$[]$ data, int n$)\{$

if $($n $==0)$

return $0$;

else

return linearSum$($data$,$ n$-1)+$ data$[$n$-1]$;

$\}$

$/**$ Returns the sum of subarray data$[$low$]$ through data$[$high$]$ inclusive. $*/$

public static int binarySum$($int$[]$ data, int low, int high$)\{$

if $($low $>$ high$)//$ zero elements in subarray

return $0$;

else if $($low $==$ high$)//$ one element in subarray

return data$[$low$]$;

else $\{$

int mid $=($low $+$ high$)/2$;

return binarySum$($data$,$ low, mid$)+$ binarySum$($data$,$ mid$+1,$ high$)$;

$\}$

$\}$

public static void main$($String$[]$ args$)\{$

for $($int limit $=1$; limit $<100$; limit$++)\{$

int$[]$ data $=$ new int$[$limit$]$;

for $($int k$=0$; k $<$ limit; k$++)$

data$[$k$]=$ k$+1$;

int answer $=$ limit $*($limit $+1)/2$;

int linear $=$ linearSum$($data$,$ limit$)$;

if $($linear $!=$ answer$)$

System.out.println$("$Problem with linear sum for n$="+$ limit$)$;

int binary $=$ binarySum$($data$,0,$ limit$-1)$;

if $($binary $!=$ answer$)$

System.out.println$("$Problem with binary sum for n$="+$ limit$)$;

$\}$

$\}$

$\}$