Common properties of XOR and addition

A. Meximum Array

lianjie

Be careful ：

1. On the sequence a Each number in the must be operated once
2. Addition and XOR have a common function ： Change the parity of numbers , And the change of parity is synchronous
   Odd number + Odd number = even numbers , Odd number ^ Odd number = even numbers
   Odd number + even numbers = Odd number , Odd number ^ even numbers = Odd number
   even numbers + even numbers = even numbers , even numbers ^ even numbers = even numbers
3. This topic has stated that ：$x$ and $x+3$ One of them must eventually become $y$, Ask which can get , There is no process required . So we don't have to deduce the process carefully , Just find $x,x+3,y$ Nature between .
4. $x$ and $x+3$ Just one is an odd number , The other is even , Parity opposites , And we can just pass n One operation changes the parity of two numbers , If n After the first operation $x$ and $y$ It's different in parity , Description impossible .
5. from 2 The derivation of is known , Both operations have the same effect on parity , So we can just ^ operation , Finally, judge the parity .

#include<iostream>
using namespace std;
int main()
{
    
	int t;
	cin>>t;
	while(t--)
	{
    
		long long n,x,y;
		cin>>n>>x>>y;
		for(int i=1;i<=n;i++)
		{
    
			long long k;
			cin>>k;
			x^=k;
		}
		if((x%2)==(y%2)) puts("Alice");	// If parity is the same 
		else puts("Bob");
	}
	
	return 0;
}