Problem Description

Given $A,B,K,W$, Kanade wants to know the number of $(x,y)$ which satisfies the following conditions:

1. $x,y$ are integers

2. $x\in [0,A],y\in [0,B]$

3. $|x-y|\leq K$

4. $x~xor~y\leq W$

Input

There are $T$ test cases in this problem.

The first line has 1 integer $T$.

Then for every test case, the first line has 4 integers $A,B,K,W$

$1\leq T\leq 2000$

$0\leq A,B,K,W\leq 10^9$

Output

For every test case, output the answer in a line.

3
3 3 1 2
10 10 3 7
998244353 998244353 114514 123456789

8
53
228430202591616