You are given an array $Arr$ of size $N$ and two integers $S$ and $K$. $Arr$ is having a feature that its each element absolute value do not exceed $K$. You want to make the sum of all elements of $Arr$ equals to $S$. To achieve this you can add any number of integers to $Arr$ without violating its feature. Your task is to find minimum numbers of integers that you can add to $Arr$ so that sum of all elements is $S$.

Input Format:
First line contains $T$, denoting the number of test cases.
First line of each test case contains 3 space separated integers denoting $N$, $S$ and $K$.
Second line of each test case contains $N$ space separed integers denoting the intial values of $Arr$

Output Format:
For each test case print a single integer denoting minimum numbers of integers that you can add to $Arr$ so that sum of all elements is $S$ in a new line.

Constraints:
$1\leq T\leq 10^3$
$1 \leq N,K \leq 10^5$
$-K \leq \text{Array Elements} \leq K$
$-10^6\leq S \leq 10^6$

Note - Use Fast Input/Output Methods for Big Test Cases.