Problem Description

WLD is always very lucky.His secret is a lucky number $K$.$k$ is a fixed odd number. Now he meets a stranger with $N$ numbers:$a1,a2,...,aN$.The stranger asks him $M$ questions.Each question is like this:Given two ranges $[Li,Ri]$ and $[Ui,Vi]$,you can choose two numbers $X$ and $Y$ to make $aX+aY=K$.The $X$ you can choose is between $Li$ and $Ri$ and the $Y$ you can choose is between $Ui$ and $Vi$.How many pairs of numbers$(X,Y)$ you can choose?
If WLD can answer all the questions correctly,he'll be the luckiest man in the world.Can you help him?

Input

There are multiple cases.(At MOST $5$)

For each case:

The first line contains an integer $N(1 \leq N \leq 30000)$.

The following line contains an integer $K(2 \leq K \leq 2*N)$,WLD's lucky number.K is odd.

The following line contains $N$ integers $a1,a2,...,aN(1 \leq ai \leq N)$.

The following line contains an integer $M(1 \leq M \leq 30000)$,the sum of the questions WLD has to answer.

The following $M$ lines,the i-th line contains $4$ numbers $Li,Ri,Ui,Vi(1 \leq Li \leq Ri < Ui \leq Vi \leq N)$,describing the i-th question the stranger asks.

Output

For each case:

Print the total of pairs WLD can choose for each question.

5
3 
1 2 1 2 3
1 
1 2 3 5

2

Hint

a1+a4=a2+a3=3=K.
So we have two pairs of numbers (1,4) and (2,3).
Good luck!