A11035. Army Creation

As you might remember from our previous rounds, Vova really likes computer games. Now he is playing a strategy game known as Rage of Empires.

In the game Vova can hire $n$ different warriors; $i$ th warrior has the type $a_{i}$ . Vova wants to create a balanced army hiring some subset of warriors. An army is called balanced if for each type of warrior present in the game there are not more than $k$ warriors of this type in the army. Of course, Vova wants his army to be as large as possible.

To make things more complicated, Vova has to consider $q$ different plans of creating his army. $i$ th plan allows him to hire only warriors whose numbers are not less than $l_{i}$ and not greater than $r_{i}$ .

Help Vova to determine the largest size of a balanced army for each plan.

Be aware that the plans are given in a modified way. See input section for details.

The first line contains two integers $n$ and $k$ ( $1<=n,k<=100000$ ).

The second line contains $n$ integers $a_{1}$ , $a_{2}$ , ... $a_{n}$ ( $1<=a_{i}<=100000$ ).

The third line contains one integer $q$ ( $1<=q<=100000$ ).

Then $q$ lines follow. $i$ th line contains two numbers $x_{i}$ and $y_{i}$ which represent $i$ th plan ( $1<=x_{i},y_{i}<=n$ ).

You have to keep track of the answer to the last plan (let's call it $last$ ). In the beginning $last=0$ . Then to restore values of $l_{i}$ and $r_{i}$ for the $i$ th plan, you have to do the following:

1. $l_{i}=((x_{i}+last) mod n)+1$ ;
2. $r_{i}=((y_{i}+last) mod n)+1$ ;
3. If $l_{i}>r_{i}$ , swap $l_{i}$ and $r_{i}$ .

Print $q$ numbers. $i$ th number must be equal to the maximum size of a balanced army when considering $i$ th plan.

In the first example the real plans are:

1. $1 2$
2. $1 6$
3. $6 6$
4. $2 4$
5. $4 6$