• محدودیت زمان: ۱ ثانیه
• محدودیت حافظه: ۶۴ مگابایت

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You are given a tree of order k with n nodes, in other words, each node can have at most K children. The tree is constructed so it’s of the "lowest energy": the nodes are placed in a new depth of the tree only when all the places (from left to right) in the previous depth have been filled. This is also the order of enumerating the nodes, starting with 1. Image depicts an example of a tree of order 3 with 9 nodes.

You need to output answers to Q queries in the form of x y, where the answer is the minimal number of steps needed to get from node x to node y.

Input

The first line of input contains the integers n, k and Q from the task. Each of the following Q lines contains pairs x, y.

Output

Output Q lines, each line containing the answer to a query from the task.

Constraint

• $2 \leq n \leq 10^{15} $
• $1 \leq Q \leq 10^5 $
• $1 \leq k \leq 1000 $

Sample Test Data

input 1

7 2 3
1 4
4 3
5 6

output 1

2
3
4