You are given a tree of order with
nodes or, in other words, each node can have at most
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
. Image depicts an example of a tree of order
with
nodes.
You need to output answers to queries in the form of
x y
, where the answer is the minimal number of steps needed to get from node to node
.
Input
The first line of input contains the integers
,
and
from the task.
Each of the following lines contains pairs
from the task.
Output
Output lines, each line containing the answer to a query from the task.
Scoring
In test cases worth 20% of total points, it will hold .
In test cases worth 50% of total points, it will hold .
Sample Input 1
7 2 3
1 2
2 1
4 7
Sample Output 1
1
1
4
Explanation for Sample Output 1
You are given a complete binary tree. Node is a direct child of node
so the distance between them is exactly
. Nodes
and
are on complete opposite sides of the tree, so the distance between them is
:
.
Sample Input 2
9 3 3
8 9
5 7
8 4
Sample Output 2
2
2
3
Explanation for Sample Output 2
This example corresponds to the image.
Comments
Since the original data were weak, an additional test case was added, and all submissions were rejudged.