\(6^{th}\) round, February \(6^{th}\) 2016
Anica is having peculiar dream. She is dreaming about an infinite board. On that board, an infite table
consisting of infinite rows and infinite columns containing infinite numbers is drawn. Interestingly, each
number in the table appears a finite number of times.
The table is of exceptionally regular shape and its values meet the requirements of a simple recursive
relation. The first cell of each row contains the ordinal number of that row. A value of a cell that is
not in the first column can be calculated by adding up the number in the cell to the left of it and that
same number, only written in reverse (in decimal representation).
Formally, if \(A\)(i, j) denotes the value in the \(i\)^{th} row and the \(j\)^{th} column, it holds:
• \(A\)(i, 1) = \(i\)
• \(A\)(i, j) = \(A\)(i, \(j - 1\)) + rev^{1}(\(A\)(i, \(j - 1\))), for each \(j > 1\)
1
2
4
8
16
77
154
2
4
8
16
77
154
605
3
6
12
33
66
132
363
. . .
4
8
16
77
154
605
1111
5
10
11
22
44
88
176
...
...
The first few rows and columns \(of\) the table.
Notice that the table \(is\) infinite only \(in\) 2 directions.
Anica hasn’t shown too much interest in the board and obliviously passed by it. Behind the board,
she noticed a lamp that immediately caught her attention. Anica also caught the lamp’s attention, so
the friendly ghost Božo came out of it.
“Anica! If you answer correctly to my \(Q\) queries, you will win a package of Dorina wafer or Domaćica
cookies, based on your own choice! I wouldn’t want to impose my stance, but in my personal opinion,
the Dorina wafer cookies are better. Each query will consist of two integers \(A\) and \(B\). You must answer
how many appearances of numbers from the interval [A, B] there are on the board.”
Unfortunately, Anica couldn’t give an answer to the queries and woke up.
“Ah, I didn’t win the Dorina cookies, but at least I have a task for COCI”, she thought and went along
with her business.

In test cases worth 50% of total points, it will hold (1 ⩽A, B ⩽\(10^{6}\)).
^{1}rev(\(x\)) denotes the number \(x\) written in reverse in decimal representation. For example, rev(213) = 312, rev(406800)
= \(008604 = 8604\).
\(6^{th}\) round, February \(6^{th}\) 2016

The first line of input contains the integer \(Q\) (1 ⩽\(Q\) ⩽\(10^{5}\)), the number of queries.
Each of the following \(Q\) lines contains two integers \(A\) and \(B\) (1 ⩽\(A\) ⩽\(B\) ⩽\(10^{10}\)) that represent the
interval from the query.

The \(i\)^{th} line of output must contain a single integer – the answer to the \(i\)^{th} query.

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출처 COCI 2015/2016 Contest 6