Problem B
Battle of Nieuwpoort
The battle of Nieuwpoort occurred in the year $1600$. This is famously easy to remember, because it ends in two zeros. Alas, not all historical events have been so obliging!
You suspect that the problem is with the fixation of historians on the decimal system. Maybe, given the year of another battle, there exists a small base (at most $16$) in which this year would also be easy to remember?
Input
The input consists of:
-
One line with $4$ tokens:
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One integer $y$ ($1\leq y\leq 2024$, in base-$10$), the year of the battle.
-
Three words $w$ ($2\leq |w|\leq 20$), naming the battle.
The words only consist of English letters (A-Z and a-z).
-
Output
If it is possible to rewrite the year to make it easier to remember, output this base $b$ ($2\leq b\leq 16$, in base-$10$) and the year written in base-$b$. Otherwise, output “impossible”.
The year in base-$b$ must end with “00” and must not start with ‘0’.
Use letters ‘a’, ‘b’, ‘c’, etc. for the digits following ‘9’ in bases higher than $10$.
If there are multiple valid solutions, you may output any one of them.
| Sample Input 1 | Sample Output 1 |
|---|---|
1600 Battle of Nieuwpoort |
10 1600 |
| Sample Input 2 | Sample Output 2 |
|---|---|
625 Battle of Sarus |
5 10000 |
| Sample Input 3 | Sample Output 3 |
|---|---|
1600 Battle of Sekigahara |
8 3100 |
| Sample Input 4 | Sample Output 4 |
|---|---|
1815 Battle of Waterloo |
11 1400 |
| Sample Input 5 | Sample Output 5 |
|---|---|
1859 Battle of Solferino |
13 b00 |
| Sample Input 6 | Sample Output 6 |
|---|---|
1848 Battle of Bov |
2 11100111000 |
| Sample Input 7 | Sample Output 7 |
|---|---|
1453 Fall of Constantinople |
impossible |
