Canadian Computing Olympiad: 2021 Day 1, Problem 2
Alice enjoys thinking about base- numeral systems (don't we all?). As you might know, in the standard base- numeral system, an integer can be represented as where:
- Each digit is in the set , and
For example, in standard base-3, you would write as
1 2 0, since
But standard base- systems are too easy for Alice. Instead, she's thinking about weird base- systems.
A weird-base- system is just like the standard base- system,
except that instead of using the digits , you use
for some value .
For example, in a weird-base-3 system with , you could write
1 -1 -1 0, since .
Alice is wondering how to write integers, through , in a weird-base- system that uses the digits through . Please help her out!
The first line contains four space-separated integers, , , , and .
The second line contains distinct integers, through .
Finally, the -th of the next lines contains .
For 8 of the 25 available marks, .
Output lines, the -th of which is a weird-base- representation of . If multiple representations are possible, any will be accepted. The digits of the representation should be separated by spaces. Note that 0 must be represented by a non-empty set of digits.
If there is no possible representation, output
Sample Input 1
3 3 3 1 -1 0 1 15 8 -5
Sample Output 1
1 -1 -1 0 1 0 -1 -1 1 1
Explanation for Sample Output 1
Sample Input 2
10 1 3 2 0 2 -2 17
Sample Output 2