p02157 Shuffle 2
Problem Description
Problem
There is a bundle of $ n $ cards, with $ i $ written on the $ i $ th card from the bottom. Shuffle this bundle as defined below $ q $ times.
- When looking at the bundle from below, consider a bundle $ x $ made by stacking odd-numbered cards on top, and a bundle $ y $ made by stacking even-numbered cards on top. Then do whatever you like out of the following $ 2 $.
- Operation $ 0 $: Put the bundle $ y $ on the bundle $ x $ to make a bundle of $ 1 $.
- Operation $ 1 $: Put the bundle $ x $ on the bundle $ y $ to make a bundle of $ 1 $.
For example, if you consider shuffling $ 1 $ times for a bundle of $ 6 $ cards (123456 from the bottom), the bundle you get when you perform the operation $ 0 $ is ~~ 246135 ~~ from the bottom. 135246, the bundle obtained by performing the operation $ 1 $ is ~~ 135246 ~~ 246135 from the bottom. (Corrected at 14:52)
After $ q $ shuffle, I want the card with $ k $ to be $ d $ th from the bottom of the bunch. If possible, print $ q $ of shuffle operations in sequence, and if not, print $ -1 $.
Constraints
The input satisfies the following conditions.
- $ 2 \ le n \ le 10 ^ {15} $
- $ 1 \ le q \ le 10 ^ 6 $
- $ 1 \ le k, d \ le n $
- $ n $ is even
Input
The input is given in the following format.
$ n $ $ q $ $ k $ $ d $
Output
If it is possible to shuffle the conditions, output the shuffle operation on the $ q $ line.
If not possible, output $ -1 $.
Examples
Input
4 2 1 1
Output
0 0
Input
4 2 3 1
Output
0 1
Input
4 1 1 4
Output
-1
Input
7834164883628 15 2189823423122 5771212644938
Output
0 1 1 1 1 1 0 1 0 1 0 0 0 0 0
Contest Information
- Contest ID: 0
- Problem Index:
- Points: 0.0
- Rating: 0
- Tags:
- Time Limit: {'seconds': 3, 'nanos': 0} seconds
- Memory Limit: 268435456 bytes
Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.