File size: 2,001 Bytes
6ff944e | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 | # 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. |