Practice Arithmetic with the exercise "Buzzle"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Arithmetic

Statement

Goal

Buzzle is a funny little math game about multiples.
Here were added some difficulty levels which add more rules and make it more complex.

Buzzle - Level 1

Players have to alternately enumerate numbers from a to b, without forgetting to replace any number which ends with 7 or which is a multiple of 7 by "Buzzle". If a number verifies both rules (like 7 or 77), just replace it by "Buzzle"

Example (from 34 to 43):
34
Buzzle (35 = 5×7)
36
Buzzle (37 ends with 7)
38
39
40
41
Buzzle (42 = 6×7)
43

Buzzle - Level 2

Same rules as level 1, but you also have to replace the numbers by "Buzzle" when the sum of their digits is a Buzzle. For example, 88 -> 8+8=16 -> 1+6=7 -> Buzzle

Example (from 175 to 182):
175
Buzzle (176 -> 1+7+6 = 14 which is 2×7)
Buzzle (177 ends with 7)
Buzzle (178 -> 1+7+8=16 -> 1+6=7 which is 1×7)
Buzzle (179 -> 1+7+9=17 which ends with 7)
180
181
Buzzle (182 = 26×7)
183

Buzzle - Level 3

Same rules as level 2, but it is not with 7. You have to adapt the rules for the k numbers num provided in input. They are all in the range [2,9]. 1≤k≤8

Example (from 13 to 26, numbers: 5,9):
13
Buzzle (14 -> 1+4=5)
Buzzle (15 = 3×5)
16
17
Buzzle (18 = 2×9 / 18-> 1+8=9)
Buzzle (19 ends with 9 / 19 -> 1+9 = 10 = 2×5)
Buzzle (20 = 4×5)
21
22
Buzzle (23 -> 2+3 = 5)
24
Buzzle (25 = 5×5)
26

Buzzle - Level 4

Same rules as level 3, but you have to apply them in base n. Continue to display numbers in decimal, but the "last digit" and "sum of the digits" rules are in base n.
For example, in base 18, with num = 7 : 16 is not a Buzzle, because it consists in one single digit (G if we chose 0123456789ABCDEFGH as digits), so its sum is 16. 17 is not a Buzzle, because its last digit is H (17) and not 7. 48 is 2C in base 18, the sum is 2+C (2+12) = 14 which is a multiple of 7 ("multiple" rule doesn't change with the base).
Warning : in base 18, 21 is not a multiple of 7 because it is the representation of 2*18 + 1 = 37. But 1H is a multiple of 7 because it represents the number 35 = 5×7.
All the numbers provided in num are strictly inferior to n.
1≤k<n

Example: in base 12, with 7 and 9
n = 12
k = 2
num = [7, 11]
a = 78
b = 96

78
Buzzle (67 in base 12 which ends with 7)
Buzzle (68 in base 12 -> 6+8=14 which is a multiple of 7)
81
82
Buzzle (6B in base 12 : last digit is "11" ("B"))
Buzzle (84 = 12×7 / 70 in base 12 -> 7+0=7)
85
86
87
Buzzle (88 = 8×11 / 74 in base 12 -> 7+4=11)
89
90
Buzzle (91 = 13×7 / 77 in base 12 -> ends with 7 or 7+7=14)
92
93
94
Buzzle (7B in base 12 -> 7+B=18 which is 16 in base 12 -> 1+6=7 / 7B ends with 11)
96

You have to implement Level 4. But I strongly recommend to start with Level 1, 2 or 3. Tests 1 to 3 will work no matter if you implement Level 4 or not.

Input

First line : 3 space-separated integers n, a and b : The base and the bounds (a and b are included)
Second line : One integer k, how many numbers have to be taken into account
Third line : k space-separated integers for the numbers you have to use in the rules

Output

b-a+1 lines : A number or Buzzle

Constraints

2 ≤ n ≤ 64
1 ≤ a < b ≤ 10000
1 ≤ k < n
2 ≤ numbers in num < n

Example

Input

10 107 114
1
7

Output

Buzzle
108
109
110
111
Buzzle
113
114

Solve it

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