# Buzzle

Difficulty : Easy

Community success rate: 58%

Approved by AlienOGman jordan_codingame FredericLocquet

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## Learning Opportunities

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

## 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 "

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 "

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`=

**16**is not a Buzzle, because it consists in one single digit (G if we chose

**17**is not a Buzzle, because its last digit is

**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

**A number or**

`b`-`a`+1 lines :Constraints

2 ≤

1 ≤

1 ≤

2 ≤ numbers in

`n`≤ 641 ≤

`a`<`b`≤ 100001 ≤

`k`<`n`2 ≤ numbers in

`num`<`n`Example

Input

10 107 114 1 7

Output

Buzzle 108 109 110 111 Buzzle 113 114

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