You have locked your bike with a combination lock of 3 digits. Now you want to go for a ride and need to unlock it with the help of following program.

Input

1st parameter

The digit combination of your lock in locked state. It must be different from the 2nd parameter (=the combination of unlocked state). (Or else your bike could be stolen!)

Range 000..999. Leading zeros must not be omitted.

2nd parameter

The digit combination of your lock in unlocked state. This value is your goal.

Range 000..999. Leading zeros must not be omitted.

Output

A list of each state of the combination lock after each "rotation" including the initial state (which is always the 1st parameter) and the last step (which is always the 2nd paramater).

Algorithm

You start "rotating" the first digit one by one until you reach the correct digit in unlocked state. But, because you are in knowledge of the whole unlock-code, you rotate the digit in the direction in which you need the smallest amount of rotations to reach the digit in unlocked state. In case of a tie you can choose whatever direction you prefer.

When you have reached the correct first digit, you start the same procedure with the 2nd and then with the 3rd.

The order of digits is to understand as a circle:

... 9 0 1 2 3 4 5 6 7 8 9 0 1 2 ...

This means, that the smallest amount of rotations from 1 to 9 is not

1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9 = 8

but

1 -> 0 -> 9 = 2.

Notes

• You can rely on Default I/O rules
  


• You can change the order of the parameters.

Examples

Example 1, correct

Input: 999 001

Output:
999
099
009
000
001

Example 2, correct

Input: 911 232

Output:
911
011
111
211
221
231
232

Example 3, wrong output

Input: 999 121

Wrong output:
999
899 // Wrong because wrong rotation direction.
799
699
...

Correct output:
999
099
199
109
119
129
120
121

Example 4, wrong input

Input: 1 212 // Wrong because no leading zeros.

This is code-golf the shortest answer wins.

Python 2, 113 107 bytes

a,b=input()
print a
for x,y,i in zip(a,b,(0,1,2)):
 while x-y:a[i]=x=(x+1-2*((y-x)%10>(x-y)%10))%10;print a

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Takes input as lists of integers

JavaScript (ES6),  73 72  70 bytes

Saved 2 bytes thanks to @tsh

Takes input as 2 arrays of digits in curried syntax (a)(b). Returns a string.

a=>g=b=>b.some(x=>d=x-(a[++i]%=10),i=-1)?a+`
`+g(b,a[i]+=d/5<5/d||9):b

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Commented

a => // a[] = initial combination
g = b => // b[] = target combination
 b.some(x => // for each digit x in b[]:
 d = // compute the difference d:
 x - // between x
 (a[++i] %= 10), // and the corresponding digit in a[]
 // we apply a mod 10, because it may have exceed 9
 // during the previous iteration
 i = -1 // start with i = -1
 ) ? // end of some(); if it's truthy:
 a + `n` + // append a[] followed by a line feed
 g( // followed by the result of a recursive call:
 b, // pass b[] unchanged
 a[i] += // add either 1 or 9 to a[i]:
 d / 5 < 5 / d // add 1 if d / 5 < 5 / d
 || 9 // otherwise, add 9
 ) // end of recursive call
 : // else:
 b // stop recursion and return b[]

Jelly, 30 bytes

_ż+¥⁵AÞḢṠxAƊ×€ʋ"JṬ€$$Ẏ;@W}+%⁵

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A dyadic link taking as its left argument the unlock code and its right the current locked state, both as lists of integers.

This feels far too long!

PHP, 114 bytes

for([,$a,$b]=$argv;$i<3;($x=$a[$i]-$b[$i])?(print$a._).$a[$i]=($y=$a[$i]+(5/$x>$x/5?-1:1))<0?9:$y%10:++$i);echo$b;

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My solution probably sucks, but that is the best I can think of for now!

Charcoal, 48 bytes

θ≔ＥθＩιθＦ³«≔⁻﹪⁺⁻Ｉ§ηι§θι⁵χ⁵ζＦ↔櫧≔θι﹪⁺§θι÷ζ↔ζχ⸿⪫θω

Try it online! Link is to verbose version of code. Explanation:

θ

Print the initial position.

≔ＥθＩιθ

Change the initial position string into an array of numeric digits for calculation purposes.

Ｆ³«

Loop over each digit in turn.

≔⁻﹪⁺⁻Ｉ§ηι§θι⁵χ⁵ζ

Calculate the number of rotations needed to unlock that digit. This is a number from -5 to 4 where -5 means 5 downward rotations and 4 means 4 upward rotations.

Ｆ↔ζ«

Loop over each rotation.

§≔θι﹪⁺§θι÷ζ↔ζχ

Update the digit according to the sign of the rotation.

⸿⪫θω

Output the digits as a string on a new line.

Jelly, 25 bytes

_æ%5+⁹⁹rḊ€%⁵J;Ɱ"$ẎṄḢ}⁺¦¥ƒ

Try it online!

Full program.