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実行時間制限: 2 sec / メモリ制限: 256 MiB
Problem
Dave's calculator is broken. His calculator halts when put more than K kinds of number.
Dave wants to input an integer A, but if he put this number correctly the calculator might halt. Instead, he inputs the closest integer that won't halts the calculator.
Output the difference between Dave's input and the integer A.
Input
The input will be given in the following format from the Standard Input.
A K
- On the first line, you will be given the integer A (1 ≦ A ≦ 10^{15}), the integer Dave wants to input, followed by a space and K (1 ≦ K ≦ 10), the kinds of number his calculator can recognize.
Acheivements and Points
- When you pass every test case where 1 ≦ A ≦ 100,000, you will be awarded 30 points.
- In addition, if you pass all the rest test cases you will be awarded 70 more points.
Output
Output the minimum difference between Dave's input and the integer A in one line. Make sure to insert a line break at the end of the output.
Input Example 1
1234 2
Output Examle 1
12
In this case Dave can only use up to 2 kinds of numbers.
He will input the closest integer 1222, so the difference is 12.
Input Example 2
800000 1
Output Example 2
22223
Dave can use only 1 number, so 777777 is the closest integer.
Inout Example 3
7328495 10
Output Example 3
0
In this case Dave's calculator is not broken at all.
He can input the given integer A as is.
Input Example 4
262004 2
Output Example 4
218
The closest integer is 262222.