Changing Digits
Description:
Given two positive integers n and k, you are asked to generate a new integer, say m, by changing some (maybe none) digits of n, such that the following properties holds:
- m contains no leading zeros and has the same length as n (We consider zero itself a one-digit integer without leading zeros.)
- m is divisible by k
- among all numbers satisfying properties 1 and 2, m would be the one with least number of digits different from n
- among all numbers satisfying properties 1, 2 and 3, m would be the smallest one
Input:
There are multiple test cases for the input. Each test case consists of two lines, which contains n(1≤n≤10100) and k(1≤k≤104, k≤n) for each line. Both n and k will not contain leading zeros.
Output:
Output one line for each test case containing the desired number m.
Sample Input:
2 2 619103 3219
Sample Output:
2 119103
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