Little Santa made a list of all the naughty children. He created a programming problem and he will give gift to only those naughty children who will solve that problem. The problem is:
Given three integers, \(n, k, x\) (without leading zeros), you can insert at most k digits at any positions in n. You have to create the maximum number (without leading zeros) from n which is not greater than x.
All the children want gifts so they asked you to solve the problem for them.
Input format:
First line of input contains three integers, \(n, k, x\) \((1 <= n <= x <= 10^{100000})\), \((0 <= k <= 100000)\).
Output format:
Print one integer, denoting the maximum number (without leading zeros) that can be created from n which is not greater than x after inserting at most k digits at any position in n.
10 2 109
109
You have to insert at most 2 digits in number 10 to make it no larger than 109. Inserting 9 at the end is the way to get the best result. There are also other valid strategies, like not inserting digits at all or inserting 0 at second position, but they give smaller numbers.
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