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.