Find the i-th Valid Binary String

We consider all binary strings of fixed length \( N \) that have at most \( L \) ones (i.e., the number of ones is \( \leq L \)). These strings are sorted in increasing lexicographical order. Your task is to output the \( i \)-th smallest string among these valid strings. It is guaranteed that such a string exists.

For example, for the binary string 100101, we have \( N=6 \) and the number of ones is 3.

inputFormat

The input consists of three space-separated integers:

• \( N \) (\( 1 \leq N \leq 50 \)): the length of the binary strings.
• \( L \) (\( 0 \leq L \leq N \)): the maximum allowed number of ones in the string.
• \( i \) (\( 1 \leq i \leq \text{number of valid strings} \)): the 1-indexed position of the string in the sorted order.

outputFormat

Output the \( i \)-th smallest binary string (of length \( N \)) that has at most \( L \) ones.

sample

6 3 1

000000