Find the Binary Number

Time limit

Memory limit

128 MB

Problem

There is a binary string of length N. (1 <= N <= 31) A binary string may begin with 0. List every length-N binary string with at most L bits equal to 1 in increasing numeric order. Find the I-th string in that order. (1 <= L <= N)

Input

The first line contains three integers N, L, and I. The input is guaranteed to be one for which the I-th string exists.

Output

Print the I-th binary string on the first line.