Description

They are sorted and include all $N$-bit binary numbers whose number of $1$s is at most $L$ ($L \leq N$).

Your task is to output the $i$-th smallest $N$-bit binary number that has at most $L$ ones (it is guaranteed to exist).

Example: In $100101$, $N = 6$, and it contains $3$ ones.

Input Format

One line with three integers $N, L, i$.

Output Format

Output the $i$-th smallest binary number that satisfies the conditions.

5 3 19

10011

Hint

Problem translation from NOCOW.

USACO Training Section 3.2.

Translated by ChatGPT 5