Kilk Not

You are given a string $s$ consisting of zeros (0), ones (1), and question marks (?).

The number of question marks in $s$ is exactly $a + b$.

Replace $a$ question marks with zeros and $b$ question marks with ones to obtain a binary string $t$. Let $f(t)$ be the length of the longest substring of $t$ consisting of equal digits (e.g. 11111 or 0000).

Your task is to minimize $f(t)$.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^5$). Description of the test cases follows.

The first line of each test case contains three integers $n$, $a$, and $b$ ($1 \le n \le 250\\,000$; $0 \le a$; $0 \le b$).

The second line contains a string $s$ of length $n$ consisting of characters 0, 1, and ?. The number of question marks in $s$ is equal to $a + b$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $250\\,000$.

For each test case, print two lines.

In the first line, print a single integer $f(t)$, denoting the smallest possible length of the longest substring of $t$ consisting of equal digits.

In the second line, print any string $t$ achieving this value of $f(t)$ itself.