Painting Squares

Mike is playing a game with Peter. There are $n$ squares drawn on the ground in a single row, numbered $0$ to $n-1$ from left to right. At the start of the game, Peter is allowed to paint each of these squares either black or white. He will then give Mike a single positive integer $k$ ($1 \leq k \leq n$).

This game lasts a total of $q$ rounds. In each round, Mike will randomly pick a square $x$ ($0 \leq x \lt n$), and tell Peter the colours of the squares from positions $x$ to $x+k-1$ inclusive. If any of these positions are out of range, Mike will inform Peter accordingly as well. Peter will then need to correctly deduce $x$ based purely on this information alone.

Peter wishes to impress Mike, and thus wants to pick a value of $k$ that is as low as possible. Help Peter devise a strategy to win this game with the minimum possible value of $k$.

• $1 \leq r \leq 10$
• $2 \leq n, q \leq 1000$
• $-1 \leq c\[i] \leq 1$ ($0 \leq i \lt k$)