CF1556G.Gates to Another World

As mentioned previously William really likes playing video games. In one of his favorite games, the player character is in a universe where every planet is designated by a binary number from $0$ to $2^n - 1$ . On each planet, there are gates that allow the player to move from planet $i$ to planet $j$ if the binary representations of $i$ and $j$ differ in exactly one bit.

William wants to test you and see how you can handle processing the following queries in this game universe:

• Destroy planets with numbers from $l$ to $r$ inclusively. These planets cannot be moved to anymore.
• Figure out if it is possible to reach planet $b$ from planet $a$ using some number of planetary gates. It is guaranteed that the planets $a$ and $b$ are not destroyed.

The first line contains two integers $n$ , $m$ ( $1 \leq n \leq 50$ , $1 \leq m \leq 5 \cdot 10^4$ ), which are the number of bits in binary representation of each planets' designation and the number of queries, respectively.

Each of the next $m$ lines contains a query of two types:

block l r — query for destruction of planets with numbers from $l$ to $r$ inclusively ( $0 \le l \le r < 2^n$ ). It's guaranteed that no planet will be destroyed twice.

ask a b — query for reachability between planets $a$ and $b$ ( $0 \le a, b < 2^n$ ). It's guaranteed that planets $a$ and $b$ hasn't been destroyed yet.

For each query of type ask you must output "1" in a new line, if it is possible to reach planet $b$ from planet $a$ and "0" otherwise (without quotation marks).

The first example test can be visualized in the following way:

Response to a query ask 0 7 is positive.

Next after query block 3 6 the graph will look the following way (destroyed vertices are highlighted):

Response to a query ask 0 7 is negative, since any path from vertex $0$ to vertex $7$ must go through one of the destroyed vertices.