G. Gates to Another World
time limit per test
4 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

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.
Input

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.

Output

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).

Examples
Input
3 3
block 3 6

Output
1
0

Input
6 10
block 12 26
block 32 46
block 27 30
block 31 31

Output
1
1
0
0
1
0

Note

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.