$\text{[math]}$

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 ($$$0 \le l \le r \lt 2^n$$$). It's guaranteed that no planet will be destroyed twice.

ask a b — query for reachability between planets $$$a$$$ and $$$b$$$ ($$$0 \le a, b \lt 2^n$$$). 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).

Note

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

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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):

$\text{[math]}$

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.

Gates to Another World

Examples