The kid who learned to count

Kid controller operates a boat-ferry. His task is to make sure that the ferry did not sink from excess capacity. Today only two tickets left to the ship, besides the boat can withstand only $k$ kilo additionally. The forest has only one long road along which the animals live. Help the kid to find out whether he can find two passengers in a particular area of the forest.

Input

The first line contains two numbers $n(2\le n\le 10^6)$ and $k(1\le k\le 10^9)$ — the number of animals in the forest and the remaining capacity of the ferry, respectively. The second line contains $n$ numbers — the mass of each of the animals. Then given the number of queries $m$. Each of the next $m(1\le m\le 10^5)$ lines contains three integers — the query type, $l$ and $r$ (if query type is $1$, then $1\le l<r\le n$, otherwise $1\le l\le n,1\le r\le 10^9)$.

Output

For each query of type $1$ print the line "Yes", if the Kid can find two passengers on a segment $[l;r]$ and "No" otherwise. Each query of type $2$ means that the animal with number $l$ change his weight and now weighs $r$ kilogram.

Examples