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.
The first line contains two numbers n (2≤n≤106) and k (1≤k≤109) — 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≤m≤105) lines contains three integers — the query type, l and r (if query type is 1, then 1≤l<r≤n, otherwise 1≤l≤n,1≤r≤109).
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.