CF763E Timofey and our friends animals

After his birthday party, Timofey went to his favorite tree alley in a park. He wants to feed there his favorite birds — crows. It's widely known that each tree is occupied by a single crow family. The trees in the alley form a row and are numbered from $ 1 $ to $ n $ . Some families are friends to each other. For some reasons, two families can be friends only if they live not too far from each other, more precisely, there is no more than $ k-1 $ trees between any pair of friend families. Formally, the family on the $ u $ -th tree and the family on the $ v $ -th tree can be friends only if $ |u-v|

The first line contains integers $ n $ and $ k $ ( $ 1

Print $ q $ lines. Line $ i $ should contain single integer — the answer in the $ i $ -th situation.

In the first example the following family pairs are friends: $ (1,3) $ , $ (2,3) $ and $ (4,5) $ . - In the first situation only the first family has remained, so the answer is $ 1 $ . - In the second situation the first two families have remained, and they aren't friends, so the answer is $ 2 $ . - In the third situation the families $ 2 $ and $ 3 $ are friends, so it is enough to feed any of them, the answer is $ 1 $ . - In the fourth situation we can feed the first family, then the third family will get the information from the first family, and the second family will get the information from the third. The answer is $ 1 $ . - In the fifth situation we can feed the first and the fifth families, so the answer is $ 2 $ .