Carry a Cheese

Jerry is a little mouse. He is trying to survive from the cat Tom. Jerry is carrying a parallelepiped-like piece of cheese of size A × B × C. It is necessary to trail this cheese to the Jerry's house. There are several entrances in the Jerry's house. Each entrance is a rounded hole having its own radius R. Could you help Jerry to find suitable holes to be survive?

Your task is to create a program which estimates whether Jerry can trail the cheese via each hole. The program should print "OK" if Jerry can trail the cheese via the corresponding hole (without touching it). Otherwise the program should print "NA".

You may assume that the number of holes is less than 10000.

Input

The input is a sequence of datasets. The end of input is indicated by a line containing three zeros. Each dataset is formatted as follows:

A B C n R1 R2

. . Rn

n indicates the number of holes (entrances) and Ri indicates the radius of i-th hole.

Output

For each datasets, the output should have n lines. Each line points the result of estimation of the corresponding hole.

Example

Input

10 6 8 5 4 8 6 2 5 0 0 0

Output

NA OK OK NA NA

inputFormat

Input

The input is a sequence of datasets. The end of input is indicated by a line containing three zeros. Each dataset is formatted as follows:

A B C n R1 R2

. . Rn

n indicates the number of holes (entrances) and Ri indicates the radius of i-th hole.

outputFormat

Output

For each datasets, the output should have n lines. Each line points the result of estimation of the corresponding hole.

Example

Input

10 6 8 5 4 8 6 2 5 0 0 0

Output

NA OK OK NA NA

样例

10 6 8
5
4
8
6
2
5
0 0 0

NA
OK
OK
NA
NA

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