Wolves and sheep

Task

You have $N$ wolves and $M$ sheep and you want to move all animals from one bank of a river to the other using a boat that can carry at most $K$ animals. In addition, if at any moment there exists a bank that has at least one sheep and where the wolves are in a strict majority, then you lose and the wolves will eat the sheep. Also, once you move an animal to the other bank, you cannot bring it back. You must decide whether you can move all animals to the other bank without any sheep being eaten.

Input data

• The first line contains $T$, the number of test cases.
• Each of the next $T$ lines contains a triple of natural numbers: $N$, $M$, $K$.

Output data

Print $T$ answers, each on its own line: da (affirmative) or nu (negative).

Constraints and clarifications

• $1 \leq T \leq 10^6$
• $1 \leq N, M, K \leq 10^9$
• You cannot keep animals on the boat. If you take them from the first bank, you must leave them on the second.
• We do not check the majority condition at the start and at the end.

Example

stdin

4
5 4 2
2 1 2
1 7 1
8 7 1

stdout

nu
da
da
nu

Explanation

For the first test, it can be shown that there is no way to transport the animals according to the rules. For the second test, we can first take both wolves, then take the sheep. For the third test, we can move the animals in any order we want. For the last test, it can be shown that there is no solution.