Game

Hangi and Hyoseop are staff members preparing a contest. After working through the night they took a break and played a game. The rules are as follows.

First they fix positive integers $S$, $F$, and $K$, where $S < F$. One of the two starts, and after that they take turns building a number. On your turn, if the number the previous person made is odd, you choose an integer $P$ $(1 \le P \le K)$ and add it to that number; if it is even, you choose an integer $P$ $(2 \le P \le K+1)$ and add it. The player who starts adds a number to the initial value $S$ the same way. The first player to make a number greater than or equal to $F$ loses.

Given $S$, $F$, and $K$, with Hangi starting first, write a program that decides whether Hangi has a winning strategy that always beats Hyoseop.

For example, if $S = 1$, $F = 5$, and $K = 2$, Hangi has no winning strategy. On the first turn Hangi may choose 1 or 2. If Hangi chooses 1 and makes $S + 1 = 2$, Hyoseop chooses 2 and makes 4, and then every number Hangi can make is at least 5, so Hangi loses the game. If Hangi chooses 2 and makes $S + 2 = 3$, Hyoseop chooses 1, and Hangi loses again.

Input comes from standard input. The first line has the number of test cases $T$ $(1 \le T \le 10)$. Each of the following $T$ lines has $S$, $F$, and $K$ of one test case in that order. $S$ and $F$ are integers with $1 \le S < F \le 1{,}000{,}000$, and $K$ is an integer with $1 \le K \le 1{,}000$.

Print to standard output. For each test case, print YES on one line if Hangi has a winning strategy, and NO if there is none.