Description

You have come to the wishing well for $Q$ consecutive days, everyday you have a positive integer $x$ in your hand, representing your wish.

Whether a wish can come true or not can not totally be controlled by an individual, so you are also given two parameters $y$ and $z$ each day by the well.

If there exist two unequal natural numbers $a$ and $b$, where $a\operatorname{or}b=x,|a-b|\le y,a+b\le z$, the well will consider your wish achievable and return YES as an answer, otherwise it will consider the wish too difficult to realize and give you NO.

Here, $a\operatorname{or}b$ denotes the bitwise OR operation between $a$ and $b$, you can also consider it as | in C++. $|x|$ denotes the absolute value of $x$.

You're eager to know the result every day.

Input Format

The first line of the input contains a single integer $Q$: the amount of days you make wish.

The next $Q$ lines each contains three integers: $x,y$ and $z$.

Output Format

$Q$ lines, each contains a string YES or NO, representing the result of the day.

2
5 2 9
3 9 2

YES
NO

Hint

Example Explanation

For $x = 5,y = 2,z = 9$, $a = 5,b = 4$ can meet the conditions.

For $x = 3,y = 9 ,z = 2$, no $a$ and $b$ can meet the conditions.

Constraints

This problem uses bundled testing.

Special property: It is guaranteed that $z\ge 2\times x$.

For all data, it is guaranteed that:

$1\le Q\le 10^5,1\le x,y\le 10^9,1\le z\le2\times10^9$.