#####   ######  #####    ###    #   #  ###  #   #  ######
##  ##  ##      ##  ##  ## ##   #   #   #   #   #  ##
#####   ####    #####   #   #   #   #   #   #   #  ####
##  #   ##      ##      ## ##    # #    #    # #   ##
##   #  ######  ##       ###      #    ###    #    ######

$ curl repovive.com/contests/11/problems/A

░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░██████████████████████████████████████████

Notebook Page - Repovive Standard Round 4 | Repovive | Repovive

11A. Notebook Page

500 pts1s256 MB

There is a notebook with pages numbered from $1$ to $n$ from left to right.

On each day, exactly one remaining page is read. The page must be one of the two ends of the remaining notebook, that is, either the leftmost remaining page or the rightmost remaining page.

For each test case, determine whether it is possible that page $x$ is read exactly on day $d$ .

The order of reading pages can be chosen arbitrarily, as long as the rule above is followed.

Constraints

$1 \le t \le 10^4$
$1 \le d, x \le n \le 10^9$

Input

t

\left. \begin{array}{l} n \quad d \quad x \end{array} \right\} \times t

Output

\left. \begin{array}{l} \texttt{Yes}\ \text{/}\ \texttt{No} \end{array} \right\} \times t

Samples

Input

Case 1

5 1 1

Case 2

5 1 3

Case 3

5 3 3

Case 4

7 2 6

Case 5

10 4 5

Explanation

Case 1

The page is already at one end, so it can be chosen on the first day.

Case 2

On the first day, only pages $1$ and $5$ can be read, so page $3$ cannot be read.

Case 3

For example, pages $1$ and $2$ can be read first, then page $3$ is at an end on day $3$ .

Case 4

Page $7$ can be read first, then page $6$ becomes the right end on day $2$ .

Case 5

We can prove that after 3 days, page $5$ cannot be at an end of unread pages.

Output

Case 1

Yes

Case 2

No

Case 3

Yes

Case 4

Yes

Case 5

No

There is a notebook with pages numbered from $1$ to $n$ from left to right.

On each day, exactly one remaining page is read. The page must be one of the two ends of the remaining notebook, that is, either the leftmost remaining page or the rightmost remaining page.

For each test case, determine whether it is possible that page $x$ is read exactly on day $d$ .

The order of reading pages can be chosen arbitrarily, as long as the rule above is followed.

$1 \le t \le 10^4$
$1 \le d, x \le n \le 10^9$

t

\left. \begin{array}{l} n \quad d \quad x \end{array} \right\} \times t

\left. \begin{array}{l} \texttt{Yes}\ \text{/}\ \texttt{No} \end{array} \right\} \times t

On the first day, only pages $1$ and $5$ can be read, so page $3$ cannot be read.

For example, pages $1$ and $2$ can be read first, then page $3$ is at an end on day $3$ .

Page $7$ can be read first, then page $6$ becomes the right end on day $2$ .

We can prove that after 3 days, page $5$ cannot be at an end of unread pages.

	#	Title	Points	Solved	Admin

	#	Title	Points	Solved	Admin

	#	Title	Points	Solved	Admin

	#	Title	Points	Solved	Admin

Commentary

My submissions

Sponsors

Ranking

Commentary

My submissions

Sponsors

Ranking

Commentary

My submissions

Sponsors

Ranking

Commentary

My submissions

Sponsors

Ranking

11A. Notebook Page

Constraints

Input

Output

Samples

11A. Notebook Page

Constraints

Input

Output

Samples