Not K Consecutive - Repovive Standard Round 1 | Repovive

4B. Not K Consecutive

1000 pts2s256 MB

You are given three integers $n$ , $m$ , and $k$ .

You want to build a binary string $s$ of length $n+m$ that contains exactly $n$ characters equal to 0 and exactly $m$ characters equal to 1.

Determine whether it is possible to build such a string so that there is no substring of length $k$ whose characters are all equal.
In other words, there must not exist an index $i$ such that $s_i = s_{i+1} = \cdots = s_{i+k-1}$ .

Print Yes if it is possible, otherwise print No.

Constraints:

$1 \le t \le 10^4$
$1 \le n, m, k \le 10^4$

Input

t

\left. \begin{array}{l} n \quad m \quad k \end{array} \right\} \times t

Output

\left. \begin{array}{l} \text{ans} \end{array} \right\} \times t

where $\text{ans}$ is either Yes or No.

Samples

Input

Case 1

3 3 3

Case 2

7 2 3

Case 3

6 2 3

Output

Case 1

Yes

Case 2

No

Case 3

Yes

You are given three integers $n$ , $m$ , and $k$ .

You want to build a binary string $s$ of length $n+m$ that contains exactly $n$ characters equal to 0 and exactly $m$ characters equal to 1.

Print Yes if it is possible, otherwise print No.

Constraints:

$1 \le t \le 10^4$
$1 \le n, m, k \le 10^4$

t

\left. \begin{array}{l} n \quad m \quad k \end{array} \right\} \times t

\left. \begin{array}{l} \text{ans} \end{array} \right\} \times t

where $\text{ans}$ is either Yes or No.

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4B. Not K Consecutive

Input

Output

Samples

4B. Not K Consecutive

Input

Output

Samples