Odd Sum Game - Repovive Standard Round 5 | Repovive

14A. Odd Sum Game

500 pts1s256 MB

You are given two integers $n$ and $k$ .

The numbers $1, 2, \ldots, n$ are written on a board. You must choose exactly $k$ different numbers from them.

Determine whether it is possible for the sum of the chosen numbers to be odd.

Constraints

$1 \le t \le 10^4$
$1 \le k \le n \le 10^6$

Input

t

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

Output

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

For each test case, print Yes if it is possible, and No otherwise.

Samples

Input

Case 1

1 1

Case 2

3 3

Case 3

4 2

Case 4

5 4

Case 5

8 8

Explanation

Case 1

Choosing only $1$ gives an odd sum.

Case 2

All three numbers must be chosen, and their sum is $1+2+3=6$ , which is even.

Case 3

Choosing $1$ and $2$ gives the odd sum $3$ .

Case 4

Choosing $1,3,4,5$ gives the odd sum $13$ .

Case 5

All eight numbers must be chosen, and their sum is $36$ , which is even.

Output

Case 1

Yes

Case 2

No

Case 3

Yes

Case 4

Yes

Case 5

No

You are given two integers $n$ and $k$ .

The numbers $1, 2, \ldots, n$ are written on a board. You must choose exactly $k$ different numbers from them.

Determine whether it is possible for the sum of the chosen numbers to be odd.

$1 \le t \le 10^4$
$1 \le k \le n \le 10^6$

t

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

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

For each test case, print Yes if it is possible, and No otherwise.

Choosing only $1$ gives an odd sum.

All three numbers must be chosen, and their sum is $1+2+3=6$ , which is even.

Choosing $1$ and $2$ gives the odd sum $3$ .

Choosing $1,3,4,5$ gives the odd sum $13$ .

All eight numbers must be chosen, and their sum is $36$ , which is even.

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14A. Odd Sum Game

Constraints

Input

Output

Samples

14A. Odd Sum Game

Constraints

Input

Output

Samples