Chef has the $N numbers 1, 2, 3, \dots, N.$ He wants to give exactly K of these numbers to his friend and keep the rest with him.

He can choose any K numbers such that the [GCD] of any number from Chef's set and any number from his friend's set is equal to 1.

Formally, suppose Chef gives the set of numbers A to his friend and keeps B with himself (where |A| = K and |B| = N - K). Then A and B must satisfy

$\gcd(a, b) = 1$ \ \ $\forall a\in$ $A, b\in$ B

Chef needs your help in choosing these K numbers. Please find any valid set of K numbers that will satisfy the condition, or tell him that no such set exists.

------ Input Format ------

• The first line of input contains a single integer T denoting the number of test cases. The description of T test cases follows.
• The first and only line of each test case contains two space-separated integers N and K.

------ Output Format ------

For each test case first output a single line containing "YES" (without quotes) if a set of size K satisfying Chef's condition exists; and "NO" if no such set exists. This line is not case-sensitive so "YeS", "nO", etc. are also acceptable.

Next, if the answer is "YES", print another line containing K distinct space-separated integers from 1 to N denoting the numbers which Chef will give to his friend. The integers can be printed in any order.

If there are multiple solutions, you may print any of them.

------ Constraints ------

$1 ≤ T ≤ 10^{4}$
$2 ≤ N ≤ 10^{5}$
$1 ≤ K ≤ N - 1$
- Sum of $N$ over all test cases does not exceed $5*10^{5}$

----- Sample Input 1 ------
3
4 1
4 2
6 3

----- Sample Output 1 ------
Yes
3
Yes
4 2
No

----- explanation 1 ------
Test case $1$: Chef can give $[3]$ to his friend and keep $[1, 2, 4]$ for himself. $3$ is coprime with $1, 2$ and $4$ so the condition is satisfied. Another possible solution is Chef giving $[1]$ to his friend.

Test case $2$: Chef can give $[2, 4]$ and keep $[1, 3]$ (or vice versa). It can be seen that $\gcd(2, 1) = 1$, $\gcd(2, 3) = 1$, $\gcd(4, 1) = 1$, $\gcd(4, 3) = 1$ and so the condition is satisfied.

Test case $3$: There is no set of 3 numbers that can satisfy the given condition.

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