Write java to solve: You are given an array of integers $1,2,...,$a$1,$a$2,...,$an of length $$n and an integer $$k$.$

Two players are playing a game. The first player chooses an index $11$i$$n$.$ Then the second player chooses a different index $1,1$j$$n$,$i$$j$.$ The first player wins if $|||$ai$$aj$|$ is not divisible by $$k$.$ Otherwise, the second player wins.

We play as the first player. Determine whether it is possible to win, and if so$,$ which index $$i should be chosen.

The absolute value of a number $$x is denoted by $|||$x$|$ and is equal to $$x if $0$x$0,$ and $$x otherwise.

Input

Each test contains multiple test cases. The first line of input contains a single integer $$t $(11001$t$100)$ the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $$n and $$k $(11001$n$100$; $11001$k$100)$ the length of the array and the number $$k$.$

The second line of each test case contains $$ integers $1,2,...,$a$1,$a$2,...,$an $(11001$ai$100)$ the elements of the array $.$

Output

For each test case, if it is impossible for the first player to win, print $"$NO$"($without quotes$).$

Otherwise, print "YES" $($without quotes$)$ and on the next line the appropriate index $11$i$$n$.$ If there are multiple solutions, print any of them.

Example

Input

$7$

$32$

$123$

$42$

$1245$

$53$

$107345$

$53$

$131155536$

$21$

$1717$

$22$

$1718$

$13$

$6$

Output

YES $2$ NO YES $3$ NO NO YES $2$ YES $1$