Printing Sequences

문제

Bessie is learning to code using a simple programming language. She first defines a valid program, then executes it to produce some output sequence.

Defining:

• A program is a nonempty sequence of statements.
• A statement is either of the form "PRINT $cc$" where $cc$ is an integer, or "REP $oo$", followed by a program, followed by "END," where $oo$ is an integer that is at least 1.

Executing:

• Executing a program executes its statements in sequence.
• Executing the statement "PRINT $cc$" appends $cc$ to the output sequence.
• Executing a statement starting with "REP $oo$" executes the inner program a total of $oo$ times in sequence.

An example of a program that Bessie knows how to write is as follows.

REP 3
    PRINT 1
    REP 2
        PRINT 2
    END
END

The program outputs the sequence $[1,2,2,1,2,2,1,2,2][1,2,2,1,2,2,1,2,2]$.

Bessie wants to output a sequence of $NN$ ($1\le N\le 1001\; \backslash le\; N\; \backslash le\; 100$) positive integers. Elsie challenges her to use no more than $KK$ ($1\le K\le 31\; \backslash le\; K\; \backslash le\; 3$) "PRINT" statements. Note that Bessie can use as many "REP" statements as she wants. Also note that each positive integer in the sequence is no greater than $KK$.

For each of $TT$ ($1\le T\le 1001\; \backslash le\; T\; \backslash le\; 100$) independent test cases, determine whether Bessie can write a program that outputs some given sequence using at most $KK$ "PRINT" statements.

입력

The first line contains $TT$.

The first line of each test case contains two space-separated integers, $NN$ and $KK$.

The second line of each test case contains a sequence of $NN$ space-separated positive integers, each at most $KK$, which is the sequence that Bessie wants to produce.

출력

For each test case, output "YES" or "NO" (case sensitive) on a separate line.

2
1 1
1
4 1
1 1 1 1

YES
YES

11
4 2
1 2 2 2
4 2
1 1 2 1
4 2
1 1 2 2
6 2
1 1 2 2 1 1
10 2
1 1 1 2 2 1 1 1 2 2
8 3
3 3 1 2 2 1 2 2
9 3
1 1 2 2 2 3 3 3 3
16 3
2 2 3 2 2 3 1 1 2 2 3 2 2 3 1 1
24 3
1 1 2 2 3 3 3 2 2 3 3 3 1 1 2 2 3 3 3 2 2 3 3 3
9 3
1 2 2 1 3 3 1 2 2
6 3
1 2 1 2 2 3

YES
NO
YES
NO
YES
YES
YES
YES
YES
NO
NO