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B. Orac and Medians

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputSlime has a sequence of positive integers $$$a_1, a_2, \ldots, a_n$$$.

In one operation Orac can choose an arbitrary subsegment $$$[l \ldots r]$$$ of this sequence and replace all values $$$a_l, a_{l + 1}, \ldots, a_r$$$ to the value of median of $$$\{a_l, a_{l + 1}, \ldots, a_r\}$$$.

In this problem, for the integer multiset $$$s$$$, the median of $$$s$$$ is equal to the $$$\lfloor \frac{|s|+1}{2}\rfloor$$$-th smallest number in it. For example, the median of $$$\{1,4,4,6,5\}$$$ is $$$4$$$, and the median of $$$\{1,7,5,8\}$$$ is $$$5$$$.

Slime wants Orac to make $$$a_1 = a_2 = \ldots = a_n = k$$$ using these operations.

Orac thinks that it is impossible, and he does not want to waste his time, so he decided to ask you if it is possible to satisfy the Slime's requirement, he may ask you these questions several times.

Input

The first line of the input is a single integer $$$t$$$: the number of queries.

The first line of each query contains two integers $$$n\ (1\le n\le 100\,000)$$$ and $$$k\ (1\le k\le 10^9)$$$, the second line contains $$$n$$$ positive integers $$$a_1,a_2,\dots,a_n\ (1\le a_i\le 10^9)$$$

The total sum of $$$n$$$ is at most $$$100\,000$$$.

Output

The output should contain $$$t$$$ lines. The $$$i$$$-th line should be equal to 'yes' if it is possible to make all integers $$$k$$$ in some number of operations or 'no', otherwise. You can print each letter in lowercase or uppercase.

Example

Input

5 5 3 1 5 2 6 1 1 6 6 3 2 1 2 3 4 3 3 1 2 3 10 3 1 2 3 4 5 6 7 8 9 10

Output

no yes yes no yes

Note

In the first query, Orac can't turn all elements into $$$3$$$.

In the second query, $$$a_1=6$$$ is already satisfied.

In the third query, Orac can select the complete array and turn all elements into $$$2$$$.

In the fourth query, Orac can't turn all elements into $$$3$$$.

In the fifth query, Orac can select $$$[1,6]$$$ at first and then select $$$[2,10]$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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