Time Limit: 1.0 s

Memory Limit: 256.0 MB

Description

Imti has two lists, each containing single-digit numbers. He wants to know if it’s possible to create all the dates from 01 to 31 using these two lists. Here's how he forms a date:

He picks one digit from the first list.
He picks one digit from the second list.
He combines the two digits (first digit followed by the second digit) to form a two-digit number.

For example:
If the first list is [0, 1, 2] and the second list is [1, 2, 3], Imti can form dates like 01, 12, and 23.

However, he cannot form a date like 04 because 4 is not in either list.

Can Imti use the digits in these two lists to form all dates from 01 to 31?

Input

The first line T, (1<=T <=1000)- number of test case.

In each test case contains following line:

The first line contains two integers, 𝑁 and 𝑀 ( 1 ≤ 𝑁 , 𝑀 ≤ \(10^5\) ) representing the sizes of the two lists.

The second line contains 𝑁 integers, the elements of the first list 𝑋 ( 0 ≤ 𝑋 ≤ 9 )

The second line contains 𝑀 integers, the elements of the first list 𝑌 ( 0 ≤ 𝑌 ≤ 9 )

Sum of N over all test cases doesn't exceed \(10^5\).
Sum of M over all test cases doesn't exceed \(10^5\).

Output

In each test case, print "YES" if it's possible to form all dates from 01 to 31, otherwise print "NO".

Sample

5

5 10

9 3 5 1 4

4 4 9 6 0 3 6 8 4 0

4 2

3 0 4 1

7 9

11 4

7 8 0 6 4 8 9 9 8 8 5

9 0 6 5

20 10

4 6 4 5 1 8 0 7 3 9 5 5 8 9 2 4 5 8 4 3

7 3 2 4 9 5 8 0 1 6

20 7

4 8 5 2 1 8 9 7 1 5 6 1 6 0 4 6 1 4 1 9

2 9 9 7 2 9 1

NO

NO

NO

YES

NO