Binary search

Time limit 5 seconds

Memory limit 128 MiB

Sorted array of n integers is given. You must answer q queries: whether the given number x is in the array.

Input data

First line contains two numbers n and q\:(n, q \le 10^6). Second line contains n integers sorted in increasing order. Each of the next q lines contains value of x. The numbers in array do not exceed 10^9 by absolute value.

Output data

For each value of x print on a separate line "YES" if x is present in array and "NO" otherwise.

Examples

Input example #1

6 3
2 4 4 8 11 14
10
4
2

Output example #1

NO
YES
YES

Input example #3

10 5
0 0 1 1 2 3 4 5 6 8 
8
2
0
12
10

Output example #3

YES
YES
YES
NO
NO

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