A candidate necklace matches a sample if it is a cyclic rotation of the sample. Check each candidate independently.

Input

The first line contains n and k (1 ≤ n ≤ 100000, 1 ≤ k ≤ 10). The second line is the sample lowercase string of length n. The next k lines are candidate strings.

Output

For each candidate print YES if it is a cyclic rotation of the sample; otherwise print NO.

Examples

Input #1

5 4
abcde
abcde
bcdea
cbaed
cdeab

Output #1

YES
YES
NO
YES

Input #2

1 3
a
a
b
aa

Output #2

YES
NO
NO