You have been given two strings, A and B (of length N each) and Q queries.
The strings contain only 0s and/or 1s.

For every query, you are given an index i. You have to update the value at index i to 1 in string B and check if B is lexicographically equal to or larger than A or not.
If yes, then print "$YES$" and if not, print "$NO$" (without quotes).

Input format

• First line contains two space-separated integers N and Q.
• Next line contains the string A.
• Next line contains the string B.
• Next Q lines contains an integer i (1 - based indexing)

Output Format

For each query, print the desired output in a new line.

Input Constraints
$1 \le N$ , $Q \le 10^6$
$1 \le i \le N$