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
\(1 \le N\) , \(Q \le 10^6\)
\(1 \le i \le N\)