In a distant land, there are 
~N~ islands. Each island has a value of accessibility denoted by 
~v_i~. You are a bridge building contractor that has been given the task of trying to connect the islands by building bridges. However, because you want to save resources, you have decided to only build bridges such that the XOR of the accessibilities of the islands you connect with a bridge, is less than or equal to 
~M~. That is, you will build a bridge between island 
~i~ and 
~j~ if and only if 
~v_i \oplus v_j \le M~. Now, your boss has given you 
~Q~ queries, each asking if islands 
~p_i~ and 
~q_i~ will be connected by the bridges.
Constraints
For all subtasks:
~1 \le N, Q \le 200\,000~
~0 \le M, v_i \le 10^9~
~1 \le p_i, q_i \le N~
Subtask 1 [5%]
~1 \le N, Q \le 100~
~0 \le M, v_i \le 100~
Subtask 2 [5%]
~1 \le N, Q \le 5\,000~
~0 \le M \le 5\,000~
Subtask 3 [10%]
~M = 2^k-1~ for some non-negative integer 
~k~ and 
~0 \le M \le 10^9~.
Subtask 4 [80%]
No additional constraints.
Input Specification
The first line contains three space-separated integers 
~N, M, Q~.
The second line contains ~N~ space-separated integers, ~v_i~, denoting the accessibility of island ~i~.
The next ~Q~ lines contain two space-separated integers ~p_i~ and ~q_i~, a query asking if islands ~p_i~ and ~q_i~ are connected by a set of bridges.
Output Specification
For each of the queries, print YES if the islands are connected, or NO otherwise.
Sample Input
4 5 4
1 2 3 10
1 4
2 3
3 4
1 2
Sample Output
NO
YES
NO
YES
Comments
how can I deal with bad_alloc ??
You're using too much memory. You can pass the first two subtasks by making your array sizes smaller, but your approach won't work for subtasks 3 and 4.