Sum of Pairs

A sequence of ~N~ integers is given. We want to be able to answer the question "Is there a pair of terms in the sequence whose sum equals ~X~?" for any integer ~X~.

Problem

Write a program in one of the IOI languages that reads the sequence of ~N~ numbers and then answers a series of such questions, for different values of ~X~. If the answer is "yes", then your program should print the word "~true~"; otherwise, it should print the word "~false~".

Input Files:

The input files named sumpair.in are text files consisting of three lines: The first line contains two integers separated by a single space: the number ~N~ of sequence numbers ~(1 \le N \le 1.000.000)~ and the number ~Q~ of questions ~(1 \le Q \le 1.000)~. The second line contains ~N~ integers (the absolute value of which does not exceed ~10^9~ ), separated in pairs by a single space: the terms of the sequence. The third line contains ~Q~ integers separated in pairs by a single space: the questions to be answered.

Output Files:

The output files named sumpair.out are text files consisting of ~Q~ lines. The ~i~-th line contains the answer to the ~i~-th question: one of the words "~true~" or "~false~".

Example of Input - Output Files:

STDIN (sumpair.in)

12 5
2 42 5 -6 5 7 10 29 0 21 29 15
17 30 42 -4 58

STDOUT (sumpair.out)

true    // 2+15 = 7+10 = 17
false   // it does not result in 30
true    // 42+0 = 42
true    // 2+(-6) = -4
true    // 29+29 = 58

Formatting: In the output, each line terminates with a newline character.
Maximum execution time: 2 sec.
Maximum available memory: 16 MB.