/*
 4 good guy, 4 bad guy, test 7 as interval
 instance:
 1 2 3 4 5 6 (7) 8
 if 7 is good, fail
 else after killing 7, we re number them as:
 1 2 3 4 5 6 7
 prev(7) is (still) 6, good guys are still 1~4, bad guys changed a bit
 the next one to be killed (in new instance) is: next(prev(7), 7), and we still know if it's good/bad
 so, we can throw old instance and bad guy number, still know if next one is good/bad
 
 recursively doing this, we can tell if 7 saves all good guys
 help:
 1. m>k, or good guy will be killed in 1st round
 2. m is c(k+1), or c(k+1)+1. because in last round(k good, 1 bad), prev(dead) is k or k+1, m has to be [1+] multiple of k+1 to kill the last 1 bad
 */