The elections to Berland parliament are happening today. Voting is in full swing! Totally there are n candidates, they are numbered from 1 to n . Based on election results k ( 1 ≤ k ≤ n ) top candidates will take seats in the parliament. After the end of the voting the number of votes for each candidate is calculated. In the resulting table the candidates are ordered by the number of votes. In case of tie (equal number of votes) they are ordered by the time of the last vote given. The candidate with ealier last vote stands higher in the resulting table. So in the resulting table candidates are sorted by the number of votes (more votes stand for the higher place) and if two candidates have equal number of votes they are sorted by the time of last vote (earlier last vote stands for the higher place). There is no way for a candidate with zero votes to take a seat in the parliament. So it is possible that less than k candidates will take a seat in the parliament. In Berland there are m citizens who can vote. Each of them will vote for some candidate. Each citizen will give a vote to exactly one of n candidates. There is no option "against everyone" on the elections. It is not accepted to spoil bulletins or not to go to elections. So each of m citizens will vote for exactly one of n candidates. At the moment a citizens have voted already ( 1 ≤ a ≤ m ). This is an open election, so for each citizen it is known the candidate for which the citizen has voted. Formally, the j -th citizen voted for the candidate g j . The citizens who already voted are numbered in chronological order; i.e. the ( j + 1) -th citizen voted after the j -th. The remaining m - a citizens will vote before the end of elections, each of them will vote for one of n candidates. Your task is to determine for each of n candidates one of the three possible outcomes: a candidate will be elected to the parliament regardless of votes of the remaining m - a citizens; a candidate has chance to be elect