In the year 2500 the annual graduation ceremony in the German University in Cairo (GUC) has run smoothly for almost 500 years so far. The most important part of the ceremony is related to the arrangement of the professors in the ceremonial hall. Traditionally GUC has n professors. Each professor has his seniority level. All seniorities are different. Let's enumerate the professors from 1 to n , with 1 being the most senior professor and n being the most junior professor. The ceremonial hall has n seats, one seat for each professor. Some places in this hall are meant for more senior professors than the others. More specifically, m pairs of seats are in "senior-junior" relation, and the tradition requires that for all m pairs of seats ( a i , b i ) the professor seated in "senior" position a i should be more senior than the professor seated in "junior" position b i . GUC is very strict about its traditions, which have been carefully observed starting from year 2001. The tradition requires that: The seating of the professors changes every year. Year 2001 ceremony was using lexicographically first arrangement of professors in the ceremonial hall. Each consecutive year lexicographically next arrangement of the professors is used. The arrangement of the professors is the list of n integers, where the first integer is the seniority of the professor seated in position number one, the second integer is the seniority of the professor seated in position number two, etc. Given n , the number of professors, y , the current year and m pairs of restrictions, output the arrangement of the professors for this year. The first line contains three integers n , y and m ( 1 ≤ n ≤ 16, 2001 ≤ y ≤ 10 18 , 0 ≤ m ≤ 100 ) — the number of professors, the year for which the arrangement should be computed, and the number of pairs of seats for which the seniority relation should be kept, respectively. The next m lines contain one pair of integers each, " a i b i ", indicating that profes