Sample Input 13 23 1 2 1 3 2 4 2 5 3 6 3 7 4 8 4 9 6 10 6 11 7 12 7 13 2 1 0 8 13 3 0 9 12 5 2 9 2 8 2 2 0 10 12 1 2 2 1 3 2 7 2 1 0 9 5 6 2 4 2 5 1 7 0 9 12 4 0 10 5 7 2 1 2 4