12 13 10 9 8 4 11 5 7 6 2 1 3
l              m             r

index at 11

M = 7 < index, A[M] =11 > k=2, need one < 2

L = 8, R = 13 M = 10
12 13 10 9 8 4 11 5 7 6 2 1 3
l                     M      r

M = 8 < index, A[M] = 6 > k = 2, need one < 2

L = 11, R = 13, M = 12, 

M > index, a[M] < k -> need one > 2
L = 11, R = 11 -> good

overall, needed 2 lt 2, 1 gt 2

12 13 10 9 8 4 1 5 7 6 2 1 3

there aren't 2 lt 2 -> no

1  2  3  4 5 6 7  8 9 10 11 12 13
12 13 10 9 8 4 11 5 7  6  2  1  3
1 13 2

M = 7, 1 lt (11 > 2, Left)
M = 10, 2 lt (6 > 2, Right)
L = 11, R = 13, M = 12, 1 gt

done


7 4
3 1 5 2 7 6 4
3 4 2
2 3 5
1 5 6
1 7 3



1  2 3  4 5 6 7  8 9 10 11 12 13 14 15 16
14 1 3 15 4 5 6 16 7  8  9 10 11 12 13 2
1 16 14

L = 1, R = 16, M = 8 -> 16, go left (no cost)
L = 1, R = 7, M = 4 -> 15, left (no cost)
L = 1, R = 3, M = 2 -> go left (1 gt)