School Dance - Edge Cases

Edge cases:

$1.$ No preferences: max flow is $0$, output $0$ pairs.

$2.$ More boys than girls (or vice versa): max flow is limited by the smaller set.

$3.$ One boy likes all girls: he gets paired with one, others remain.

$4.$ Disconnected preferences: some boys or girls remain unpaired.

Always check if $k = 0$ (no preferences). Return $0$ immediately. Also handle $n = 0$ or $m = 0$. These cases should not crash your program.