In every round of a certain game show , \( v \) votes are cast by the public to decide which contestants out of \( c \) contestants continue to the next round. The contestant with the lowest amount of votes in every round is eliminated. The next round proceeds with \( c - 1 \) contestants and so on. What is the minimum number of votes needed to guarantee that a contestant will proceed to the next round, assuming that he/she does not forfeit?
\( c \) is updated at the start of every round to represent the number of remaining contestants.
\( v \) may vary with each round.
Every round, one contestant must be eliminated, by voting, forfeit or tiebreaker.
\( c \geq 2 \)