One Person "The Price is Right"
Time Limit: 2 Seconds
Memory Limit: 65536 KB
In the game show "The Price is Right", a number of players (typically
4) compete to get on stage by guessing the price of an item. The winner is the
person whose guess is the closest one not exceeding the actual price. Because
of the popularity of the one-person game show "Who Wants to be a Millionaire",
the American Contest Management (ACM) would like to introduce a one-person version
of the "The Price is Right". In this version, each contestant is allowed
G (1 <= G <= 30) guesses and L (0 <= L <= 30) lifelines. The contestant
makes a number of guesses for the actual price. After each guess, the contestant
is told whether it is correct, too low, or too high. If the guess is correct,
the contestant wins. Otherwise, he uses up a guess. Additionally, if his guess
is too high, a lifeline is also lost. The contestant loses when all his guesses
are used up or if his guess is too high and he has no lifelines left. All prices
are positive integers.
It turns out that for a particular pair of values for G and L, it is possible
to obtain a guessing strategy such that if the price is between 1 and N (inclusive)
for some N, then the player can guarantee a win. The ACM does not want every
contestant to win, so it must ensure that the actual price exceeds N. At the
same time, it does not want the game to be too diffcult or there will not be
enough winners to attract audience. Thus, it wishes to adjust the values of
G and L depending on the actual price. To help them decide the correct values
of G and L, the ACM has asked you to solve the following problem. Given G and
L, what is the largest value of N such that there is a strategy to win as long
as the price is between 1 and N (inclusive)?
The input consists of a number of cases. Each case is specified by one line
containing two integers G and L, separated by one space. The end of input is
specified by a line in which G = L = 0.
For each case, print a line of the form:
Case c: N
where c is the case number (starting from 1) and N is the number computed.
Case 1: 3
Case 2: 6
Case 3: 847
Case 4: 127
Source: East Central North America 2002