第一次程序实验

1264

Description

A bee larva living in a hexagonal cell of a large honeycomb decides to creep for a walk. In each “step” the larva may move into any of the right cells.The struct of the honeycomb is showed in the picture.

Your program has to compute how many different ways of larva walks from the begin-cell a to the end-cell b.

Input

The first line contains an integer giving the number of test cases to follow.Each case consists of one line containing 2 integers a and b, wh ere 1 ≤ a ≤ b <50 .

Output

For each test case, output one line containing the number of walks.

Sample Input

Sample Output

HINT

Source

yehr

1265

Description

Some people believe that there are three cycles in a

person's life that start the day he or she is born. These three cycles are the physical, emotional, and intellectual cycles, and they have periods of lengths 23, 28, and 33 days, respectively. There is one peak in each period of a cycle.

At the peak of a cycle, a person performs at his or her best in the corresponding field (physical, emotional or mental). For example, if it is the mental curve, thought processes

will be sharper and concentration will be easier. Since the three cycles have different periods, the peaks of the three cycles generally occur at different times. We would like to determine when a triple peak occurs (the peaks of all three cycles occur in the same day) for any person. For each cycle, you will be given the number of days from the beginning of

the current year at which one of its peaks (not necessarily the first) occurs. You will also be given a date expressed

as the number of days from the beginning of the current year. You task is to determine the number of days from the given date to the next triple peak. The given date is not counted. For example, if the given date is 10 and the next triple

peak occurs on day 12, the answer is 2, not 3. If a triple peak occurs on the given date, you should give the number of days to the next occurrence of a triple peak.

Input

You will be given a number of cases. The input for each case consists of one line of four integers p, e, i, and d. The values p, e, and i are the number of days from the beginning of the current year at which the physical, emotional, and intellectual cycles peak, respectively. The value d is the given date and may be smaller than any of p, e, or i. All values are non-negative and at most 365, and you may assume that a triple peak will occur within 21252 days of the given date. The end of input is indicated by a line in which p = e = i = d = -1.

Output

For each test case, print the case number followed by a message indicating the number of days to the next triple peak, in the form: Case 1: the next triple peak occurs in 1234 days. Use the plural form ``days'' even if the answer

is 1.

Sample Input

Sample Output

HINT

Source

1266

Description

Sam and Ella run a catering service. They like to put on a show when serving meatballs to guests seated at round tables. They march out of the kitchen with pots of meatballs and

start serving adjacent guests. Ella goes counterclockwise

and Sam goes clockwise, until they both plop down their last meatball, at the same time, again at adjacent guests. This impressive routine can only be accomplished if they can

divide the table into two sections, each having the same number of meatballs. You are to write a program to assist them. At these catering events, each table seats 2 <= N <=

30 guests. Each guest orders at least one and at most nine meatballs. Each place at the table is numbered from 1 to N, with the host at position 1 and the host's spouse at

position N. Sam always serves the host first then proceeds

to serve guests in increasing order. Ella serves the spouse first, then serves guests in decreasing order. The figures illustrate the first two example input cases.

Input

Input consists of one or more test cases. Each test case contains the number of guests N followed by meatballs ordered by each guest, from guest 1 to guest N. The end of the input is a line with a single zero.

Output

For each table, output a single line with the ending positions for Sam and Ella, or the sentence indicating an equal partitioning isn't possible. Use the exact formatting shown below.

Sample Input

Sample Output

HINT

Source

Mid-Central USA 2002

1267

Description

Contest time again! How excited it is to see balloons

floating around. But to tell you a secret, the judges' favorite time is guessing the most popular problem. When the contest is over, they will count the balloons of each color and find the result. This year, they decide to leave this lovely job to you.

Input

Input contains multiple test cases. Each test case starts with a number N (0 < N <= 1000) -- the total number of balloons distributed. The next N lines contain one color each. The color of a balloon is a string of up to 15 lower-case letters. A test case with N = 0 terminates the input and this test case is not to be processed.

Output

For each case, print the color of balloon for the most popular problem on a single line. It is guaranteed that

there is a unique solution for each test case.

Sample Input

Sample Output

HINT

Source

Zhejiang Provincial Programming Contest 2004

1268

Description

A number sequence is defined as follows: f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) +

B * f(n - 2)) mod 7. Given A, B, and n, you are to calculate the value of f(n).

Input

The input consists of multiple test cases. Each test case contains 3 integers A, B and n on a single line (1 <= A, B

<= 1000, 1 <= n <= 100,000,000). Three zeros signal the end

of input and this test case is not to be processed. Output

For each test case, print the value of f(n) on a single line. Sample Input

Sample Output

HINT

Source

Zhejiang Provincial Programming Contest 2004