## ECOO '18 R3 P1 - Balanced

View as PDF

Points: 12 (partial)
Time limit: 13.0s
Memory limit: 64M

Problem type
Allowed languages
Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

Ms. Daisy teaches a class of boys and girls that need to line up every morning to take attendance. Ms. Daisy thinks that a line is "balanced" if at least one of the boys is equidistant from two of the girls in the line. For example, a girl-boy-boy-girl line is not balanced because both boys are closer to one of the girls, but a girl-girl-boy-boy-girl line is balanced because the first boy is equidistant from the first and last girls.

Ms. Daisy likes it when the students form a balanced line. Can you help her figure out the number of balanced lines that the students can form? Two lines are considered distinct if at least one student has a different position in each line.

#### Input Specification

the standard input will contain 10 datasets. Each dataset contains two integers , .

For the first four datasets,

#### Output Specification

For each data set, output the number of balanced lines that can be formed, modulo .

Note: modulo is the remainder of .

#### Sample Input (Three Datasets Shown)

1 2
2 2
3 2

#### Sample Output

2
8
48

#### Explanation of Sample Input

In the first case, a balanced line must have a girl, then the boy, and then the other girl. Either girl can come first, which gives us two balanced lines. In the second case, a balanced line has either a boy-girl-boy-girl pattern or a girl-boy-girl-boy pattern. In the third case, an example balanced line would have a girl-boy-boy-boy-girl pattern (the boy in the middle is equidistant from the two girls).

Educational Computing Organization of Ontario - statements, test data and other materials can be found at ecoocs.org