(* -------------------------------------------------------------------- *
 *                                                                      *
 * At one point in their history, the Egyptians did not have a general  *
 * way of writing fractions as m/n.  Instead, they wrote such fractions *
 * as the sums of k unit fractions 1/m, for different values of m.      *
 *                                                                      *
 *                  3    1    1                                         *
 * They would write - as - + --, which we can abbreviate as [2, 10],    *
 *                  5    2   10                                         *
 *                                                                      *
 *     12                     1   1    1    1                           *
 * and -- could be written as - + - + -- + ---, or [2, 3, 12, 156].     *
 *     13                     2   3   12   156                          *
 *                                                                      *
 * This program prints the first k-1 denominators and returns the last  *
 * denominator, which the executable prints.                            *
 *                                                                      *
 * https://www.cs.uni.edu/~wallingf/teaching/cs4550/sessions/10.html    *
 *                                         #a-klein-program-to-write    *
 * -------------------------------------------------------------------- *)

function main(m: integer, n: integer): integer
    if (m = 1)
       then n
       else
         if MOD(n, m) = 0
            then n / m
            else print_and_continue(m, n, n/m + 1)

(* print the unit fraction that was found,    *)
(* then compute the fraction for m/n - 1/unit *)

function print_and_continue(m: integer, n: integer, unit: integer): integer
    print(unit)
    main((unit * m) - n, n * unit)

(* from the Klein library *)

function MOD(m: integer, n: integer): integer
    m - m/n * n