function b = f(r, m, n)
  x = factorial(r * m) / factorial(m) ^ r;
  if n < 1 || x < n, b = []; return, end
  a = repelem(1:r, m);
  b = zeros(size(a));
  for j = 1:numel(b)
    y = x / numel(a);
    i = 1 + floor(mod(n - 1, x) / y);
    x = sum(a == a(i)) * y;
    n -= sum(a < a(i)) * y;
    [a(i) b(j)] = deal([], a(i));
  end
end
a = cell2mat(arrayfun(@(n) {f(9, 1, n)}, [1;2;3;123456;234567;362880]))
b = cell2mat(arrayfun(@(n) {f(4, 3, n)}, [1;2;3;123456;234567;369600]))
 

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