#834Continued Fractions

Let b₀, b₁, b₂, . . . , b_n be integers with b_k > 0 for k > 0. The continued fraction of order n with coeficients b₁, b₂, . . . , b_n and the initial term b₀ is defined by the following expression

which can be abbreviated as [b₀; b₁, . . . , b_n].

An example of a continued fraction of order n = 3 is [2; 3, 1, 4]. This is equivalent to

Write a program that determines the expansion of a given rational number as a continued fraction. To ensure uniqueness, make b_n > 1.

Input

The input consists of an undetermined number of rational numbers. Each rational number is defined by two integers, numerator and denominator.

Output

For each rational number given in the input, you should output the corresponding continued fraction.

LOCAL platform clarification

The denominator is nonzero. Normalize its sign and use floor quotients, allowing a negative first coefficient. For an integral rational, print [b0;] (including the semicolon); the final-coefficient-greater-than-one condition applies only when a fractional tail exists.