# From Rational to Factorial

A factorial number N denoted by N = [, a, b] consists of three parts.

• the sign part which is either 0 or 1,

• the whole part a = [a_{n}, . . . , a_{1}, a_{0}], where a_{k} = 0, 1, . . . , k + 1, for k
= 0, 1, . . . , n and,

• the fractional part b = [b_{1}, b_{2}, . . . , b_{m}], where b_{k} = 0, 1, . . . , k for k
= 1, 2, . . . ,m

such that N is equivalent to the decimal number

For example, the factorial number [1, [3, 2, 1, 1, 1, 0], [0, 0, 2, 2]] is equivalent to

which is equivalent to the rational number -24321/10 or 24321/-10.

It can be shown that any rational number can be represented uniquely by a
factorial

number of the form [, a, b] where a and b are of finite lengths.

**Write a program that converts a rational number to a factorial number.**

**INPUT**

One line of input per case. The line represents a rational number R in the form
n/d where n

and d are integers with d not equal zero .

**OUTPUT
**One line of output per test case. The line represents the factorial number
that corresponds

to the rational number in the input. It must have the form

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