0201. Ellipse and the Line

Input file name:	ellipse.in
Output file name:	ellipse.out
Time limit:	250 ms
Memory limit:	32 megabytes

You are given an ellipse x²/a² + y²/b² = 1 by real numbers a, b (1 ≤ a,b ≤ 100) and a straight line that goes through points (x₁,y₁) and (x₂,y₂) with real coordinates (-500 ≤ x₁,y₁,x₂,y₂ ≤ 500). It is required to find the ratio of the smaller area to the greater area of parts of an ellipse into which it is broken with a straight line. If the straight line does not cross an ellipse, the given ratio should be considered equal to zero.

Input file

Input file contains numbers a,b,x₁,y₁,x₂,y₂ ( (x₁,y₁) ≠ (x₂,y₂) ). All numbers are real and consist of no more than two digits after decimal point.

Output file

You must output the required ratio with precision of six digits after decimal point.

Examples:

ellipse.in	ellipse.out
100 100 1 0 4 2	0.985974

Source: Petrozavodsk Summer 2003. Saratov SU Contest, Wednesday, August 27

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