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USU Open Personal Contest 2010

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C. Cake

Time limit: 0.5 second
Memory limit: 64 MB
Karlsson and Little Boy have found a cake in the fridge. It is written on the box that the cake consists of n grams of cream, m grams of chocolate, and other ingredients. The friends want to divide the cake between them and eat it right there.
Little Boy is going to cut the cake into two pieces, and then Karlsson will choose the piece that he thinks is more delicious. Little Boy agrees with this method of dividing, because his and Karlsson's tastes differ and so he can cut the cake in such a way that he would get a piece that is not so bad. In addition, Karlsson is so kind that if the two pieces seem equally delicious to him then he will let Little Boy choose.
If a piece of cake contains x grams of cream and y grams of chocolate, then Little Boy evaluates the deliciousness of this cake by the number a1·x + b1·y. Karlsson evaluates the same piece by the number a2·x + b2·y. Given the coefficients a1, b1, a2, b2, tell Little Boy how to cut the cake so that he would get as delicious piece of cake as possible. Little Boy can cut off a piece containing any amount of cream and any amount of chocolate but, of course, no more than there is in the whole cake.


The first line contains the integers a1, b1, a2, b2 (0 ≤ ai, bi ≤ 100). The second line contains the integers n and m (0 ≤ n, m ≤ 1000).


Output the mass of cream and the mass of chocolate in one of the pieces into which Little Boy should cut the cake accurate to 10−8. It does not matter who will get this piece. If there are several optimal answers, output any of them.


1 2 3 2
400 300
300.00000000 0.00000000
Problem Author: Vladislav Isenbaev
Problem Source: XI USU Open Personal Contest (March 13, 2010)
To submit the solution for this problem go to the Problem set: 1755. Cake