Genos has been given n distinct lines on the Cartesian plane. Let be a list of intersection points of these lines. A single point might appear multiple times in this list if it is the intersection of multiple pairs of lines. The order of the list does not matter. Given a query point ( p , q ) , let be the corresponding list of distances of all points in to the query point. Distance here refers to euclidean distance. As a refresher, the euclidean distance between two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is . Genos is given a point ( p , q ) and a positive integer m . He is asked to find the sum of the m smallest elements in . Duplicate elements in are treated as separate elements. Genos is intimidated by Div1 E problems so he asked for your help. The first line of the input contains a single integer n ( 2 ≤ n ≤ 50 000 ) — the number of lines. The second line contains three integers x , y and m ( | x |, | y | ≤ 1 000 000 , ) — the encoded coordinates of the query point and the integer m from the statement above. The query point ( p , q ) is obtained as . In other words, divide x and y by 1000 to get the actual query point. denotes the length of the list and it is guaranteed that . Each of the next n lines contains two integers a i and b i ( | a i |, | b i | ≤ 1 000 000 ) — the parameters for a line of the form: . It is guaranteed that no two lines are the same, that is ( a i , b i ) ≠ ( a j , b j ) if i ≠ j . Print a single real number, the sum of m smallest elements of . Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6 . To clarify, let's assume that your answer is a and the answer of the jury is b . The checker program will consider your answer correct if . In the first sample, the three closest points have distances and . In the second sample, the two lines y = 1000 x - 1000 and intersect at (2000000, 1999999000) . This point has a distance of from ( - 1000, - 1000) . In the third sample, the three lines al