Problem D

There are three jugs with a volume of a, b and c liters. (a,b, and c are positive integers not greater than 200). The first and the secondjug are initially empty, while the third

is completely filled with water. It is allowed to pour waterfrom one jug into another until either the first one is empty or the second oneis full. This operation can be performed zero, one or more times.

You are to write a program that computes the least totalamount of water that needs to be poured; so that at least one of the jugscontains exactly d liters of water (d is a positive integer not greater than200). If it is not possible to measure d liters this way your program shouldfind a smaller amount of water d‘ < d which is closest to d and for which d‘liters could be produced. When d‘ is found, your program should compute theleast total amount of poured water needed to produce d‘ liters in at least oneof the jugs.

Input

The first line of input contains the number of test cases.In the next T lines, T test cases follow. Each test case is given in one lineof input containing four space separated integers - a, b, c and d.

Output

The output consists of two integers separated by a singlespace. The first integer equals the least total amount (the sum of all watersyou pour from one jug to another) of poured water. The second integer equals d,if d liters of water could be produced by such transformations, or equals theclosest smaller value d‘ that your program has found.