(python 3) A scuba diver uses a special equipment for diving. He has a cylinder with two containers: one with oxygen and the other with nitrogen. Depending on the time he wants to stay under water and the depth of diving the scuba diver needs various amount of oxygen and nitrogen. The scuba diver has at his disposal a certain number of cylinders. Each cylinder can be described by its weight and the volume of gas it contains. In order to complete his task the scuba diver needs specific amounts of oxygen and nitrogen. Theoretically, the diver can take as many cylinders as he wants/needs. Use dynamic programming to find the minimal total weight of cylinders he has to take to complete the task and which those cylinders are. In case of several acceptable solutions, printing just one of them is enough.

Example

The scuba diver has at his disposal 5 cylinders described below. Each description consists of: volume of oxygen, volume of nitrogen (both values are given in liters) and weight of the cylinder (given in decagrams):

3 36 120

10 25 129

5 50 250

1 45 130

4 20 119

If the scuba diver needs 5 liters of oxygen and 60 liters of nitrogen then he has to take two cylinders of total weight 249 (for example the first and the second ones or the fourth and the fifth ones).

Input The number of test cases c is in the first line of input, then c test cases follow separated by an empty line. In the first line of a test case there are two integers t, a separated by a single space, 1 ? t ? 21 and 1 ? a ? 79. They denote volumes of oxygen and nitrogen respectively, needed to complete the task. The second line contains one integer n, 1 ? n ? 1000, which is the number of accessible cylinders. The following n lines contain descriptions of cylinders; i-th line contains three integers ti , ai , wi separated by single spaces, (1 ? ti ? 21, 1 ? ai ? 79, 1 ? wi ? 800). These are respectively: volume of oxygen and nitrogen in the i-th cylinder and the weight of this cylinder.

Output On the first line will be printed the total weight wt and on the next line separated by spaces the index of the cylinders in order.

test input

1

5 60

5

3 36 120

10 25 129

5 50 250

1 45 130

4 20 119

test output

249

1 2