C. Drazil Likes Heaptime limit per test1.5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputDrazil likes heap very much. So he created a problem with heap:There is a max heap with a height h implemented on the array. The details of this heap are the following:This heap contains exactly 2^h - 1 distinct positive non-zero integers. All integers are distinct. These numbers are stored in the array a indexed from 1 to 2^h-1. For any 1 < i < 2^h, a[i] < a[\left \lfloor{\frac{i}{2}}\right \rfloor].Now we want to reduce the height of this heap such that the height becomes g with exactly 2^g-1 numbers in heap. To reduce the height, we should perform the following action 2^h-2^g times:Choose an index i, which contains an element and call the following function f in index i:Note that we suppose that if a[i]=0, then index i don't contain an element.After all operations, the remaining 2^g-1 element must be located in indices from 1 to 2^g-1. Now Drazil wonders what's the minimum possible sum of the remaining 2^g-1 elements. Please find this sum and find a sequence of the function calls to achieve this value.InputThe first line of the input contains an integer t (1 \leq t \leq 70\,000): the number of test cases.Each test case contain two lines. The first line contains two integers h and g (1 \leq g < h \leq 20). The second line contains n = 2^h-1 distinct positive integers a[1], a[2], \ldots, a[n] (1 \leq a[i] < 2^{20}). For all i from 2 to 2^h - 1, a[i] < a[\left \lfloor{\frac{i}{2}}\right \rfloor].The total sum of n is less than 2^{20}.OutputFor each test case, print two lines.The first line should contain one integer denoting the minimum sum after reducing the height of heap to g. The second line should contain 2^h - 2^g integers v_1, v_2, \ldots, v_{2^h-2^g}. In i-th operation f(v_i) should be called.ExampleInput
2
3 2
7 6 3 5 4 2 1
3 2
7 6 5 4 3 2 1
Output
10
3 2 3 1
8
2 1 3 1

2
3 2
7 6 3 5 4 2 1
3 2
7 6 5 4 3 2 1

10 3 2 3 1 8 2 1 3 1 
['constructive algorithms', 'data structures', 'greedy', 'implementation', '*2400']