B"Drazil 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[ <= ft 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. The first line of the input contains an integer t ( 1 <= q t <= q 70 ,000 ): the number of test cases. Each test case contain two lines. The first line contains two integers h and g ( 1 <= q g < h <= q 20 ). The second line contains n = 2^h-1 distinct positive integers a[1], a[2], ldots, a[n] ( 1 <= q a[i] < 2^{20} ). For all i from 2 to 2^h - 1 , a[i] < a[ <= ft lfloor{ frac{i}{2}} right rfloor] . The total sum of n is less than 2^{20} . For 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. "...