After an excellent family breakfast with cheese bread, Beto was put in charge of washing the dishes. After soaping everything, Beto remembered how annoying it is to put the cups in his home's linear dish rack, especially the work needed to place a cup between two others that are already drying. He estimated that the effort to place a cup in a given position of the dish rack is equal to the sum of the number of consecutive cups immediately to the left and the number of consecutive cups immediately to the right of that position at the time of placement.
In the figure above, we have the final state of a solution for Example $$$1$$$ – $$$4$$$ cups in a dish rack with $$$6$$$ positions.
Given the size $$$N$$$ of the dish rack and the number $$$C$$$ of cups, compute the minimum total effort Beto must spend to place all cups in the dish rack and provide an insertion sequence that achieves this minimum effort. The dish rack positions are numbered from $$$1$$$ to $$$N$$$, and each cup must be placed in an empty position. If there is more than one way to achieve the minimum effort, print any of them.
The only line of input contains two integers $$$N$$$ ($$$2 \leq N \leq 10^{6}$$$) and $$$C$$$ ($$$1 \leq C \leq N$$$), the size of the dish rack and the number of cups, respectively.
The first line of the output should contain a single integer, the minimum total effort Beto must spend to place all cups in the dish rack.
The second line of the output should contain $$$C$$$ integers separated by spaces, where the $$$i$$$-th integer represents the dish rack position where the $$$i$$$-th cup should be placed.
6 4
1 3 4 1 6
7 5
2 1 2 4 6 7
15 14
20 1 3 2 5 7 6 4 9 11 10 13 15 14 12
Explanation for example 2
One way to place the cups is $$$[\mathtt{1\ 2\ -\ 3\ -\ 4\ 5}]$$$. Cups 1, 3, and 4 have placement cost 0, while cups 2 and 5 have cost 1, for a total effort of 2.
