CF959E.Mahmoud and Ehab and the xor-MST

Ehab is interested in the bitwise-xor operation and the special graphs. Mahmoud gave him a problem that combines both. He has a complete graph consisting of n vertices numbered from 0 to n - 1. For all 0 ≤ u < v < n, vertex u and vertex v are connected with an undirected edge that has weight (where is the bitwise-xor operation). Can you find the weight of the minimum spanning tree of that graph?

You can read about complete graphs in https://en.wikipedia.org/wiki/Complete_graph

You can read about the minimum spanning tree in https://en.wikipedia.org/wiki/Minimum_spanning_tree

The weight of the minimum spanning tree is the sum of the weights on the edges included in it.

Ehab 对位运算异或（XOR）操作和特殊图很感兴趣。Mahmoud 给了他一道融合了这两者的题目。他有一个由 $n$ 个顶点构成的完全图，顶点编号为 $0$ 到 $n-1$。对所有满足 $0 \le u < v < n$ 的顶点对 $(u, v)$，顶点 $u$ 与顶点 $v$ 之间均存在一条无向边，其边权为 （其中 表示按位异或运算）。你能求出该图的最小生成树（MST）的总权重吗？

你可参阅关于完全图的介绍：https://en.wikipedia.org/wiki/Complete_graph

你可参阅关于最小生成树的介绍：https://en.wikipedia.org/wiki/Minimum_spanning_tree

最小生成树的权重即为其所包含的所有边的权重之和。

The only line contains an integer n (2 ≤ n ≤ 1012), the number of vertices in the graph.

唯一一行包含一个整数 $n$（$2 \leq n \leq 10^{12}$），表示图中顶点的数量。

The only line contains an integer x, the weight of the graph's minimum spanning tree.

唯一的一行包含一个整数 $x$，即该图的最小生成树的权重。

In the first sample: The weight of the minimum spanning tree is 1+2+1=4.

在第一个样例中： 最小生成树的权重为 $1+2+1=4$。