B"You are given an initially empty undirected graph with n nodes, numbered from 1 to n (i. e. n nodes and 0 edges). You want to add m edges to the graph, so the graph won't contain any self-loop or multiple edges. If an edge connecting two nodes u and v is added, its weight must be equal to the greatest common divisor of u and v , i. e. gcd(u, v) . In order to add edges to the graph, you can repeat the following process any number of times (possibly zero): For example, if you can add 5 more edges to the graph of weight 6 , you may add them, and it will cost 6 for the whole pack of 5 edges. But if you can only add 4 edges of weight 6 to the graph, you can't perform this operation for k = 5 . Given two integers n and m , find the minimum total cost to form a graph of n vertices and exactly m edges using the operation above. If such a graph can't be constructed, output -1 . Note that the final graph may consist of several connected components. Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= q t <= q 10^4 ). Description of the test cases follows. The first line of each test case contains two integers n and m ( 2 <= q n <= q 10^6 ; 1 <= q m <= q frac{n(n-1)}{2} ). It is guaranteed that the sum of n over all test cases does not exceed 10^6 . For each test case, print the minimum cost to build the graph, or -1 if you can't build such a graph. In the first test case, we can add an edge between the vertices 2 and 4 with gcd = 2 . This is the only possible way to add 1 edge that will cost 2 . In the second test case, there is no way to add 10 edges, so the answer is -1 . In the third test case, we can add the following edges: "...