B"Today is Devu's birthday. For celebrating the occasion, he bought n sweets from the nearby market. He has invited his f friends. He would like to distribute the sweets among them. As he is a nice guy and the occasion is great, he doesn't want any friend to be sad, so he would ensure to give at least one sweet to each friend. He wants to celebrate it in a unique style, so he would like to ensure following condition for the distribution of sweets. Assume that he has distributed n sweets to his friends such that ith friend is given ai sweets. He wants to make sure that there should not be any positive integer x xe2 x80 x89> xe2 x80 x891, which divides every ai. Please find the number of ways he can distribute sweets to his friends in the required way. Note that the order of distribution is important, for example [1, 2] and [2, 1] are distinct distributions. As the answer could be very large, output answer modulo 1000000007 (109 xe2 x80 x89+ xe2 x80 x897). To make the problem more interesting, you are given q queries. Each query contains an n, f pair. For each query please output the required number of ways modulo 1000000007 (109 xe2 x80 x89+ xe2 x80 x897). The first line contains an integer q representing the number of queries (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89q xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89105). Each of the next q lines contains two space space-separated integers n, f (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89f xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89105). For each query, output a single integer in a line corresponding to the answer of each query. For first query: n xe2 x80 x89= xe2 x80 x896, xe2 x80 x89f xe2 x80 x89= xe2 x80 x892. Possible partitions are [1, 5] and [5, 1]. For second query: n xe2 x80 x89= xe2 x80 x897, xe2 x80 x89f xe2 x80 x89= xe2 x80 x892. Possible partitions are [1, 6] and [2, 5] and [3, 4] and [4, 3] and [5, 3] and [6, 1]. So in total there are 6 possible ways of partitioning."...