B"Let's define a function f(p) on a permutation p as follows. Let g_i be the greatest common divisor (GCD) of elements p_1 , p_2 , ..., p_i (in other words, it is the GCD of the prefix of length i ). Then f(p) is the number of distinct elements among g_1 , g_2 , ..., g_n . Let f_{max}(n) be the maximum value of f(p) among all permutations p of integers 1 , 2 , ..., n . Given an integers n , count the number of permutations p of integers 1 , 2 , ..., n , such that f(p) is equal to f_{max}(n) . Since the answer may be large, print the remainder of its division by 1000 ,000 ,007 = 10^9 + 7 . The only line contains the integer n ( 2 <= n <= 10^6 ) -- the length of the permutations. The only line should contain your answer modulo 10^9+7 . Consider the second example: these are the permutations of length 3 : The maximum value f_{max}(3) = 2 , and there are 4 permutations p such that f(p)=2 . "...