Let (f)((x)) be the floor of the binary logarithm of (x). In other words, (f)((x)) is largest non-negative integer (y), such that (2^y) does not exceed (x). Let (g)((x)) be the floor of the logarithm of (x) with base (f)((x)). In other words, (g)((x)) is the largest non-negative integer (z), such that ({f(x)}^{z}) does not exceed (x). You are given (q) queries. The (i)-th query consists of two integers (l_i) and (r_i). The answer to the query is the sum of (g)((k)) across all integers (k), such that (l_i \leq k \leq r_i). Since the answers might be large, print them modulo ({10^9 + 7}). The first line contains a single integer (q) — the number of queries ((1 \leq q \leq 10^5)). The next (q) lines each contain two integers (l_i) and (r_i) — the bounds of the (i)-th query ((4 \leq l_i \leq r_i \leq 10^{18})). For each query, output the answer to the query modulo (10^9 + 7). The table below contains the values of the functions (f)((x)) and (g)((x)) for all (x) such that (1 \leq x \leq 8).