Description:
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 $$${10^9 + 7}$$$.
Input Format:
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 ($$$4 \leq l_i \leq r_i \leq 10^{18}$$$).
Output Format:
For each query, output the answer to the query modulo $$$10^9 + 7$$$.
Note:
The table below contains the values of the functions $$$f$$$($$$x$$$) and $$$g$$$($$$x$$$) for all $$$x$$$ such that $$$1 \leq x \leq 8$$$.
$$$x$$$$$$1$$$$$$2$$$$$$3$$$$$$4$$$$$$5$$$$$$6$$$$$$7$$$$$$8$$$$$$f$$$$$$0$$$$$$1$$$$$$1$$$$$$2$$$$$$2$$$$$$2$$$$$$2$$$$$$3$$$$$$g$$$$$$-$$$$$$-$$$$$$-$$$$$$2$$$$$$2$$$$$$2$$$$$$2$$$$$$1$$$