# Problem 508: Integers in base i-1
Consider the Gaussian integer i-1. A base i-1 representation of a
Gaussian integer a+bi is a finite sequence of digits dn-1dn-2...d1d0
such that: a+bi = dn-1(i-1)n-1 + dn-2(i-1)n-2 + ... + d1(i-1) + d0 Each
dk is in {0,1} There are no leading zeroes, i.e. dn-1 ≠ 0, unless a+bi
is itself 0 Here are base i-1 representations of a few Gaussian
integers: 11+24i → 111010110001101 24-11i → 110010110011 8+0i →
111000000 -5+0i → 11001101 0+0i → 0 Remarkably, every Gaussian integer
has a unique base i-1 representation! Define f(a+bi) as the number of 1s
in the unique base i-1 representation of a+bi. For example, f(11+24i) =
9 and f(24-11i) = 7. Define B(L) as the sum of f(a+bi) for all integers
a, b such that |a| ≤ L and |b| ≤ L. For example, B(500) = 10795060. Find
B(1015) mod 1 000 000 007.