A DNA sequence consists of four letters, A, C, G, and T. The GC-ratio of a DNA sequence is the number of
Cs and Gs of the sequence divided by the length of the sequence. GC-ratio is important in gene finding
because DNA sequences with relatively high GC-ratios might be good candidates for the starting parts of
genes. Given a very long DNA sequence, researchers are usually interested in locating a subsequence whose
GC-ratio is maximum over all subsequences of the sequence. Since short subsequences with high GC-ratios
are sometimes meaningless in gene finding, a length lower bound is given to ensure that a long subsequence
with high GC-ratio could be found. If, in a DNA sequence, a 0 is assigned to every A and T and a 1 to every C
and G, the DNA sequence is transformed into a binary sequence of the same length. GC-ratios in the DNA
sequence are now equivalent to averages in the binary sequence.

For the binary sequence above, if the length lower bound is 7, the maximum average is 6/8 which happens in
the subsequence [7,14]. Its length is 8, which is greater than the length lower bound 7. If the length lower
bound is 5, then the subsequence [7,11] gives the maximum average 4/5. The length is 5 which is equal to the
length lower bound. For the subsequence [7,11], 7 is its starting index and 11 is its ending index.

Given a binary sequence and a length lower bound L, write a program to find a subsequence of the binary
sequence whose length is at least L and whose average is maximum over all subsequences of the binary
sequence. If two or more subsequences have the maximum average, then find the shortest one; and if two or
more shortest subsequences with the maximum average exist, then find the one with the smallest starting
index.