def binary_search(i, vals):
#Returns the index of i in vals, or -1 if does not appear    
    return divide(i, vals, 0, len(vals) - 1)
 
def divide(i, vals, lower, upper):
# Helper to binary_search; divides-and-conquers.
    midpt = (int) ((upper - lower) / 2) + lower
    if vals[midpt] == i:
        return midpt
    if lower == upper:
        return -1
    if vals[midpt] > i:
        return divide(i, vals, lower, midpt)
    return divide(i, vals, midpt + 1, upper)