# b_binary_incr.py

# b_binary_incr.py

cache = {}
def b_binary_incr(b, incr=1):
    if b in cache:
        return cache[b]

    value = int(b, 2)
    value = (value + incr) % (2 ** len(b))
    result = f"{value:0{len(b)}b}"

    cache[b] = result
    return result

xy = end = '0' * 16
while 1:
    print(xy)
    xy = b_binary_incr(xy)
    if xy == end:
        break