def patch(state,p):
    for k in p.keys():
        if p[k] is None:
            del state[k]
        elif k in state and isinstance(state[k], dict) and isinstance(p[k], dict):
            patch(state[k], p[k])
        else:
            state[k] = p[k]

def diff(state, newstate):
    d = {}

    for k in state.keys():
        if not k in newstate:
            d[k] = None
    
    for k in newstate.keys():
        if k in state:
            if isinstance(state[k], dict) and isinstance(newstate[k], dict):
                dc = diff(state[k], newstate[k])
                if dc: 
                    d[k] = dc
            elif state[k] != newstate[k]:
                d[k] = newstate[k]
        else:
            d[k] = newstate[k]

    return d