Is the vow fast to be consecutive or separate if it is for a full month without specification?

If one vows to fast for a month, then either the month is specified, such as "Rajab" or "Sha'ban," or they say: "I vow to fast for a month starting now." In these two cases, consecutive fasting is required. However, if they vow for an unspecified month, there are two opinions: The first requires consecutive fasting (the Hanbali madhhab), and the second does not require it except by intention (the madhhab of the majority). According to the madhhab of the majority, if one chooses to fast non-consecutively, they must fast thirty days. If they choose to fast consecutively and begin fasting at the beginning of the crescent month, they fast until its end, even if it is twenty-nine days. If they begin during the month, they must fast thirty days.