Thoroughly Bureaucratic Organization

Once n people simultaneously signed in to the reception at the recently opened, but already thoroughly bureaucratic organization (abbreviated TBO). As the organization is thoroughly bureaucratic, it can accept and cater for exactly one person per day. As a consequence, each of n people made an appointment on one of the next n days, and no two persons have an appointment on the same day.

However, the organization workers are very irresponsible about their job, so none of the signed in people was told the exact date of the appointment. The only way to know when people should come is to write some requests to TBO.

The request form consists of m empty lines. Into each of these lines the name of a signed in person can be written (it can be left blank as well). Writing a person's name in the same form twice is forbidden, such requests are ignored. TBO responds very quickly to written requests, but the reply format is of very poor quality — that is, the response contains the correct appointment dates for all people from the request form, but the dates are in completely random order. Responds to all requests arrive simultaneously at the end of the day (each response specifies the request that it answers).

Fortunately, you aren't among these n lucky guys. As an observer, you have the following task — given n and m, determine the minimum number of requests to submit to TBO to clearly determine the appointment date for each person.