Dat Bae

A research consortium has built a new database system for their new data center. The database is made up of one master computer and N worker computers, which are given IDs from 0 to N-1. Each worker stores exactly one bit of information... which seems rather wasteful, but this is very important data!

You have been hired to evaluate the following instruction for the database:

• TEST_STORE <bits>: The master reads in <bits>, which is a string of N bits, and sends the i-th bit to the i-th worker for storage. The master will then read the bits back from the workers and return them to the user, in the same order in which they were read in.

During normal operation, TEST_STORE should return the same string of bits that it read in, but unfortunately, B of the workers are broken!

The broken workers are correctly able to store the bits given to them, but whenever the master tries to read from a broken worker, no bit is returned. This causes the TEST_STORE operation to return only N-B bits, which are the bits stored on the non-broken workers (in ascending order of their IDs). For example, suppose N = 5 and the 0th and 3rd workers are broken (so B = 2). Then:

• TEST_STORE 01101 returns 111.
• TEST_STORE 00110 returns 010.
• TEST_STORE 01010 returns 100.
• TEST_STORE 11010 also returns 100.

For security reasons, the database is hidden in an underground mountain vault, so calls to TEST_STORE take a very long time. You have been tasked with working out which workers are broken using at most F calls to TEST_STORE.

• 1 ≤ T ≤ 100.
• 2 ≤ N ≤ 1024.
• 1 ≤ B ≤ min(15, N-1).