BAPC20-051.\problemyamlname

You are organizing a programming competition in which the rank of a team is first determined by how many problems they have solved. In case of a tie, the team with the lowest time penalty is ranked above the other. However, contrary to the BAPC, the time penalty is equal to $t$ if the latest accepted submission was submitted in the $t$th minute, or $0$ if no problem was solved.

For example, if team A solved their first problem in the $5$th minute, their second problem in the $10$th minute and their third problem in the $60$th minute, then their time penalty is $60$. If team B also solved three problems, in the $30$th, $40$th and $50$th minute, their time penalty is $50$ and they would rank above team A.

The contest has finished and you would like to enter the final standings. However, due to a corrupted file you have lost part of the scoreboard. In particular, the column indicating how many problems each team has solved is gone. You do still have the time penalties of all the teams and know that they are in the right order. You also remember how many problems the contest had. You wonder whether, given this information, it is possible to uniquely reconstruct the number of problems that each team has solved.