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  if the latest accepted submission was submitted in the th minute, or  if no problem was solved.

    For example, if team A solved their first problem in the th minute, their second problem in the th minute and their third problem in the th minute, then their time penalty is . If team B also solved three problems, in the th, th and th minute, their time penalty is  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.

输入描述:

The input consists of:
- One line containing two integers:  (), the number of teams participating, and  (), the number of contest problems.
-  lines with on line  the time score  in minutes () of the team that is ranked in the th place.
A positive time score of  indicates that a team has submitted their last accepted submission in the th minute. A time score of  indicates that a team hasn't solved any problem.
The input always originates from a valid scoreboard.

输出描述:

If it is possible to uniquely reconstruct the scores of all the teams, output  lines containing the number of problems that the th team has solved on the th line. Otherwise, output "ambiguous".

9 3
140
75
101
120
30
70
200
0
0

3
2
2
2
1
1
1
0
0

6 3
100
40
40
50
0
0

ambiguous