## USACO 2012 December Contest, Gold

## Problem 1. Gangs of Instanbull/Cowstantinople

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Problem 1: Gangs of Istanbull/Cowstantinople [Mark Gordon, 2012]
Life is tough on the farm, and when life is tough you have to get tough.
The cows have formed gangs (conveniently numbered 1 to M). The gangs
coexisted in peace for a while, but now things are really getting out of
control!
The cows are competing over control of a great grazing field. This
conflict happens over a series of minutes. Each minute a single cow walks
into the field. If the field is empty the new cow's gang is considered to
take control of the field. If the field is already controlled by the new
cow's gang then the cow just starts grazing. Otherwise, a single cow from
the controlling gang that is grazing confronts the new cow.
These confrontations between two cows start with some arguing and
inevitably end up with the pair coming to realize how much more more alike
than different they are. The cows, seeing the error in their ways, leave
the gang and the field and get a cold glass of soy milk at FJ's tavern. If
after this confrontation the field is empty than no gang controls the field.
Bessie realizes how these confrontations will occur. She knows how many
cows are in each gang. Bessie really wants her gang to control the field
after the conflict is over and all cows are either on the field or at FJ's
tavern. Help Bessie determine if it is possible for her gang, labeled 1,
to control the field in the end.
If it is possible, Bessie wants to know the maximum number of cows from her
gang that could be on the field at the end. Output this number and the
lexicographically earliest ordering of cows that results in this number of
cows from Bessie's gang at the end. An ordering X is said to be
lexicographically earlier than Y if there is some k such that X[k] < Y[k] and
X[i] = Y[i] for i < k.
PROBLEM NAME: gangs
INPUT FORMAT:
* Line 1: N (1 <= N <= 100) and M (1 <= M <= N) separated by a space.
The total number of cows in all the gangs will be N. The
total number of gangs is M.
* Lines 2..1+M: The (1+i)th line indicates how many members are in
gang i. Each gang has at least 1 member.
SAMPLE INPUT (file gangs.in):
5 3
2
1
2
INPUT DETAILS:
There are 5 cows and 3 gangs. Bessie's gang (gang 1) has 2 members, gang 2
has 1 member, and gang 3 has 2 members.
OUTPUT FORMAT:
* Line 1: Output YES on a single line if Bessie's gang can control the
field after the conflict. Otherwise output NO on a single
line.
* Line 2: If Bessie's gang can control the field after the conflict
output the maximum number of cows that could be on the field
on a single line.
* Lines 3..2+N: On the (i+2)th line output the index of the gang of
the cow that appears in the ith minute in the
lexicographically earliest ordering that leaves the maximum
number of cows on the field after the conflict.
SAMPLE OUTPUT (file gangs.out):
YES
1
1
3
2
3
1
OUTPUT DETAILS:
Only one cow from Bessie's gang can end up on the field.

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