Race

There is a straight race track of length N.

You need to place M judges on the track. Judges cannot be placed anywhere; they may only be placed at one of K predetermined candidate positions.

Choose the candidate positions so that the distance between the closest pair of placed judges is as large as possible.

The first line contains N, M, and K.

• N is a positive integer not greater than 1,000,000.
• M is a positive integer not greater than K.
• K is between 2 and 50, inclusive.

The second line contains the K candidate positions where judges may be placed, in increasing order. Each position is either 0 or a positive integer not greater than N.

Print one binary string of length K. The i-th character must be 1 if a judge is placed at the i-th candidate position, and 0 otherwise.

If there is more than one placement that maximizes the closest-pair distance, print the lexicographically largest binary string.