Frog

Memory limit: 128 MB

On the bed of one particularly long and straight Byteotian brook there lie rocks jutting above the water level. Their distances from the brook's spring are respectively. A small frog sitting on one of these is about to begin its leaping training. Each time the frog leaps to the rock that is the -th closest to the one it is sitting on. Specifically, if the frog is sitting on the rock at position , then it will leap onto such that:

and

If is not unique, then the frog chooses among them the rock that is closest to the spring. On which rock the frog will be sitting after leaps depending on the rock is started from?

Input

The first line of the standard input holds three integers, , and (, ), separated by single spaces, that denote respectively: the number of rocks, the parameter , and the number of intended leaps. The second line holds integers (), separated by single spaces, that denote the positions of successive rocks on the bed of the brook.

Output

Your program should print a single line on the standard output, with integers from the interval in it, separated by single spaces. The number denotes the number of the rock that the frog ends on after making leaps starting from the rock no. (in the input order).

Example

For the input data:

5 2 4
1 2 4 7 10

the correct result is:

1 1 3 1 1

The figure presents where the frog leaps to (in a single leap) from each and every rock.

Task author: Jakub Radoszewski.