8198번 - Frog 다국어

On the bed of one particularly long and straight Byteotian brook there lie n rocks jutting above the water level. Their distances from the brook's spring are p₁ < p₂ < … < p_n 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 k-th closest to the one it is sitting on. Specifically, if the frog is sitting on the rock at position pi, then it will leap onto such pj that:

|{p_a : |p_a-p_i| < |p_j-p_i|}| ≤ k and |{p_a : |p_a-p_i| ≤ |p_j-p_i|}| > k.

If pj 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 m leaps depending on the rock is started from?

The first line of the standard input holds three integers, n, k and m (1 ≤ k < n ≤ 1,000,000, 1 ≤ m ≤ 10¹⁸), separated by single spaces, that denote respectively: the number of rocks, the parameter k, and the number of intended leaps. The second line holds n integers p_j (1 ≤ p₁ < p₂ < … < p_n ≤ 10¹⁸), separated by single spaces, that denote the positions of successive rocks on the bed of the brook.

Your program should print a single line on the standard output, with n integers r₁, r₂, …, r_n from the interval [1,n] in it, separated by single spaces. The number ri denotes the number of the rock that the frog ends on after making m leaps starting from the rock no. i (in the input order).

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