Sounds and Silences

In the digital recording of sound, sound is described by a sequence of ~N~ integers representing measurements at regular time intervals. Each value in the sequence is called a sample.

In many audio processing applications, we are interested in silences. Silences are intervals of samples of size ~M~ where the difference between the minimum and maximum value does not exceed a threshold value ~C~.

Problem:

Develop a program in one of the IOI languages which, after reading the values of ~N~, ~M~, and ~C~, as well as the integers corresponding to the digital recording of a sound, identifies the silences.

Input Files:

The input files named sound.in are text files with the following structure: The first line contains three integers ~N\;(1 \le N \le 1.000.000)~, ~M\;(1 \le M \le 10.000)~, and ~C\;(0 \le C \le 10.000)~, separated in pairs by a single space. The second line contains sequentially the ~N~ integers ~a[1]~, ~a[2]~, ~...~, ~a[N]~, corresponding to the samples of the digital sound recording, separated in pairs by a single space. These integers will be between ~0~ and ~1.000.000~.

Output Files:

The output files named sound.out are text files with the following structure: Each line contains one value of ~i~ such that

$$\displaystyle max \Big\{ a[i], \ldots \;a[i+M-1] \Big\} - min \Big\{a[i], \ldots \;a[i+M-1]\Big\} \le C$$

The values of ~i~ should appear in ascending order.
Note: We assume that the numbering of samples starts from ~1~ (i.e., the first sample is ~a[1]~ and the last sample is ~a[N]~).

If there is no such value of ~i~, the output file should contain only one line with the word "~NULL~".

Example of Input - Output Files:

STDIN (sound.in)

7 2 0
0 1 1 2 3 2 2

STDOUT (sound.out)

2
6

Explanation of the Example:

In this example of ~N = 7~ samples, a silence is a sequence of ~M = 2~ samples where the difference between their minimum and maximum value does not exceed ~C = 0~ (meaning silences are pairs of samples with the same value). There are two silences: ~1~, ~1~ (starting from position ~a[2]~) and ~2~, ~2~ (starting from position ~a[6]~).

Formatting: In the output, each line terminates with a newline character.
Maximum execution time: 1 sec.
Maximum available memory: 64 MB.