On the numerical axis, in the interval from
L to
R, Vasily drew
N vertical sticks. After thinking, Vasily decided that he needed an empty gap on the number axis with a width of at least
W.
Help Vasily determine what is the minimum number of sticks that Vasily needs to erase and which ones.
After Vasily erases a certain number of sticks, there should be a gap with a width greater than or equal to
W. The gap can be between the two remaining sticks, or between the remaining stick and the end of the number line gap, or between the two ends of the number line gap.
Input
The first line contains two integers
N and
W — the number of drawn sticks and the minimum required gap width, respectively. It is guaranteed that 0 <= N<= 1 000 000 and 0 <= W <= 1 000 000.
The second line contains two numbers
L and
R — coordinates of the left and right ends of the span of the numerical axis (L <=<R). The third line contains
N numbers — coordinates of the drawn sticks. All coordinates (including
L and
R) — various integers, modulo not exceeding 1 000 000. It is guaranteed that all sticks are drawn between the left and right ends of the side.
Imprint
In the first line print the minimum number of sticks Vasily needs to erase. The numbers of these sticks should follow in the second line. The sticks are numbered in the order they are specified in the input, starting from 1.
If there are several solutions, then you can print any. If there is no solution, then print a single line containing the number - 1.
Examples
| # |
Input |
Output |
| 1 |
3 2
26
3 4 5
|
1
1
|
| 2 |
3 2
16
4 3 5
|
0
|
| 3 |
3 5
17
5 3 4
|
3
2
3
1
|