Josh lives on a street with ~N~ houses conveniently numbered from ~1~ to ~N~ from left to right, where Josh lives at house number ~S~. Nils doesn't know what ~S~ is, but Josh tells him that he'll be going for a walk.

Starting from his house ~S~, he will repeatedly travel along the street to adjacent houses, never going to the left of house ~1~ or to the right of house ~N~. His walk ends back at his house ~S~, though he can pass by his house multiple times during the walk. Let ~p~ be the list of house numbers that Josh visited on his walk, in order.

Nils also knows that Josh never visits more than ~K~ consecutive houses in a row. More formally, if ~a~ is a monotonic subarray of ~p~, then ~|a| \le K~. Note that an array is monotonic if the elements are either all strictly increasing or all strictly decreasing.

After going on his walk, he constructs an array ~f~, where ~f_i~ is the number of times he visited house number ~i~ during his walk.

Confident that his address is hidden, Josh gives Nils ~f~. Using this array, can you help Nils determine Josh's possible house numbers, or determine that the array is inconsistent?

Constraints

~3 \le N \le 10^6~

~3 \le K \le N~

~1 \le f_i \le 10^9~

Subtask 1 [20%]

~N \le 3 \times 10^3~

~K = N~

Subtask 2 [20%]

~K = N~

Subtask 3 [30%]

~N \le 3 \times 10^3~

Subtask 4 [30%]

No additional constraints.

Input Specification

The first line contains two integers ~N~ and ~K~.

The next line contains ~N~ integers ~f_1, \ldots, f_N~.

Output Specification

First output a line containing an integer ~X~, the number of possible house numbers ~S~.

If ~X \ge 1~, output ~X~ distinct integers, the possible house numbers on the next line in ascending order.

Sample Input 1

4 4
1 3 3 2

Sample Output 1

2
2 4

Explanation for Sample 1

A possible walk Josh could have taken is ~p=[2,1,2,3,4,3,4,3,2]~, which starts and ends at house ~2~. In this walk, the longest monotonic subarray is ~[1,2,3,4]~, which has a length of ~4~.

Another possible walk Josh could have taken is ~p=[4,3,2,1,2,3,2,3,4]~, which starts and ends at house ~4~.

Sample Input 2

5 3
2 2 2 2 1

Sample Output 2

0

Explanation for Sample 2

There are no possible paths that satisfy the given constraints. Even though ~p=[1,2,3,4,5,4,3,2,1]~ is a path that starts and ends at house ~1~, it does not satisfy the constraints since the monotonic subarray ~[1,2,3,4,5]~ has a length greater than ~K~.