CF479D Long Jumps

Valery is a PE teacher at a school in Berland. Soon the students are going to take a test in long jumps, and Valery has lost his favorite ruler! However, there is no reason for disappointment, as Valery has found another ruler, its length is $ l $ centimeters. The ruler already has $ n $ marks, with which he can make measurements. We assume that the marks are numbered from 1 to $ n $ in the order they appear from the beginning of the ruler to its end. The first point coincides with the beginning of the ruler and represents the origin. The last mark coincides with the end of the ruler, at distance $ l $ from the origin. This ruler can be repesented by an increasing sequence $ a_{1},a_{2},...,a_{n} $ , where $ a_{i} $ denotes the distance of the $ i $ -th mark from the origin ( $ a_{1}=0 $ , $ a_{n}=l $ ). Valery believes that with a ruler he can measure the distance of $ d $ centimeters, if there is a pair of integers $ i $ and $ j $ ( $ 1

The first line contains four positive space-separated integers $n, l, x, y (2 ≤ n ≤ 10^5, 2 ≤ l ≤ 10^9, 1 ≤ x 

In the first line print a single non-negative integer $v$ — the minimum number of marks that you need to add on the ruler. In the second line print v space-separated integers $p_1, p_2,\dots, p_v (0 ≤ p_i ≤ l)$. Number $p_i$ means that the $i$-th mark should be at the distance of $p_i$ centimeters from the origin. Print the marks in any order. If there are multiple solutions, print any of them.

In the first sample it is impossible to initially measure the distance of $ 230 $ centimeters. For that it is enough to add a $ 20 $ centimeter mark or a $ 230 $ centimeter mark. In the second sample you already can use the ruler to measure the distances of $ 185 $ and $ 230 $ centimeters, so you don't have to add new marks. In the third sample the ruler only contains the initial and the final marks. We will need to add two marks to be able to test the children's skills.