A sequence $A = \{a_1, a_2, a_3, \cdots, a_N\}$ of length $N$ is a finite arithmetic progression with the first term $a$ and common difference $d$.

For a positive integer $M$, find the longest subsequence of $A$ whose sum is $M$.

A subsequence is a sequence obtained by deleting zero or more elements from the given sequence while maintaining the original order.

The first line contains four integers $N$, $a$, $d$, and $M$ separated by spaces. $(1 \leq N, a, d \leq 10^6;$ $1 \leq M \leq 10^{18})$

The first line should output the length $L$ of the longest subsequence of $A$ whose sum is $M$.

The second line should output the $L$ elements of such a subsequence, separated by spaces. If there are multiple possible answers, output any one of them.

If no such subsequence exists, output $-1$ on the first line instead.

Examples

Input 1

5 2 2 10

Output 1

2
4 6

Input 2

3 1 2 7

Output 2

-1

Note

In Example 1, the given sequence is $A = \{2, 4, 6, 8, 10\}$. Excluding the length condition, the possible candidates for $B$ are $\{10\}$, $\{2, 8\}$, and $\{4, 6\}$. Among these, the longest subsequences are $\{2, 8\}$ and $\{4, 6\}$, so either one can be output.