You are given two numbers $N$ and $M$. Your task is to print an array $A$ such that:

• $A_{i}$  is in the range $[L : R]$
• $A$ is sorted in increasing order
• $N \ \% \ A_{i}$ = $N\ \%\ M$
• $A_{i}$ $!= M$

The array can be of a large size. Therefore, if the array size is strictly more than $K$, then you must skip the task and print $-1$.

Input format

• First line: $N$ and $M$
• Second line: $L$ and $R$
• Third line: $K$

Output format

The format of the output is as follows:

• First line: Print the length of the required array.
• Second line: Print $N$ integers that denote the required array or print $-1$ if the required array length is more than $K$.

Constraints

$1\le N,\ M\le 10^{12}\\ 1\le L,\ R\le 10^{12},\ L<=R\\  0\le K\le 10^5$