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

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