You are given a rooted tree with \(n\) vertices (the root is vertex \(1\)). The beautifulness of a tree sum of each vertex's subtree size.

You have lost the tree but you know \(n\) and the beautifulness of the tree is \(m\). Can you construct a rooted tree with \(n\) vertices (the root is vertex \(1\)) and beautifulness \(m\)?

In a rooted tree, a subtree of vertex \(v\) is all vertices like \(u\) that the path from \(u\) to root includes \(v\).

Input format

The first line contains two integers \(n\) and \(m\) denoting the number of the tree's vertices and their beautifulness.

Output format

If there is no tree with \(n\) vertices and \(m\) beautifulness, print \(-1\). Otherwise, print \(n-1\) lines where each contains edges of the constructed tree.

Constraints

\(1 \leq n \leq 10^5\)

\(1 \leq m \leq 10^{18} \)