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

$1 \leq n \leq 10^5$

$1 \leq m \leq 10^{18}$