Valera had an undirected connected graph without self-loops and multiple edges consisting of $*n*$ vertices. The graph had an interesting property: there were at most $*k*$ edges adjacent to each of its vertices. For convenience, we will assume that the graph vertices were indexed by integers from 1 to $*n*$.

One day Valera counted the shortest distances from one of the graph vertices to all other ones and wrote them out in array $*d*$. Thus, element $*d*[*i*]$ of the array shows the shortest distance from the vertex Valera chose to vertex number $*i*$.

Then something irreparable terrible happened. Valera lost the initial graph. However, he still has the array $*d*$. Help him restore the lost graph.

Input

The first line contains two space-separated integers $*n*$ and $*k*$ $(1 ≤ *k* < *n* ≤ 10^{5})$. Number $*n*$ shows the number of vertices in the original graph. Number $*k*$ shows that at most $*k*$ edges were adjacent to each vertex in the original graph.

The second line contains space-separated integers $*d*[1], *d*[2], ..., *d*[*n*]$ $(0 ≤ *d*[*i*] < *n*)$. Number $*d*[*i*]$ shows the shortest distance from the vertex Valera chose to the vertex number $*i*$.

Output

If Valera made a mistake in his notes and the required graph doesn't exist, print in the first line number -1. Otherwise, in the first line print integer $*m*$ $(0 ≤ *m* ≤ 10^{6})$ — the number of edges in the found graph.

In each of the next $*m*$ lines print two space-separated integers $*a*_{*i*}$ and $*b*_{*i*}$ $(1 ≤ *a*_{*i*}, *b*_{*i*} ≤ *n*; *a*_{*i*} ≠ *b*_{*i*})$, denoting the edge that connects vertices with numbers $*a*_{*i*}$ and $*b*_{*i*}$. The graph shouldn't contain self-loops and multiple edges. If there are multiple possible answers, print any of them.