You are given an undirected graph with $n$ nodes and $m$ edges. The graph is simple and connected.
You start at a specific node, and on each turn
you must move through an edge to another node.
Your task is to answer $q$ queries of the form: "is it possible to start at node $a$ and end up on node $b$ after exactly $x$ turns?"
The first line contains three integers $n$ , $m$ and $q$ :
the number of nodes, edges and queries. The nodes are numbered $1,2,\dots,n$ .
After this, there are $m$ lines which describe the edges. Each line contains two integers $a$ and $b$ : there is an edge between nodes $a$ and $b$ .
Finally, there are $q$ lines, each describing a query.
Each line contains three integers $a$ , $b$ and $x$ .
For each query, print the answer ( YES or NO ) on its own line.
4 5 6 1 2 2 3 1 3 2 4 3 4 1 2 2 1 4 1 1 4 5 2 2 1 2 2 2 3 4 8· · \n · \n · \n · \n · \n · \n · · \n · · \n · · \n · · \n · · \n · · \n
YES NO YES NO YES YES\n \n \n \n \n \n