Trade

Trading is a subtle business. A successful merchant should not only know how to timely sell the right goods and attract customers, but also thoroughly understand the situation in the market. Among other things, it's important to know which merchants trade with each other and which do not. Sometimes, merchants do not trade directly, but their goods can still reach each other through other merchants. For example, if merchants A and B trade directly, and merchants B and C also trade directly, then goods from A and C can reach each other through merchant B. Another important concept is that of inseparable pairs—these are pairs of merchants who trade directly, and for whom no sequence of intermediate merchants exists through whom they could trade indirectly.

Mano wants to become a successful merchant. We do not know which necessary qualities he possesses, but he certainly lacks knowledge about the market situation. All he knows is that there are $N$ merchants in the market, $M$ pairs that trade directly, and $K$ of them are inseparable pairs. What he needs is more concrete information, such as "A trades with B, C trades with D, X trades with A". Of course, this is not always unique, but any arrangement matching this information will suffice for him.

You are given $T$ scenarios, each with their own values of $N$, $M$, and $K$. For each one, determine whether such a trade network exists and, if it does, present its description. Merchants are numbered from $1$ to $N$ in any order, and the description of the trade network is the set of all different pairs of merchants who trade directly.