Did Abram give tithe to Melchizedek? Or did Melchizedek give the tithe to Abram?

Tithes Paid to Whom?

Here is the context of this question, taken from the war of the kings which Abram fought to rescue his nephew Lot who was captured, Genesis 14.

1. Who was Melchizedek? He was king of Shalem (vs 17). Was Shalem a place? Or was he King of Shalom (Peace) as some commentators say? Was this Yerushalyim (Jerusalem)? The name Melchizedek means righteous king (in Hebrew). He was priest of El Elyon, Most High God. (vs 18) He brought out bread and wine. Even in modern times this is seen as the act of a priest.
2. The context does not fully indicate who gave tithe to whom, but there are points to be considered. Melchizedek gave Abram a blessing, this is the job of a priest. But priests do not pay tithe to others according to the Torah. If Abram saw him as priest of Elyon, then it would be Abram’s place to pay tithe to him and not the other way around.
3. The spoils from the war were taken and brought back by Abram (vs) 16. It appears that it was from these spoils that the tithe was taken. Melchizedek would not claim the acquisition of the spoils because he did not take part in the war (he is not mentioned). He came to bless Abram. Could he have been the last survivor of the flood? Shem? Many Torah Students think so. This is not given in the Torah. The only thing we can speculate is that Noah was the only righteous man (Zadek) living at the time of the flood, and from him, the righteous lineage was through Shem. Logically, the person gave the tithe of the spoils would have been Abram, for he had collected them. It does not make sense for Melchizedek to come and give what he has no control of to the one who possessed them, because he was not the one who had taken them.
4. Another point is that after the tithe was given, the king of Sodom (vs 21) said to Abram “give me the persons and take the goods to yourself.” But Abram refused, saying that he had sworn an oath to YHVH El Elyon, that he would take nothing, not even a shoe latchet, nor anything that belonged to the kings, “lest thou shouldst say, I have made Abram rich…” (vs 23-24), “except only what the young men have eaten and the share of the young men who went with me….”Abram did not receive anything and refused even the gifts offered to him by the king of Sodom. Nevertheless, he insisted on tithing the goods that were in his possession.
   Again, it would make no sense to have Melchizedek arrive on the scene to divide up the spoils and give Abram a tithe, since the spoils really belonged to Abram.
5. This is the first instance in the Bible of giving tithe. It shows that Abram had a sense of Torah, by giving Tithe to the priest of the time.