Archery hunter describes possible stalking incident outside the town of Headquarters witnessed in Clearwater County, Idaho

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I was archery hunting in Idaho not far from Headquarters Idaho, actually between Township Saddle and Township butte, when I encountered something that I have never experienced before in the mountains. I heard something heavy running ahead of me to my left as I was walking up on old railroad grade that has been used by 4-wheelers. My first impression was it may have been an elk, but I didn't see what was making the sound. I had walked about 1/4 mile from my partner and was closing in on an area where we had seen elk earlier in the week and thought I would try to push ahead to get into the area I had seen the elk. I was walking very quietly when I heard a sound that I thought was a bird flying overhead. I looked up since the sound came from in front of me, when I heard something hit a tree and then the ground behind me. As I turned around, I noticed a branch on a small tree behind me that was moving as if something had hit it. Before I could walk back to the tree which was only about...