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Training to prepare for oxygen deficiency in the high mountains

My girlfriend and I are looking to do a portion of the Annapurna pass (Jomsom trek). She has climbed Kilimanjaro (not without difficulty) 3 years ago and I am a beginner with basic hiking experience in Himalayas. My question is what are some good gym exercises to prepare for a 8 day trek in Himalayas? We go a max height of 5000m at thorung la pass. Are there exercises specifically to train you for lack of oxygen? Or does any aerobic exercise(running,biking,swimming) count?