def binary_search(i, vals):
        """Finds index of item i in list vals, assuming vals is in increasing order.
           Returns index of item if found, -1 if not found."""
        hi = len(vals)-1
        if(hi < 0): #empty list
                return -1
        if(i == vals[0]): #list with one item
                return 0  #or coincidentally first item
        lo = 0
        mid = (hi+lo)//2
        hi = hi+1 #keeps while loop from terminating before last index
        while(hi != mid and mid != lo):
                if(i == vals[mid]): #found it
                        return mid
                elif(i < vals[mid]): #i in lower half
                        hi = mid
                        mid = (hi+lo)//2
                else: #i in upper half
                        lo = mid
                        mid = round((hi+lo)/2+.1)
                        #Python sometimes rounds .5 down
                        #add .1 so it always rounds up
                        #otherwise end of list may not be reached
        return -1