next =: {{%/-:+/2 x:max,y}}
start =: 2r5
max =: 3r7

solve =: {{
	lowBound =. 0
	highBound =. y
	guess =. 0
	whilst. guess ~: lastGuess do.
		lastGuess =. guess
		guess =. <. -: lowBound+highBound
		'num denum' =. 2 x: next^:guess start
		if. denum > y do.
			highBound =. guess
		elseif. denum < y do.
			lowBound =. guess
		end.
	end.
	num
}}

problem71 =: solve 1e6