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solve =: monad define
	ns =. p:i._1 p: y
	for_length. |.I.y>+/\ns do.
		sums =. length+/\ns
		vals =. sums#~(y>sums)*.1 p: sums
		if. 0<#vals do.
			return. >./vals
		end.
	end.
)

problem50 =: solve 1e6