How and why stock prices move is a centuries-old question still not answered conclusively. More recently, attention shifted to higher frequencies, where trades are processed piecewise across different time scales. Here we reveal that price impact has a universal nonlinear shape for trades aggregated on any intraday scale. Its shape varies little across instruments, but drastically different master curves are obtained for order-volume and -sign impact. The scaling is largely determined by the relevant Hurst exponents. We further show that extreme order-flow imbalance is not associated with large returns. To the contrary, it is observed when the price is pinned to a particular level. Prices move only when there is sufficient balance in the local order flow. In fact, the probability that a trade changes the midprice falls to zero with increasing (absolute) order-sign bias along an arc-shaped curve for all intraday scales. Our findings challenge the widespread assumption of linear aggregate impact. They imply that market dynamics on all intraday time scales are shaped by correlations and bilateral adaptation in the flows of liquidity provision and taking.