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Generating exploitable heap layouts is a fundamental step to produce working exploits for heap overflows. For this purpose, the heap primitives identified from the target program, serving as functional units to manipulate the heap layout, are strategically leveraged to construct exploitable states. To flexibly use primitives, prior efforts only focus on particular program types or programs with dispatcher-loop structures. Beyond that, automatically generating exploitable heap layouts is hard for general-purpose programs due to the difficulties in explicitly and flexibly using primitives. This paper presents Scatter, enabling the generation of exploitable heap layouts for heap overflows in general-purpose programs in a primitive-free manner. At the center of Scatter is a fuzzer that is guided by a new manipulation distance which measures the distance to the corruption of a victim object in the heap layout space. To make the fuzzing-based approach practical, Scatter leverages a set of techniques to improve the efficiency and handle the side effects introduced by the heap manager's sophisticated behaviors in the real-world environment. Our evaluation demonstrates that Scatter can successfully generate a total of 126 exploitable heap layouts for 18 out of 27 heap overflows in 10 general-purpose programs.