directx – Cascaded Shadow Maps – Handling shadows that cast into different cascades

For example I have 3 shadow cascades. A shadow is cast by a hill in my 2nd cascade, but the shadow itself is cast into not only the 2nd cascade but also the 1st. In the shader program, in order to locate the correct cascade, I check which bounds the Z clip space that the pixel resides within. Since the shadow was cast from the 2nd cascade, the portion of the shadow that is cast into the 1st is cut off, as shown in my image.
How can I get around this? Is there something I’m missing, or is my implementation wrong?

enter image description here

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