Kuroshuto

Kuroshuto (meaning “black shot”) is a Japanese logic puzzle. Blacken some cells with the correct distance to the given numbers.

Rules: Colour the grey cells of the grid black or white. Cells with numbers may not be blacked out. Black cells cannot be orthogonally adjacent.
Starting from a cell with number N, exactly one of the cells at distance N must be black. All white cells must form a single orthogonally contiguous area.