# Route posted mouse messages to the actual child control in the target window.
# Screen hit testing is deliberately not used: another window may cover the target.
function Resolve-InputWindow([IntPtr]$root, [int]$screenX, [int]$screenY) {
    $current = $root
    for ($depth = 0; $depth -lt 32; $depth++) {
        $point = New-Object OCUWin32+POINT
        $point.X = $screenX
        $point.Y = $screenY
        if (-not [OCUWin32]::ScreenToClient($current, [ref]$point)) {
            throw 'The target window is no longer available; observe again before acting.'
        }
        # Skip invisible, disabled and transparent child windows.
        $child = [OCUWin32]::ChildWindowFromPointEx($current, $point, 7)
        if ($child -eq [IntPtr]::Zero -or $child -eq $current) { return $current }
        $current = $child
    }
    throw 'Target child window nesting exceeded the input limit.'
}