-p  Create any missing intermediate pathname components.

    For each dir operand that does not name an existing directory,
    before performing the actions described in the DESCRIPTION above
    the mkdir utility shall create any pathname components of the path
    prefix of dir that do not name an existing directory by performing
    actions equivalent to first calling the mkdir() function with the
    following arguments:

      1. A pathname naming the missing pathname component, ending
         with a trailing <slash> character, as the path argument.

      2. The value zero as the mode argument.

    and then calling the chmod() function with the following
    arguments:

      1. The same path argument as in the mkdir() call.

      2. The value (S_IWUSR|S_IXUSR|~filemask)&0777 as the mode argument,
         where filemask is the file mode creation mask of the process
         (see [xref to umask()]).

    Each dir operand that names an existing directory shall be ignored
    without error.