Lighthouse light pattern

Turn a lighthouse's chart abbreviation into the second-by-second pattern of its lamp.

Charts describe a light as TYPE, then an optional group list in parentheses, then an optional colour letter, then the repeat period, for example Fl(2+1) W 12s. The pattern covers exactly one period, one character per second: "1" when the lamp is lit, "0" when dark.

• Fl (flash): every flash is 1 lit second. LFl (long flash): every flash is 3 lit seconds.
• Every flash is followed by 1 dark second. When the group list has several groups, such as (2+1), there is one extra dark second between consecutive groups. With no group list there is a single flash. After the last flash the lamp stays dark until the period ends.
• Oc (occulting): take the pattern the same group list would give for Fl, then swap every "1" and "0".
• Iso (isophase): never has a group list. The lamp is lit for the first half of the period and dark for the second half, so the period must be even.
• The colour letter (W, R, G or Y) never changes the pattern.

If the flashes (each together with its dark second) and the extra between-group seconds need more seconds than the period provides, or if an Iso period is odd, the characteristic is impossible: return the empty string. A pattern that fits the period exactly is fine.

Input: characteristic, a string such as "Fl(3) R 15s", "LFl 10s", "Oc(2+2) 20s" or "Iso 8s". Parts are separated by single spaces, except that the group list follows the type directly.

Output: a string of "1" and "0" characters whose length equals the period, or "" if the characteristic is impossible.