Count Partitions with Exactly Two Zeros Each

Problem Given a binary string, count the number of ways to partition it into contiguous substrings such that every substring contains exactly two 0s.

Input / Output

• Input: a string s of characters '0' and '1'.
• Output: the number of valid partitions. Return the count modulo 10^9+7 if it can overflow.

Constraints

• Length up to 10^5.
• Characters are only '0' or '1'.
• Every character must belong to exactly one piece — the pieces tile the whole string.

Example

• "100100" -> 2. Zeros sit at indices 1, 2, 4, 5. The only cut must fall between index 2 and index 4, giving "100" | "100" and "1001" | "00".
• "0000" -> 1 — the single cut "00" | "00".
• Tricky cases: an odd number of zeros -> 0; a string with no zeros at all -> 0, since every piece needs two.