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# 1987. Number of Unique Good Subsequences

<https://leetcode.com/problems/number-of-unique-good-subsequences>

## Description

You are given a binary string `binary`. A **subsequence** of `binary` is considered **good** if it is **not empty** and has **no leading zeros** (with the exception of `"0"`).

Find the number of **unique good subsequences** of `binary`.

* For example, if `binary = "001"`, then all the **good** subsequences are `["0", "0", "1"]`, so the **unique** good subsequences are `"0"` and `"1"`. Note that subsequences `"00"`, `"01"`, and `"001"` are not good because they have leading zeros.

Return *the number of **unique good subsequences** of* `binary`. Since the answer may be very large, return it **modulo** `109 + 7`.

A **subsequence** is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

**Example 1:**

```
**Input:** binary = "001"
**Output:** 2
**Explanation:** The good subsequences of binary are ["0", "0", "1"].
The unique good subsequences are "0" and "1".
```

**Example 2:**

```
**Input:** binary = "11"
**Output:** 2
**Explanation:** The good subsequences of binary are ["1", "1", "11"].
The unique good subsequences are "1" and "11".
```

**Example 3:**

```
**Input:** binary = "101"
**Output:** 5
**Explanation:** The good subsequences of binary are ["1", "0", "1", "10", "11", "101"]. 
The unique good subsequences are "0", "1", "10", "11", and "101".
```

**Constraints:**

* `1 <= binary.length <= 105`
* `binary` consists of only `'0'`s and `'1'`s.

## ac

```java
```