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# 1850. Minimum Adjacent Swaps to Reach the Kth Smallest Number

<https://leetcode.com/problems/minimum-adjacent-swaps-to-reach-the-kth-smallest-number>

## Description

You are given a string `num`, representing a large integer, and an integer `k`.

We call some integer **wonderful** if it is a **permutation** of the digits in `num` and is **greater in value** than `num`. There can be many wonderful integers. However, we only care about the **smallest-valued** ones.

* For example, when `num = "5489355142"`:
  * The 1st smallest wonderful integer is `"5489355214"`.
  * The 2nd smallest wonderful integer is `"5489355241"`.
  * The 3rd smallest wonderful integer is `"5489355412"`.
  * The 4th smallest wonderful integer is `"5489355421"`.

Return *the **minimum number of adjacent digit swaps** that needs to be applied to* `num` *to reach the* `kth` ***smallest wonderful** integer*.

The tests are generated in such a way that `kth` smallest wonderful integer exists.

**Example 1:**

```
**Input:** num = "5489355142", k = 4
**Output:** 2
**Explanation:** The 4th smallest wonderful number is "5489355421". To get this number:
- Swap index 7 with index 8: "5489355142" -> "5489355412"
- Swap index 8 with index 9: "5489355412" -> "5489355421"
```

**Example 2:**

```
**Input:** num = "11112", k = 4
**Output:** 4
**Explanation:** The 4th smallest wonderful number is "21111". To get this number:
- Swap index 3 with index 4: "11112" -> "11121"
- Swap index 2 with index 3: "11121" -> "11211"
- Swap index 1 with index 2: "11211" -> "12111"
- Swap index 0 with index 1: "12111" -> "21111"
```

**Example 3:**

```
**Input:** num = "00123", k = 1
**Output:** 1
**Explanation:** The 1st smallest wonderful number is "00132". To get this number:
- Swap index 3 with index 4: "00123" -> "00132"
```

**Constraints:**

* `2 <= num.length <= 1000`
* `1 <= k <= 1000`
* `num` only consists of digits.

## ac

```java
```