<p>You are given a string <code>num</code> representing <strong>the digits</strong> of a very large integer and an integer <code>k</code>. You are allowed to swap any two adjacent digits of the integer <strong>at most</strong> <code>k</code> times.</p>

<p>Return <em>the minimum integer you can obtain also as a string</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/06/17/q4_1.jpg" style="width: 500px; height: 40px;" />
<pre>
<strong>Input:</strong> num = &quot;4321&quot;, k = 4
<strong>Output:</strong> &quot;1342&quot;
<strong>Explanation:</strong> The steps to obtain the minimum integer from 4321 with 4 adjacent swaps are shown.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;100&quot;, k = 1
<strong>Output:</strong> &quot;010&quot;
<strong>Explanation:</strong> It&#39;s ok for the output to have leading zeros, but the input is guaranteed not to have any leading zeros.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;36789&quot;, k = 1000
<strong>Output:</strong> &quot;36789&quot;
<strong>Explanation:</strong> We can keep the number without any swaps.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= num.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>num</code> consists of only <strong>digits</strong> and does not contain <strong>leading zeros</strong>.</li>
	<li><code>1 &lt;= k &lt;= 10<sup>9</sup></code></li>
</ul>

class BIT {
private:
    vector<int> tree;
    int n;

public:
    BIT(int _n): n(_n), tree(_n + 1) {}

    static int lowbit(int x) {
        return x & (-x);
    }
    
    void update(int x) {
        while (x <= n) {
            ++tree[x];
            x += lowbit(x);
        }
    }

    int query(int x) const {
        int ans = 0;
        while (x) {
            ans += tree[x];
            x -= lowbit(x);
        }
        return ans;
    }

    int query(int x, int y) const {
        return query(y) - query(x - 1);
    }
};

class Solution {
public:
    string minInteger(string num, int k) {
        int n = num.size();
        vector<queue<int>> pos(10);
        for (int i = 0; i < n; ++i) {
            pos[num[i] - '0'].push(i + 1);
        }
        string ans;
        BIT bit(n);
        for (int i = 1; i <= n; ++i) {
            for (int j = 0; j < 10; ++j) {
                if (!pos[j].empty()) {
                    int behind = bit.query(pos[j].front() + 1, n);
                    int dist = pos[j].front() + behind - i;
                    if (dist <= k) {
                        bit.update(pos[j].front());
                        pos[j].pop();
                        ans += (j + '0');
                        k -= dist;
                        break;
                    }
                }
            }
        }
        return ans;
    }
};

13000