<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 FenwickTree{
public:
    vector<int> mList;
    FenwickTree(int n){
        mList.resize(n,0);
    }
    void add(int idx,int value){
        while(idx < mList.size()){
            mList[idx] += value;
            idx += (idx&-idx);
        }
    }
    int sum(int idx){
        int ret = 0;
        while(idx > 0){
            ret += mList[idx];
            idx-=(idx&-idx);
        }
        return ret;
    }
};

class Solution {
public:
    string minInteger(string num, int k) {
        map<char,deque<int>> m;
        for(int i = 0;i < num.length();++i){
            char c = num[i];
            m[c].push_back(i);
        }
        FenwickTree ft(num.length() + 1);
        for(int i = 0;i < num.length();i++){
            auto it = m.begin();
            char c = num[i];
            if(c == it->first){
                m[c].pop_front();
                if(m[c].size() == 0){
                    m.erase(c);
                }
                continue;
            }

            int nearIdx =INT_MAX;
            for(char cand = '0' ;cand < c;cand++){
                if(m.count(cand) == 0){
                    continue;
                }
                int original = *(m[cand].begin());
                int idx = original + ft.sum(original+1);
                if(idx - i <= k){
                    nearIdx= idx;
                    ft.add(original+1,-1);
                    ft.add(1,1);
                    break;
                }
            }
            if(nearIdx == INT_MAX){
                m[c].pop_front();
                if(m[c].size() == 0){
                    m.erase(c);
                }

                continue;
            }


            char other = num[nearIdx];

            num.erase(num.begin() + nearIdx);
            num.insert(num.begin() + i,other);

            m[other].pop_front();
            if(m[other].size() == 0){
                m.erase(other);
            }

            k -= (nearIdx-i);
            if(k <= 0){
                break;
            }
        }
        return num;
    }
};
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