<p>Given a string <code>num</code> that contains only digits and an integer <code>target</code>, return <em><strong>all possibilities</strong> to insert the binary operators </em><code>&#39;+&#39;</code><em>, </em><code>&#39;-&#39;</code><em>, and/or </em><code>&#39;*&#39;</code><em> between the digits of </em><code>num</code><em> so that the resultant expression evaluates to the </em><code>target</code><em> value</em>.</p>

<p>Note that operands in the returned expressions <strong>should not</strong> contain leading zeros.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;123&quot;, target = 6
<strong>Output:</strong> [&quot;1*2*3&quot;,&quot;1+2+3&quot;]
<strong>Explanation:</strong> Both &quot;1*2*3&quot; and &quot;1+2+3&quot; evaluate to 6.
</pre>

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

<pre>
<strong>Input:</strong> num = &quot;232&quot;, target = 8
<strong>Output:</strong> [&quot;2*3+2&quot;,&quot;2+3*2&quot;]
<strong>Explanation:</strong> Both &quot;2*3+2&quot; and &quot;2+3*2&quot; evaluate to 8.
</pre>

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

<pre>
<strong>Input:</strong> num = &quot;3456237490&quot;, target = 9191
<strong>Output:</strong> []
<strong>Explanation:</strong> There are no expressions that can be created from &quot;3456237490&quot; to evaluate to 9191.
</pre>

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

<ul>
	<li><code>1 &lt;= num.length &lt;= 10</code></li>
	<li><code>num</code> consists of only digits.</li>
	<li><code>-2<sup>31</sup> &lt;= target &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution {
public:
    void Recur(string rem_str, string op_string, long long eval, long long to_add, int target, vector<string>& ans) {
        if (rem_str.empty()) {
            if (eval + to_add == target) {
                ans.push_back(op_string);
            }
            return;
        }
        long long value = 0;
        for (int i = 0; i < rem_str.size(); ++i) {
            value = (value * 10) + (rem_str[i] - '0');
            if (i > 0 && rem_str[0] == '0') break;
            // Add
            Recur(rem_str.substr(i + 1), op_string + "+" + rem_str.substr(0, i + 1), eval + to_add, value, target, ans);
            // Sub
            Recur(rem_str.substr(i + 1), op_string + "-" + rem_str.substr(0, i + 1), eval + to_add, -value, target, ans);
            // Mul
            Recur(rem_str.substr(i + 1), op_string + "*" + rem_str.substr(0, i + 1), eval, value * to_add, target, ans);
        }

    }
    vector<string> addOperators(string num, int target) {
        long long eval = 0;
        long long to_add = 0;
        vector<string> ans;
        for (int i = 0; i < num.size(); ++i) {
            to_add = (to_add * 10) + (num[i] - '0');
            if (i > 0 && num[0] == '0') continue;
            Recur(num.substr(i + 1), num.substr(0, i + 1), eval, to_add, target, ans);
        }
        return ans;
    }
};
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