<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 helper(string &num, int target, long long sum, long long prev, int i, string curr, vector<string> &ans) {
        if (i >= num.size()) {
            if (sum == target) {
                ans.push_back(curr);
            }
            return;
        }

        for (int j = i; j < num.size(); j++) {
            if (j > i && num[i] == '0') {
                continue; // Skip leading zeros
            }

            string r = num.substr(i, j - i + 1);
            long long number = stoll(r);

            if (i == 0) {
                // For the first number, just call without any operator
                helper(num, target, number, number, j + 1, r, ans);
            } else {
                helper(num, target, sum + number, number, j + 1, curr + "+" + r, ans);
                helper(num, target, sum - number, -number, j + 1, curr + "-" + r, ans);
                helper(num, target, sum - prev + prev * number, prev * number, j + 1, curr + "*" + r, ans);
            }
        }
    }

    vector<string> addOperators(string num, int target) {
        vector<string> ans;
        if (num.empty()) return ans;
        helper(num, target, 0, 0, 0, "", ans);
        return ans;
    }
};

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