<p>Given two integers n and k, return <em>an array of all the integers of length </em><code>n</code><em> where the difference between every two consecutive digits is </em><code>k</code>. You may return the answer in <strong>any order</strong>.</p>

<p>Note that the integers should not have leading zeros. Integers as <code>02</code> and <code>043</code> are not allowed.</p>

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

<pre>
<strong>Input:</strong> n = 3, k = 7
<strong>Output:</strong> [181,292,707,818,929]
<strong>Explanation:</strong> Note that 070 is not a valid number, because it has leading zeroes.
</pre>

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

<pre>
<strong>Input:</strong> n = 2, k = 1
<strong>Output:</strong> [10,12,21,23,32,34,43,45,54,56,65,67,76,78,87,89,98]
</pre>

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

<ul>
	<li><code>2 &lt;= n &lt;= 9</code></li>
	<li><code>0 &lt;= k &lt;= 9</code></li>
</ul>

class Solution {
public:
    vector<int> numsSameConsecDiff(int n, int k) {
        std::vector<int> ans;
        for (int i = 1; i <= 9; i++) {
            int curr = i;
            backtrace(ans, curr, 1, n, k);
        }
        return ans;
    }
    
private:
    void backtrace(std::vector<int>& ans, int& curr,
                  const int digits, const int n, const int k) {
        if (digits == n) {
            ans.push_back(curr);
            return;
        }
        
        const int last_digit = curr % 10;
        const int curr_origin = curr;
        if (last_digit >= k) {
            curr = curr * 10 + last_digit - k;
            backtrace(ans, curr, digits + 1, n, k);
            curr = curr_origin;
        }
        if (last_digit + k <= 9 && k != 0) {
            curr = curr * 10 + last_digit + k;
            backtrace(ans, curr, digits + 1, n, k);
            curr = curr_origin;
        }
    }
};
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