<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>

from typing import List


class Solution:
    def solve(self, dig, rem):
        if rem == 0:
            return [dig]
        # if (dig, rem) in self.memo:
        #     return self.memo[dig, rem]
        solutions = []
        if dig + self.k < 10:
            solutions.extend([f"{dig}{e}" for e in self.solve(dig + self.k, rem - 1)])
        if 0 <= dig - self.k:
            solutions.extend([f"{dig}{e}" for e in self.solve(dig - self.k, rem - 1)])

        self.memo[dig, rem] = solutions
        return solutions

    def numsSameConsecDiff(self, n: int, k: int) -> List[int]:
        self.n = n
        self.k = k
        self.memo = {}
        found = []
        for i in range(1, 10):
            found.extend(self.solve(i, n - 1))
        return list({int(e) for e in found})


print(Solution().numsSameConsecDiff(n=3, k=0))
# print(Solution().numsSameConsecDiff(n=3, k=7))
# print(Solution().numsSameConsecDiff(n=2, k=1))

17200