<p>Given two positive integers <code>low</code> and <code>high</code> represented as strings, find the count of <strong>stepping numbers</strong> in the inclusive range <code>[low, high]</code>.</p>

<p>A <strong>stepping number</strong> is an integer such that all of its adjacent digits have an absolute difference of <strong>exactly</strong> <code>1</code>.</p>

<p>Return <em>an integer denoting the count of stepping numbers in the inclusive range</em> <code>[low, high]</code><em>. </em></p>

<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p><strong>Note:</strong> A stepping number should not have a leading zero.</p>

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

<pre>
<strong>Input:</strong> low = &quot;1&quot;, high = &quot;11&quot;
<strong>Output:</strong> 10
<strong>Explanation: </strong>The stepping numbers in the range [1,11] are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. There are a total of 10 stepping numbers in the range. Hence, the output is 10.</pre>

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

<pre>
<strong>Input:</strong> low = &quot;90&quot;, high = &quot;101&quot;
<strong>Output:</strong> 2
<strong>Explanation: </strong>The stepping numbers in the range [90,101] are 98 and 101. There are a total of 2 stepping numbers in the range. Hence, the output is 2. </pre>

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

<ul>
	<li><code>1 &lt;= int(low) &lt;= int(high) &lt; 10<sup>100</sup></code></li>
	<li><code>1 &lt;= low.length, high.length &lt;= 100</code></li>
	<li><code>low</code> and <code>high</code> consist of only digits.</li>
	<li><code>low</code> and <code>high</code> don&#39;t have any leading zeros.</li>
</ul>

class Solution:
  def countSteppingNumbers(self, low: str, high: str) -> int:
    kMod = 1_000_000_007
    low = '0' * (len(high) - len(low)) + low

    @functools.lru_cache(None)
    def dp(i: int, prevDigit: int, isLeadingZero: bool, isTight1: bool, isTight2: bool) -> int:
      """
      Returns the number of valid integers, considering the i-th digit, where
      `prevDigit` is the previous digit, `isTight1` indicates if the current
      digit is tightly bound for `low`, and `isTight2` indicates if the current
      digit is tightly bound for `high`.
      """
      if i == len(high):
        return 1

      res = 0
      minDigit = int(low[i]) if isTight1 else 0
      maxDigit = int(high[i]) if isTight2 else 9

      for d in range(minDigit, maxDigit + 1):
        nextIsTight1 = isTight1 and (d == minDigit)
        nextIsTight2 = isTight2 and (d == maxDigit)
        if isLeadingZero:
          # Can place any digit in [minDigit, maxDigit].
          res += dp(i + 1, d, isLeadingZero and d ==
                    0, nextIsTight1, nextIsTight2)
        elif abs(d - prevDigit) == 1:
          res += dp(i + 1, d, False, nextIsTight1, nextIsTight2)
        res %= kMod

      return res

    return dp(0, -1, True, True, True)
18300