<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>

MOD_CONSTANT = 10**9 + 7

@cache
def count_stepping_numbers(
    current_length: int,
    check_max: bool,
    previous_digit: int,
    leading_zero: bool,
    max_num: str,
) -> int:
    if current_length == len(str(max_num)):
        return 1
    max_digit = int(max_num[current_length]) if check_max else 9
    current_count_stepping_numbers = 0
    for digit in range(max_digit + 1):
        next_check_max = check_max and digit == max_digit
        next_leading_zero = leading_zero and digit == 0
        if next_leading_zero:
            current_count_stepping_numbers = (
                current_count_stepping_numbers
                + count_stepping_numbers(
                    current_length + 1,
                    next_check_max,
                    previous_digit,
                    next_leading_zero,
                    max_num,
                )
            ) % MOD_CONSTANT
        elif previous_digit == -1 or abs(previous_digit - digit) == 1:
            current_count_stepping_numbers = (
                current_count_stepping_numbers
                + count_stepping_numbers(
                    current_length + 1,
                    next_check_max,
                    digit,
                    next_leading_zero,
                    max_num,
                )
            ) % MOD_CONSTANT
    return current_count_stepping_numbers


class Solution:
    def countSteppingNumbers(self, low: str, high: str) -> int:
        low_num_stepping_number_count = count_stepping_numbers(
            0, True, -1, True, str(int(low) - 1)
        )
        high_num_stepping_number_count = count_stepping_numbers(0, True, -1, True, high)
        return (
            high_num_stepping_number_count - low_num_stepping_number_count
        ) % MOD_CONSTANT
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