<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>

P = 1_000_000_007

def count_step_numbers(high):
    is_step_number = True
    num = int(high[0]) + 1
    counts = [0] * 10
    tmp = [0] * 10
    for i, ch in enumerate(high):
        for j in range(1, 9):
            tmp[j] = (counts[j - 1] + counts[j + 1]) % P
        tmp[0] = counts[1]
        tmp[9] = counts[8]

        num0 = int(ch)

        for j in range(1, 10 if i > 0 else num0):
            tmp[j] += 1

        if is_step_number:
            if abs(num - num0) != 1:
                is_step_number = False
            if 0 <= num - 1 < num0:
                tmp[num - 1] += 1
            if num + 1 < num0:
                tmp[num + 1] += 1

        tmp, counts = counts, tmp
        num = num0

    return sum(counts) % P, is_step_number


class Solution:
    def countSteppingNumbers(self, low: str, high: str) -> int:
        num1, is_step1 = count_step_numbers(high)
        num0, is_step0 = count_step_numbers(low)
        return (num1 + int(is_step1) - num0) % P
16600