<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, high):
        low = "0"*(len(high)-len(low)) + low
        
        mod = 10**9 + 7
        
        @lru_cache(None)
        def dfs(i,is_greater_thn_low,is_less_thn_high,prev_digit,nonzero):
            if i == len(high):
                return 1
            
            total = 0
            
            start = int(low[i]) if not is_greater_thn_low else 0
            end = int(high[i]) + 1 if not is_less_thn_high else 10
            
            for nx_digit in range(start,end):
                if not nonzero or abs(prev_digit - nx_digit) == 1:
                    total += dfs(i+1,is_greater_thn_low or nx_digit > int(low[i]),is_less_thn_high or nx_digit < int(high[i]),nx_digit,nonzero or nx_digit != 0)
                    
            return total%mod

        return dfs(0, False, False, -1, False)
18500