<p>You are given two numeric strings <code>num1</code> and <code>num2</code> and two integers <code>max_sum</code> and <code>min_sum</code>. We denote an integer <code>x</code> to be <em>good</em> if:</p>

<ul>
	<li><code>num1 &lt;= x &lt;= num2</code></li>
	<li><code>min_sum &lt;= digit_sum(x) &lt;= max_sum</code>.</li>
</ul>

<p>Return <em>the number of good integers</em>. Since the answer may be large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>

<p>Note that <code>digit_sum(x)</code> denotes the sum of the digits of <code>x</code>.</p>

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

<pre>
<strong>Input:</strong> num1 = &quot;1&quot;, num2 = &quot;12&quot;, <code>min_sum</code> = 1, max_sum = 8
<strong>Output:</strong> 11
<strong>Explanation:</strong> There are 11 integers whose sum of digits lies between 1 and 8 are 1,2,3,4,5,6,7,8,10,11, and 12. Thus, we return 11.
</pre>

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

<pre>
<strong>Input:</strong> num1 = &quot;1&quot;, num2 = &quot;5&quot;, <code>min_sum</code> = 1, max_sum = 5
<strong>Output:</strong> 5
<strong>Explanation:</strong> The 5 integers whose sum of digits lies between 1 and 5 are 1,2,3,4, and 5. Thus, we return 5.
</pre>

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

<ul>
	<li><code>1 &lt;= num1 &lt;= num2 &lt;= 10<sup>22</sup></code></li>
	<li><code>1 &lt;= min_sum &lt;= max_sum &lt;= 400</code></li>
</ul>

class Solution:
    def count(self, num1: str, num2: str, min_sum: int, max_sum: int) -> int:
        
        def fill_arr(num, lst):
            while num != 0:
                lst.append(num % 10)
                num = num // 10
                
        num1_arr = []
        num2_arr = []
        
        fill_arr(int(num2), num2_arr)
        num2_arr = num2_arr[::-1]
        
        fill_arr(int(num1) - 1, num1_arr)
        num1_arr = num1_arr[::-1]
        lst = []

        @cache
        def recurse(index, digit_sum, restrict, num_array):
            if digit_sum > max_sum:
                return 0
            
            if index == len(num_array):
                if min_sum <= digit_sum <= max_sum:
                    return 1
                else:
                    return 0
            
            ans = 0
                
            for i in range((num_array[index] if restrict else 9) + 1):
                ans = (ans % 1_000_000_007 + recurse(index + 1, digit_sum + i, restrict and num_array[index] == i, num_array) % 1_000_000_007) % 1_000_000_007  
            
            return ans % 1_000_000_007
        
        return (recurse(0, 0, True, tuple(num2_arr)) - recurse(0, 0, True, tuple(num1_arr))) % 1_000_000_007
    
    

                
            
    
        
         
        
        
                
19000