<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 digitSum(s):
            return sum(int(c) for c in s)
        
        def countInRange(num):
            n = len(num)
            
            @lru_cache(None)
            def dp(pos, tight, sum_so_far):
                if pos == n:
                    return min_sum <= sum_so_far <= max_sum
                
                res = 0
                max_digit = int(num[pos]) if tight else 9
                
                for digit in range(max_digit + 1):
                    new_tight = tight and (digit == max_digit)
                    res += dp(pos + 1, new_tight, sum_so_far + digit)
                
                return res
            
            return dp(0, 1, 0)
        
        # Convert num1 and num2 to strings
        num1 = str(int(num1) - 1)
        num2 = str(int(num2))
        
        # Calculate the count for num2 and num1 separately
        count_num2 = countInRange(num2)
        count_num1 = countInRange(num1)
        
        # The result is the difference between the counts
        return (count_num2 - count_num1) % (10**9 + 7)

# Example usage:
solution = Solution()
num1 = "1"
num2 = "12"
min_sum = 1
max_sum = 8
print(solution.count(num1, num2, min_sum, max_sum))  # Output: 11
293