<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:
        MOD = 10**9 + 7

        def digit_sum(n: str) -> int:
            return sum(int(d) for d in n)

        def dp(pos, tight, sum_val, num_str, memo):
            if pos == len(num_str):
                return min_sum <= sum_val <= max_sum
            if (pos, tight, sum_val) in memo:
                return memo[(pos, tight, sum_val)]

            limit = int(num_str[pos]) if tight else 9
            res = 0
            for dig in range(0, limit + 1):
                res = (res + dp(pos + 1, tight and (dig == limit), sum_val + dig, num_str, memo)) % MOD
            
            memo[(pos, tight, sum_val)] = res
            return res
        
        def count_up_to(num_str: str) -> int:
            memo = {}
            return dp(0, True, 0, num_str, memo)

        # Count good integers between "0" and num2
        cnt_num2 = count_up_to(num2)

        # Count good integers between "0" and num1 - 1
        num1_prev = str(int(num1) - 1)
        cnt_num1_minus_1 = count_up_to(num1_prev) if int(num1_prev) >= 0 else 0

        # Number of good integers between num1 and num2
        result = (cnt_num2 - cnt_num1_minus_1) % MOD
        return result
17100