<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 count_less_equal(num):
            n = len(num)
            dp = [[[-1] * (max_sum + 1) for _ in range(2)] for _ in range(n + 1)]
            
            def count_rec(idx, tight, sum_val):
                if sum_val > max_sum:
                    return 0
                if idx == n:
                    return 1 if min_sum <= sum_val <= max_sum else 0
                if dp[idx][tight][sum_val] != -1:
                    return dp[idx][tight][sum_val]
                
                limit = int(num[idx]) if tight else 9
                count = 0
                for digit in range(limit + 1):
                    new_tight = tight and (digit == limit)
                    count = (count + count_rec(idx + 1, new_tight, sum_val + digit)) % MOD
                
                dp[idx][tight][sum_val] = count
                return count
            
            return count_rec(0, True, 0)
        
        return (count_less_equal(num2) - count_less_equal(str(int(num1) - 1)) + MOD) % MOD
18500