<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:
        # Digit DP
        @cache
        def dp(i, digit_sum, max_bound, is_limit, is_num):
            if i == len(max_bound):
                if min_sum <= digit_sum <= max_sum:
                    return 1
                return 0
            # Skip this number if we haven't started putting number
            res = 0
            # if not is_num:
            #     res += dp(i+1, digit_sum, max_bound, is_limit, is_num)
            # minDigit = 1 if not is_num else 0 # Leading zero not allowed when is_num is not set
            maxDigit = int(max_bound[i]) if is_limit else 9
            # print(i, minDigit, maxDigit, digit_sum, max_bound, is_limit, is_num)
            for d in range(maxDigit+1):
                res += dp(i+1, digit_sum+d, max_bound, is_limit and d == maxDigit, True)
            return res
        return ((dp(0, 0, num2, True, False) - dp(0,0,str(int(num1)-1),True,False)) % (10**9+7))
18900