<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:
        lth = len(num2) 
        num1 = (lth - len(num1)) * '0' + num1
        res = 0
        @cache
        def get_zero(total):
            return '0' * total
        @cache
        def get_nine(total):
            return '9' * total
            
        @cache
        def sum_count(target, num1, num2):
            if target < 0:
                return 0
            lth = len(num1)
            f1 = int(num1[0])
            f2 = int(num2[0])
            if f2 == f1:
                if lth == 1:
                    if target == f1:
                        return 1
                    else:
                        return 0
                return sum_count(target-f1, num1[1:], num2[1:])
            else:
                if lth == 1:
                    for fi in range(f1, f2 + 1):
                        if target == fi:
                            return 1
                    return 0
                else:
                    res = 0
                    res += sum_count(target-f1, num1[1:], get_nine(lth - 1))
                    for fi in range(f1 + 1, f2):
                        res += sum_count(target-fi, get_zero(lth - 1), get_nine(lth - 1))
                    res += sum_count(target-f2, get_zero(lth - 1), num2[1:])
                    return res % (1000000007)
            
        for target in range(min_sum, max_sum + 1):
            res += sum_count(target, num1, num2)
            res = res % (1000000007)
        return res
1321