<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
        @cache
        def recurse(index, remDigits, num, strictMode):
            if(remDigits < 0):
                return 0
            if(index == len(num)):
                return 1

            ans = 0
            if(strictMode):
                for i in range(int(num[index])+1):
                    ans = (ans + recurse(index+1, remDigits - i, num, i == int(num[index]))) % MOD
            else:
                for i in range(10):
                    ans = (ans + recurse(index+1, remDigits - i, num, False)) % MOD
            return ans % MOD
        
        doesMinSumQualify = 0
        sumDigits = 0
        for i in range(len(num1)):
            sumDigits += int(num1[i])
        if(sumDigits <= max_sum and sumDigits >= min_sum):
            doesMinSumQualify = 1

        print(recurse(0, max_sum, num2, True))
        print(recurse(0, min_sum-1, num2, True))
        print(recurse(0, min_sum-1, num1, True))
        print(recurse(0, max_sum, num1, True))
        return doesMinSumQualify + (recurse(0, max_sum, num2, True) - recurse(0, min_sum-1, num2, True) - recurse(0, max_sum, num1, True) + recurse(0, min_sum-1, num1, True)) % MOD
                
387