<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:
        
        def g(num: str, mins: int, maxs: int, mod: int) -> int:
            digits = [int(e) for e in num]
            # print(digits)
            @lru_cache(None)
            def dfs(idx, tight, sm):
                nonlocal mins, maxs, mod
                if idx == len(digits):
                    return 1 if mins <= sm <= maxs else 0
                if sm > maxs:
                    return 0
                k = digits[idx] if tight else 9
                count = 0
                for i in range(k+1):
                    new_tight = tight and i==digits[idx]
                    count += dfs(idx+1, new_tight, sm+i)
                    count %= mod
                return count
            ans = dfs(0,1,0)
            dfs.cache_clear()
            return ans

        mod = int(1e9+7)
        n1 = g(num2, min_sum, max_sum,  mod)
        n2 = g(num1, min_sum, max_sum, mod)
        ans =  n1 - n2 + mod
        ans %= mod

        sm = sum([int(e) for e in num1])  
        if min_sum <= sm <= max_sum:
            ans += 1
            ans %= mod
        

        # print(n1, n2)

        return ans
17200