<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:
        n=len(num2)
        num1='0'*(n-len(num1))+num1
        dp=[[[[-1 for _ in range(401)] for _ in range(2)] for _ in range(2)] for _ in range(n)] # i, t1, t2, sum
        def count(i,t1,t2,s):
            if s<0:
                return 0
            if i==n:
                return 1
            if dp[i][int(t1)][int(t2)][s]!=-1:
                return dp[i][int(t1)][int(t2)][s]
            lo = int(num1[i]) if t1 else 0
            hi = int(num2[i]) if t2 else 9
            total=0
            for d in range(lo,hi+1):
                t1n = t1 and d==lo
                t2n = t2 and d==hi
                total+=count(i+1,t1n,t2n,s-d)
            dp[i][int(t1)][int(t2)][s]=total
            return total
        return (count(0,True,True,max_sum)-count(0,True,True,min_sum-1))%(10**9+7)
19900