<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
        
        def digitSum(x):
            s = 0
            while x > 0:
                s += x % 10
                x //= 10
            return s
        
        def countDP(num):
            n = len(num)
            dp = [[[-1 for _ in range(2)] for _ in range(401)] for _ in range(n + 1)]
            
            def dfs(pos, sum_, tight):
                if pos == n:
                    return min_sum <= sum_ <= max_sum
                if dp[pos][sum_][tight] != -1:
                    return dp[pos][sum_][tight]
                
                limit = int(num[pos]) if tight else 9
                total = 0
                
                for digit in range(limit + 1):
                    newTight = tight and (digit == limit)
                    total += dfs(pos + 1, sum_ + digit, newTight)
                    total %= MOD
                
                dp[pos][sum_][tight] = total
                return total
            
            return dfs(0, 0, 1)
        
        return (countDP(num2) - countDP(str(int(num1) - 1)) + MOD) % MOD

# Example usage:
solution = Solution()
num1 = "1"
num2 = "12"
min_sum = 1
max_sum = 8
print(solution.count(num1, num2, min_sum, max_sum))  # Output: 11

num1 = "1"
num2 = "5"
min_sum = 1
max_sum = 5
print(solution.count(num1, num2, min_sum, max_sum))  # Output: 5
901