<p>Given the integers <code>zero</code>, <code>one</code>, <code>low</code>, and <code>high</code>, we can construct a string by starting with an empty string, and then at each step perform either of the following:</p>

<ul>
	<li>Append the character <code>&#39;0&#39;</code> <code>zero</code> times.</li>
	<li>Append the character <code>&#39;1&#39;</code> <code>one</code> times.</li>
</ul>

<p>This can be performed any number of times.</p>

<p>A <strong>good</strong> string is a string constructed by the above process having a <strong>length</strong> between <code>low</code> and <code>high</code> (<strong>inclusive</strong>).</p>

<p>Return <em>the number of <strong>different</strong> good strings that can be constructed satisfying these properties.</em> Since the answer can be large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> low = 3, high = 3, zero = 1, one = 1
<strong>Output:</strong> 8
<strong>Explanation:</strong> 
One possible valid good string is &quot;011&quot;. 
It can be constructed as follows: &quot;&quot; -&gt; &quot;0&quot; -&gt; &quot;01&quot; -&gt; &quot;011&quot;. 
All binary strings from &quot;000&quot; to &quot;111&quot; are good strings in this example.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> low = 2, high = 3, zero = 1, one = 2
<strong>Output:</strong> 5
<strong>Explanation:</strong> The good strings are &quot;00&quot;, &quot;11&quot;, &quot;000&quot;, &quot;110&quot;, and &quot;011&quot;.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= low&nbsp;&lt;= high&nbsp;&lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= zero, one &lt;= low</code></li>
</ul>

class Solution:
    def countGoodStrings(self, low: int, high: int, zero: int, one: int) -> int:
        # dp[i] stores num strings we can build of length i
        dp = [0] * (high+1)

        # problem reduces to adding a big num or small num
        # how many ways can we add num between [low,high]?
        # big = max(zero, one)
        # small = min(zero,one)

        # Start getting all lengths
        dp[one] += 1
        dp[zero] += 1

        # for all possible lengths
        for length in range(len(dp)):
            if length - one > 0:
                dp[length] += dp[length - one]
            if length - zero > 0:
                dp[length] += dp[length - zero]
        return sum(dp[low:]) % (10**9+7)
393800