<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 = [0] * (high+1)
        dp[zero] = 1
        dp[one] = 1
        if one == zero:
            dp[one] += 1
        
        res = 0
        for i in range(high+1):
            if i - zero >= 0:
                dp[i] += dp[i-zero]
            if i - one >= 0:
                dp[i] += dp[i-one]
            if low <= i <= high:
                res += dp[i]
        
        return res % (10**9 + 7)
        


        
814