<p>You are given 3 positive integers <code>zero</code>, <code>one</code>, and <code>limit</code>.</p>

<p>A <span data-keyword="binary-array">binary array</span> <code>arr</code> is called <strong>stable</strong> if:</p>

<ul>
	<li>The number of occurrences of 0 in <code>arr</code> is <strong>exactly </strong><code>zero</code>.</li>
	<li>The number of occurrences of 1 in <code>arr</code> is <strong>exactly</strong> <code>one</code>.</li>
	<li>Each <span data-keyword="subarray-nonempty">subarray</span> of <code>arr</code> with a size greater than <code>limit</code> must contain <strong>both </strong>0 and 1.</li>
</ul>

<p>Return the <em>total</em> number of <strong>stable</strong> binary arrays.</p>

<p>Since the answer may be very 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>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">zero = 1, one = 1, limit = 2</span></p>

<p><strong>Output:</strong> <span class="example-io">2</span></p>

<p><strong>Explanation:</strong></p>

<p>The two possible stable binary arrays are <code>[1,0]</code> and <code>[0,1]</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">zero = 1, one = 2, limit = 1</span></p>

<p><strong>Output:</strong> <span class="example-io">1</span></p>

<p><strong>Explanation:</strong></p>

<p>The only possible stable binary array is <code>[1,0,1]</code>.</p>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">zero = 3, one = 3, limit = 2</span></p>

<p><strong>Output:</strong> <span class="example-io">14</span></p>

<p><strong>Explanation:</strong></p>

<p>All the possible stable binary arrays are <code>[0,0,1,0,1,1]</code>, <code>[0,0,1,1,0,1]</code>, <code>[0,1,0,0,1,1]</code>, <code>[0,1,0,1,0,1]</code>, <code>[0,1,0,1,1,0]</code>, <code>[0,1,1,0,0,1]</code>, <code>[0,1,1,0,1,0]</code>, <code>[1,0,0,1,0,1]</code>, <code>[1,0,0,1,1,0]</code>, <code>[1,0,1,0,0,1]</code>, <code>[1,0,1,0,1,0]</code>, <code>[1,0,1,1,0,0]</code>, <code>[1,1,0,0,1,0]</code>, and <code>[1,1,0,1,0,0]</code>.</p>
</div>

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

<ul>
	<li><code>1 &lt;= zero, one, limit &lt;= 1000</code></li>
</ul>

class Solution:
    def numberOfStableArrays(self, zero: int, one: int, limit: int) -> int:
        dpone = [[0]*(max(one, limit)+2) for _ in range(max(zero, limit)+2)]
        dpzero = [[0]*(max(one, limit)+2) for _ in range(max(zero, limit)+2)]

        modulo = pow(10, 9) + 7
        for i in range(limit+1):
            dpzero[i][0] = 1
            dpone[0][i] = 1
        
        zerosum = 0
        onesum = 0

        for i in range(1, zero+2):
            for j in range(1, one+2):
                if j >= limit+1:
                    dpone[i][j] += dpone[i][j-1] - dpzero[i][j-1-limit]+ dpzero[i][j-1]
                else:
                    dpone[i][j] = dpone[i][j-1] + dpzero[i][j-1]

                if i >= limit+1:
                    dpzero[i][j] += dpzero[i-1][j] - dpone[i-1-limit][j] + dpone[i-1][j]
                else:
                    dpzero[i][j] = dpzero[i-1][j] + dpone[i-1][j]
 
                dpone[i][j]%=modulo
                dpzero[i][j]%=modulo

        return (dpzero[zero][one] + dpone[zero][one])%modulo
95400