<div><p>You have an infinite number of stacks arranged in a row and numbered (left to right) from 0, each of the stacks has the same maximum <code>capacity</code>.</p>
<p>Implement the <code>DinnerPlates</code> class:</p>
<ul>
<li><code>DinnerPlates(int capacity)</code> Initializes the object with the maximum <code>capacity</code> of the stacks.</li>
<li><code>void push(int val)</code> Pushes the given positive integer <code>val</code> into the leftmost stack with size less than <code>capacity</code>.</li>
<li><code>int pop()</code> Returns the value at the top of the rightmost non-empty stack and removes it from that stack, and returns <code>-1</code> if all stacks are empty.</li>
<li><code>int popAtStack(int index)</code> Returns the value at the top of the stack with the given <code>index</code> and removes it from that stack, and returns -1 if the stack with that given <code>index</code> is empty.</li>
</ul>
<p><strong>Example:</strong></p>
<pre><b>Input: </b>
["DinnerPlates","push","push","push","push","push","popAtStack","push","push","popAtStack","popAtStack","pop","pop","pop","pop","pop"]
[[2],[1],[2],[3],[4],[5],[0],[20],[21],[0],[2],[],[],[],[],[]]
<b>Output: </b>
[null,null,null,null,null,null,2,null,null,20,21,5,4,3,1,-1]
<b>Explanation: </b>
DinnerPlates D = DinnerPlates(2); // Initialize with capacity = 2
D.push(1);
D.push(2);
D.push(3);
D.push(4);
D.push(5); // The stacks are now: 2 4
1 3 5
﹈ ﹈ ﹈
D.popAtStack(0); // Returns 2. The stacks are now: 4
1 3 5
﹈ ﹈ ﹈
D.push(20); // The stacks are now: 20 4
1 3 5
﹈ ﹈ ﹈
D.push(21); // The stacks are now: 20 4 21
1 3 5
﹈ ﹈ ﹈
D.popAtStack(0); // Returns 20. The stacks are now: 4 21
1 3 5
﹈ ﹈ ﹈
D.popAtStack(2); // Returns 21. The stacks are now: 4
1 3 5
﹈ ﹈ ﹈
D.pop() // Returns 5. The stacks are now: 4
1 3
﹈ ﹈
D.pop() // Returns 4. The stacks are now: 1 3
﹈ ﹈
D.pop() // Returns 3. The stacks are now: 1
﹈
D.pop() // Returns 1. There are no stacks.
D.pop() // Returns -1. There are still no stacks.
</pre>
<p> </p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 <= capacity <= 20000</code></li>
<li><code>1 <= val <= 20000</code></li>
<li><code>0 <= index <= 100000</code></li>
<li>At most <code>200000</code> calls will be made to <code>push</code>, <code>pop</code>, and <code>popAtStack</code>.</li>
</ul>
</div>