<p>You are given an integer array <code>nums</code>. Two players are playing a game with this array: player 1 and player 2.</p>

<p>Player 1 and player 2 take turns, with player 1 starting first. Both players start the game with a score of <code>0</code>. At each turn, the player takes one of the numbers from either end of the array (i.e., <code>nums[0]</code> or <code>nums[nums.length - 1]</code>) which reduces the size of the array by <code>1</code>. The player adds the chosen number to their score. The game ends when there are no more elements in the array.</p>

<p>Return <code>true</code> if Player 1 can win the game. If the scores of both players are equal, then player 1 is still the winner, and you should also return <code>true</code>. You may assume that both players are playing optimally.</p>

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

<pre>
<strong>Input:</strong> nums = [1,5,2]
<strong>Output:</strong> false
<strong>Explanation:</strong> Initially, player 1 can choose between 1 and 2. 
If he chooses 2 (or 1), then player 2 can choose from 1 (or 2) and 5. If player 2 chooses 5, then player 1 will be left with 1 (or 2). 
So, final score of player 1 is 1 + 2 = 3, and player 2 is 5. 
Hence, player 1 will never be the winner and you need to return false.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,5,233,7]
<strong>Output:</strong> true
<strong>Explanation:</strong> Player 1 first chooses 1. Then player 2 has to choose between 5 and 7. No matter which number player 2 choose, player 1 can choose 233.
Finally, player 1 has more score (234) than player 2 (12), so you need to return True representing player1 can win.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 20</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>7</sup></code></li>
</ul>

class Solution:
    def predictTheWinner(self, arr: List[int]) -> bool:
        def combinations(l=0,r=len(arr)-1,suma=0,sumb=0,turn=True):
            if l>r: return suma>=sumb
            if turn: return combinations(l+1, r, suma+arr[l], sumb, False) or combinations(l, r-1, suma+arr[r], sumb, False) 
            else: return combinations(l+1, r, suma, sumb+arr[l], True) and combinations(l, r-1, suma, sumb+arr[r], True) 
        return combinations()
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