<p>In the "100 game" two players take turns adding, to a running total, any integer from <code>1</code> to <code>10</code>. The player who first causes the running total to <strong>reach or exceed</strong> 100 wins.</p> <p>What if we change the game so that players <strong>cannot</strong> re-use integers?</p> <p>For example, two players might take turns drawing from a common pool of numbers from 1 to 15 without replacement until they reach a total >= 100.</p> <p>Given two integers <code>maxChoosableInteger</code> and <code>desiredTotal</code>, return <code>true</code> if the first player to move can force a win, otherwise, return <code>false</code>. Assume both players play <strong>optimally</strong>.</p> <p> </p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> maxChoosableInteger = 10, desiredTotal = 11 <strong>Output:</strong> false <strong>Explanation:</strong> No matter which integer the first player choose, the first player will lose. The first player can choose an integer from 1 up to 10. If the first player choose 1, the second player can only choose integers from 2 up to 10. The second player will win by choosing 10 and get a total = 11, which is >= desiredTotal. Same with other integers chosen by the first player, the second player will always win. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> maxChoosableInteger = 10, desiredTotal = 0 <strong>Output:</strong> true </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> maxChoosableInteger = 10, desiredTotal = 1 <strong>Output:</strong> true </pre> <p> </p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 <= maxChoosableInteger <= 20</code></li> <li><code>0 <= desiredTotal <= 300</code></li> </ul>