**Can I Win** In the “100 game” two players take turns adding, to a running total, any integer from `1`

to `10`

. The player who first causes the running total to **reach or exceed** 100 wins.

What if we change the game so that players **cannot** re-use integers?

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.

Given two integers `maxChoosableInteger`

and `desiredTotal`

, return `true`

if the first player to move can force a win, otherwise, return `false`

. Assume both players play **optimally**.

**Example 1:**

Input:maxChoosableInteger = 10, desiredTotal = 11Output:falseExplanation: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.

**Example 2:**

Input:maxChoosableInteger = 10, desiredTotal = 0Output:true

**Example 3:**

Input:maxChoosableInteger = 10, desiredTotal = 1Output:true

**Constraints:**

`1 <= maxChoosableInteger <= 20`

`0 <= desiredTotal <= 300`

### Can I Win Solutions

✅**Time:** O(n)

✅**Space:** O(n)

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