m0464.py

"""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 = 11
* Output: false
* Explanation: 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 = 0
* Output: true

Example 3:

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

Constraints:

* 1 <= maxChoosableInteger <= 20
* 0 <= desiredTotal <= 300
"""