Two boys boyA and boyB are playing a simple game called Number Cutting Game. Now I will introduce it to you, my friend.
At the beginning of the game, a machine will generate two numbers, N(10 < N < 10 ^ 19) and K(2 <= K <= length(N)). Then boyA and boyB are take turns to play it:
When one player receives two numbers N and K, his task is to cut N into K nonempty pieces. If length(N) < K, that is to say he can not able to cut, he loses the game. Otherwise, he adds these K pieces together and get the sum SUM. Then let N = SUM and throw N and K to another player.
We assume boyA receives the two numbers from the machine firstly and they are smart enough to choose the best strategy for himself.
Now please help boyA to calculate weather he can win if he receives N and K firstly.
Here is a sample for you N = 103, K = 2.
Fisrtly, boyA receives N = 103, K = 2. He has two ways to cut like: 1|03 => 1 + 03 = 4, or 10|3 => 10 + 3 = 13.
Then, boyB receives from boyA. If boyB receives N = 4, K = 2, he loses the game. If boyB receives N = 13 and K = 2, he has only one way to cut: 1|3 = 1 + 3 = 4, then he will win the game.
So you can see boyA will win if he choose the best strategy.