19526번 - Cups and Beans 다국어

There are $N$ cups numbered 0 through $N-1$. For each $i (1 \leq i \leq N-1)$, the cup $i$ contains $A_i$ beans, and this cup is labeled with an integer $C_i$.

Two people will play the following game:

• In each turn, the player chooses a bean from one of the cups except for the cup $0$.
• If he chooses a bean from the cup $i$, he must move it to one of the cups $i-C_i, \ldots, i-1$.
• The players take turns alternately. If a player can't choose a bean, he loses.

Who will win if both players play optimally?

$N$
$C_1$ $A_1$
$C_2$ $A_2$
$\vdots$
$C_{N-1}$ $A_{N-1}$

Print the name of the winner: "First" or "Second".

• $2 \leq N \leq 10^5$
• $1 \leq C_i \leq i$
• $0 \leq A_i \leq 10^9$
• At least one of $A_i$ is nonzero.
• All values in the input are integers.

Notes to the Sample 1:

• In the first turn, the first player must move a bean from $2$ to $1$.
• In the second turn, the second player must move a bean from $1$ to $0$.
• In the third turn, the first player can't choose a bean and loses.