The Kingdom of Takahashi has N towns, numbered 1 through N.

There is one teleporter in each town. The teleporter in Town $i (1 \leq i \leq N)$ sends you to Town A_i.

Takahashi, the king, loves the positive integer K. The selfish king wonders what town he will be in if he starts at Town 1 and uses a teleporter exactly K times from there.

Help the king by writing a program that answers this question.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq N$
• $1 \leq K \leq 10^{18}$

Input

Input is given from Standard Input in the following format:

N K
$A_1 A_2 \dots A_N$

Output

Print the integer representing the town the king will be in if he starts at Town 1 and uses a teleporter exactly K times from there.

Examples

Input

4 5
3 2 4 1

Output

4

Input

6 727202214173249351
6 5 2 5 3 2

Output

2

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