Teleporter

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

inputFormat

Input

Input is given from Standard Input in the following format:

N K A_1 A_2 \dots A_N

outputFormat

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

样例

6 727202214173249351
6 5 2 5 3 2

2