Problem:
Score: 400 points

Problem Statement

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.

Sample Input 1

4 5
3 2 4 1

Sample Output 1

4

If we start at Town 1 and use the teleporter 5 times, our travel will be as follows: 1 \to 3 \to 4 \to 1 \to 3 \to 4.

Sample Input 2

6 727202214173249351
6 5 2 5 3 2

Sample Output 2

2

Solution in Lua (LuaJIT 2.1.0) (judge verdict: Wrong Answer)

N=io.read"*n"
K=io.read"*n"
A={}
for i=1,N do
	A[i]=io.read"*n"
end

local function count(t)local r=0 for _,_ in pairs(t)do r=r+1 end return r end

B={[1]=0}
C={[0]=1}
for i=1,math.min(N,K) do
	C[i]=A[C[i-1]]
	if(B[C[i]])then
		t=C[i]
		for j=i-1,1,-1 do
			if(C[j]==t)then
				print(C[j+(K-j)%(i-j)])
				return
			end
		end
	end
	B[C[i]]=0
end
print(C[K])