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 (Lua 5.3.5) (judge verdict: Runtime Error)


local n = io.read("*n")
local k = io.read("*n")
local tbA = {}
for i = 1,n do
    table.insert(tbA,io.read("*n"))
end

function isNumInTb(num,tb)
    for k,v in ipairs(tb) do
        if v == num then
            return k
        end
    end
    return 0
end

-- function print_tb(tb)
--     for k,v in ipairs(tb) do
--         print(v.." ")
--     end
-- end

local new_tb = {}
local new_new_tb = {}
local idx = 0

local i = 1
while tbA[i] do
    if isNumInTb(i,new_tb) > 0 then
        
        local j = isNumInTb(i,new_tb)
        idx = isNumInTb(i,new_tb)
        for m=idx,#new_tb do
            table.insert(new_new_tb,new_tb[m])
            j = j + 1
        end
        break
    else
        table.insert(new_tb,i)
        i = tbA[i]
    end
end
k = k - idx + 1
local numTb = #new_new_tb

local kk = math.mod(k,numTb)
if kk==0 then kk = kk + numTb end
print(tbA[new_new_tb[kk]])

-- for i = 1, string.len(a) do
--     table.insert(b,string.sub(a,i,i))
-- end