p02684 AtCoder Beginner Contest 167 - 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
```python
n, k = map(int, input().split())
a = list(map(int, input().split()))

s = []
ord = [-1] * (n+1)

v = 1
while ord[v] == -1:
    ord[v] = len(s)
    s.append(v)
    v = a[v-1]

c = len(s) - ord[v]
l = ord[v]

ans = 0
if k < l:
    ans = s[k]
else:
    k -= l
    k %= c
    ans = s[l+k]
print(ans)




```