No submission language available for this problem.

Description

Input

The first line of the input contains two integers $n, q$ ($2 \le n \le 10^5$, $1 \le q \le 10^5$).

The second line of the input contains $2n+1$ integers $p_1, p_2, \ldots, p_{2n+1}$ ($1 \le p_i \le 2n+1$, all $p_i$ are distinct)  — the elements of $p$.

The $i$-th of the next $q$ lines contains two integers $u_i, v_i$ ($1 \le u_i, v_i \le 2n+1$, $u_i \neq v_i$)  — indicating that you have to swap elements $p_{u_i}, p_{v_i}$ in the $i$-th update.

Output

After each update, output any $k$ $(0 \le k \le 2n)$, such that the length of the longest increasing subsequence of $(p_{k+1}, p_{k+2}, \ldots, p_{2n+1}, p_1, \ldots, p_k)$ doesn't exceed $n$, or $-1$, if there is no such $k$.

Samples

2 6
1 2 3 4 5
1 5
1 5
4 5
5 4
1 4
2 5

-1
-1
2
-1
4
0

Note

After the first update, our permutation becomes $(5, 2, 3, 4, 1)$. We can show that all its cyclic shifts have $LIS \ge 3$.

After the second update, our permutation becomes $(1, 2, 3, 4, 5)$. We can show that all its cyclic shifts have $LIS \ge 3$.

After the third update, our permutation becomes $(1, 2, 3, 5, 4)$. Its shift by $2$ is $(3, 5, 4, 1, 2)$, and its $LIS = 2$.

After the fourth update, our permutation becomes $(1, 2, 3, 4, 5)$. We can show that all its cyclic shifts have $LIS \ge 3$.

After the fifth update, our permutation becomes $(4, 2, 3, 1, 5)$. Its shift by $4$ is $(5, 4, 2, 3, 1)$, and its $LIS = 2$.

After the fifth update, our permutation becomes $(4, 5, 3, 1, 2)$. Its shift by $0$ is $(4, 5, 3, 1, 2)$, and its $LIS = 2$.