Permutation Period

You have a permutation $p$ of $N$ integers. Initially $p_i = i$ holds for $1 \le i \le N$. For each $j \ (1 \le j \le N)$, let $p^0_j = j$ and $p^k_j = p^{k-1}_{p_j}$ for any $k \ge 1$. The period of $p$ is the minimum positive integer $k$ such that $p^k_j = j$ for every $j \ (1 \le j \le N)$.

You are given $Q$ queries. The $i$-th query is given by two distinct indices $x_i$ and $y_i$. For each query, swap $p_{x_i}$ and $p_{y_i}$, then compute the period of the updated $p$ modulo $10^9 + 7$, in the given order.

The period of $p$ always exists.

The input consists of a single test case of the following format.

$N \ Q$
$x_1 \ y_1$
$\vdots$
$x_Q \ y_Q$

The first line contains two integers $N$ and $Q$ ($2 \le N \le 10^5, 1 \le Q \le 10^5$). The $(i+1)$-th line contains two integers $x_i$ and $y_i$ ($1 \le x_i, y_i \le N, x_i \ne y_i$).

For each query, print the answer on its own line.