Daylight

Noah owns an unrooted tree with $n$ vertices numbered from 1 to $n$. Every morning Noah picks two vertices $u$ and $v$ to receive influence from daylight. The influence spreads through the edges, but it disappears once it has passed through more than $w$ edges.

For each day, count the vertices influenced by the daylight. The input is encrypted, so your solution must work online.

The first line contains $T$, the number of test cases.

For each test case, the first line contains $n$ and $m$. Each of the next $n-1$ lines contains $u$ and $v$, an edge between vertices $u$ and $v$.

Let $lastans$ be the answer to the previous day. At the start of each test case, $lastans$ is 0. Each of the next $m$ lines contains $u'$, $v'$, and $w'$, and the actual values are

$u = ((u' + lastans) \bmod n) + 1,\quad v = ((v' + lastans) \bmod n) + 1,\quad w = (w' + lastans) \bmod n$

Constraints: $1 \le T \le 100$, $1 \le n, m \le 10^5$, $1 \le u, v, u', v' \le n$, $0 \le w' < n$.

No more than 10 test cases fail to satisfy $n, m \le 10^3$, and the input file is at most 32 MiB.

For each day, print the answer on one line.

The output file is at most 7 MiB.

The decrypted values are as follows. Day 1: $u = 1$, $v = 2$, $w = 0$. Day 2: $u = 1$, $v = 2$, $w = 1$. Day 3: $u = 1$, $v = 2$, $w = 2$. Day 4: $u = 1$, $v = 2$, $w = 3$. Day 5: $u = 1$, $v = 2$, $w = 4$.