+⊕ and query

Two sequences $A=(A_1,A_2,\cdots,A_N)$ and $B=(B_1,B_2,\cdots,B_N)$ of length $N$ are given.

You may perform either of the following operations on $A$ any number of times.

• Choose an integer $x$ and replace $A_i$ with $A_i+x$ for every $i$. Every element must be nonnegative after the operation.
• Choose a nonnegative integer $x$ and replace $A_i$ with $A_i\mathbin{\mathrm{xor}}x$ for every $i$.

Here, $\mathrm{xor}$ denotes the bitwise XOR operation.

We want to determine whether $A$ can be made equal to $B$ by performing these operations appropriately.

There are $Q$ queries. Each query has one of the following forms.

• 1 $i$ $x$: Replace $A_i$ with $x$.
• 2 $i$ $x$: Replace $B_i$ with $x$.

After each query, determine whether the current $A$ can be made equal to the current $B$ by performing the operations any number of times.

The input is given from Standard Input in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$

Each case is given in the following format:

$N\ Q$ $A_1\ A_2\ \cdots\ A_N$ $B_1\ B_2\ \cdots\ B_N$ $\mathrm{query}_1$ $\mathrm{query}_2$ $\vdots$ $\mathrm{query}_Q$

Each query is given in the form 1 $i$ $x$ or 2 $i$ $x$.

For each query of each test case, print YES if the current $A$ can be transformed into the current $B$, and print NO otherwise.

• $1 \leq T \leq 20$.
• $1 \leq N,Q \leq 200\,000$.
• The sum of $N$ over all test cases does not exceed $200\,000$.
• The sum of $Q$ over all test cases does not exceed $200\,000$.
• $0 \leq A_i,B_i \leq 10^9$ ($1 \leq i \leq N$).
• Each query has the form 1 $i$ $x$ or 2 $i$ $x$.
• $1 \leq i \leq N$.
• $0 \leq x \leq 10^9$.