+⊕ 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 . Every element must be nonnegative after the operation.

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 $i$ $$: Replace with .

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:

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

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 $$ over all test cases does not exceed .