Jayden has an array $a$ which is initially empty. There are $n$ operations of two types he must perform in the given order.

1. Jayden appends an integer $x$ ($1 \leq x \leq n$) to the end of array $a$.
2. Jayden appends $x$ copies of array $a$ to the end of array $a$. In other words, array $a$ becomes $[a,\underbrace{a,\ldots,a}_{x}]$. It is guaranteed that he has done at least one operation of the first type before this.

Jayden has $q$ queries. For each query, you must tell him the $k$-th element of array $a$. The elements of the array are numbered from $1$.

Input

Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 5000$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $n$ and $q$ ($1 \leq n, q \leq 10^5$) — the number of operations and the number of queries.

The following $n$ lines describe the operations. Each line contains two integers $b$ and $x$ ($b \in \{1, 2\}$), where $b$ denotes the type of operation. If $b=1$, then $x$ ($1 \leq x \leq n$) is the integer Jayden appends to the end of the array. If $b=2$, then $x$ ($1 \leq x \leq 10^9$) is the number of copies Jayden appends to the end of the array.

The next line of each test case contains $q$ integers $k_1, k_2, \ldots, k_q$ ($1 \leq k_i \leq \min(10^{18}, c)$), which denote the queries, where $c$ is the size of the array after finishing all $n$ operations.

It is guaranteed that the sum of $n$ and the sum of $q$ over all test cases does not exceed $10^5$.

Output

For each test case, output $q$ integers — answers to Jayden's queries.

Note

In the first test case:

• After the first operation $a = [1]$;
• After the second operation $a = [1, 2]$;
• After the third operation $a = [1, 2, 1, 2]$;
• After the fourth operation $a = [1, 2, 1, 2, 3]$;
• After the fifth operation $a = [1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3]$.

In the fourth test case, after all operations $a = [1, 2]$.