A16325 | Ones and Twos

You are given a $1$ -indexed array $a$ of length $n$ where each element is $1$ or $2$ .

Process $q$ queries of the following two types:

- "1 s": check if there exists a subarray $^{\dagger}$ of $a$ whose sum equals to $s$ .
- "2 i v": change $a_i$ to $v$ .

$^{\dagger}$ An array $b$ is a subarray of an array $a$ if $b$ can be obtained from $a$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. In particular, an array is a subarray of itself.

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. The description of the test cases follows.

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

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ( $a_i$ is $1$ or $2$ ) — the elements of array $a$ .

Each of the following $q$ lines of each test case contains some integers. The first integer $\mathrm{op}$ is either $1$ or $2$ .

- If $\mathrm{op}$ is $1$ , it is followed by one integer $s$ ( $1 \leq s \leq 2n$ ).
- If $\mathrm{op}$ is $2$ , it is followed by two integers $i$ and $v$ ( $1 \leq i \leq n$ , $v$ is $1$ or $2$ ).

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

For each query with $\mathrm{op}=1$ , output "YES" in one line if there exists a subarray of $a$ whose sum is equals to $s$ , otherwise output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.