Description:
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.
Input Format:
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 $$$10^5$$$.
Output Format:
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.
Note:
Consider the first example:
- The answer for the first query is "YES" because $$$a_1+a_2+a_3=2+1+2=5$$$.
- The answer for the second query is "YES" because $$$a_1+a_2+a_3+a_4=2+1+2+1=6$$$.
- The answer for the third query is "NO" because we cannot find any subarray of $$$a$$$ whose sum is $$$7$$$.
- After the fourth query, the array $$$a$$$ becomes $$$[2,1,2,2,2]$$$.
- The answer for the fifth query is "YES" because $$$a_2+a_3+a_4+a_5=1+2+2+2=7$$$.