CF1807D.Odd Queries

You have an array $a_1, a_2, \dots, a_n$. Answer $q$ queries of the following form:

• If we change all elements in the range $a_l, a_{l+1}, \dots, a_r$ of the array to $k$, will the sum of the entire array be odd?

Note that queries are independent and do not affect future queries.

你有一个数组 $a_1, a_2, \dots, a_n$。请回答 $q$ 个如下形式的查询：

• 如果我们将数组中区间 $a_l, a_{l+1}, \dots, a_r$ 内的所有元素都修改为 $k$，那么整个数组的元素和是否为奇数？

注意：各次查询相互独立，不会影响后续查询。

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

The first line of each test case consists of $2$ integers $n$ and $q$ ($1 \le n \le 2 \cdot 10^5$; $1 \le q \le 2 \cdot 10^5$) — the length of the array and the number of queries.

The second line of each test case consists of $n$ integers $a_i$ ($1 \le a_i \le 10^9$) — the array $a$.

The next $q$ lines of each test case consists of $3$ integers $l,r,k$ ($1 \le l \le r \le n$; $1 \le k \le 10^9$) — the queries.

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$, and the sum of $q$ doesn't exceed $2 \cdot 10^5$.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10^4$）。随后是各测试用例的描述。

每个测试用例的第一行包含两个整数 $n$ 和 $q$（$1 \le n \le 2 \cdot 10^5$；$1 \le q \le 2 \cdot 10^5$）——分别表示数组的长度和查询的数量。

每个测试用例的第二行包含 $n$ 个整数 $a_i$（$1 \le a_i \le 10^9$）——即数组 $a$。

每个测试用例的接下来 $q$ 行，每行包含三个整数 $l, r, k$（$1 \le l \le r \le n$；$1 \le k \le 10^9$）——表示一次查询。

保证所有测试用例的 $n$ 之和不超过 $2 \cdot 10^5$，且所有测试用例的 $q$ 之和不超过 $2 \cdot 10^5$。

For each query, output "YES" if the sum of the entire array becomes odd, and "NO" otherwise.

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.

对于每个查询，如果整个数组的和变为奇数，则输出“YES”；否则输出“NO”。

您可以以任意大小写形式输出答案（大写或小写均可）。例如，字符串 “yEs”、“yes”、“Yes” 和 “YES” 均会被识别为肯定回答。

For the first test case:

• If the elements in the range $(2, 3)$ would get set to $3$ the array would become ${2, 3, 3, 3, 2}$, the sum would be $2+3+3+3+2 = 13$ which is odd, so the answer is "YES".
• If the elements in the range $(2, 3)$ would get set to $4$ the array would become ${2, 4, 4, 3, 2}$, the sum would be $2+4+4+3+2 = 15$ which is odd, so the answer is "YES".
• If the elements in the range $(1, 5)$ would get set to $5$ the array would become ${5, 5, 5, 5, 5}$, the sum would be $5+5+5+5+5 = 25$ which is odd, so the answer is "YES".
• If the elements in the range $(1, 4)$ would get set to $9$ the array would become ${9, 9, 9, 9, 2}$, the sum would be $9+9+9+9+2 = 38$ which is even, so the answer is "NO".
• If the elements in the range $(2, 4)$ would get set to $3$ the array would become ${2, 3, 3, 3, 2}$, the sum would be $2+3+3+3+2 = 13$ which is odd, so the answer is "YES".

对于第一个测试用例：

• 如果将区间 $(2, 3)$ 内的元素全部设为 $3$，数组将变为 ${2, 3, 3, 3, 2}$，其和为 $2+3+3+3+2 = 13$，是奇数，因此答案为 “YES”。
• 如果将区间 $(2, 3)$ 内的元素全部设为 $4$，数组将变为 ${2, 4, 4, 3, 2}$，其和为 $2+4+4+3+2 = 15$，是奇数，因此答案为 “YES”。
• 如果将区间 $(1, 5)$ 内的元素全部设为 $5$，数组将变为 ${5, 5, 5, 5, 5}$，其和为 $5+5+5+5+5 = 25$，是奇数，因此答案为 “YES”。
• 如果将区间 $(1, 4)$ 内的元素全部设为 $9$，数组将变为 ${9, 9, 9, 9, 2}$，其和为 $9+9+9+9+2 = 38$，是偶数，因此答案为 “NO”。
• 如果将区间 $(2, 4)$ 内的元素全部设为 $3$，数组将变为 ${2, 3, 3, 3, 2}$，其和为 $2+3+3+3+2 = 13$，是奇数，因此答案为 “YES”。