CF1746F Kazaee

题目描述

You have an array $a$ consisting of $n$ positive integers and you have to handle $q$ queries of the following types:

• $1$ $i$ $x$ : change $a_{i}$ to $x$ ,
• $2$ $l$ $r$ $k$ : check if the number of occurrences of every positive integer in the subarray $a_{l}, a_{l+1}, \ldots a_{r}$ is a multiple of $k$ (check the example for better understanding).

输入格式

The first line of the input contains two integers $n$ and $q$ ( $1 \le n , q \le 3 \cdot 10^5$ ), the length of $a$ and the number of queries.

Next line contains $n$ integers $a_{1}, a_{2}, \ldots a_{n}$ ( $1 \le a_{i} \le 10^9$ ) — the elements of $a$ .

Each of the next $q$ lines describes a query. It has one of the following forms.

• $1$ $i$ $x$ , ( $1 \le i \le n$ , $1 \le x \le 10^9$ ), or
• $2$ $l$ $r$ $k$ , ( $1 \le l \le r \le n$ , $1 \le k \le n$ ).

输出格式

For each query of the second type, if answer of the query is yes, print "YES", otherwise print "NO".

输入输出样例 #1

输入 #1

10 8
1234 2 3 3 2 1 1 2 3 4
2 1 6 2
1 1 1
2 1 6 2
2 1 9 2
1 10 5
2 1 9 3
1 3 5
2 3 10 2

输出 #1

NO
YES
NO
YES
YES

说明/提示

In the first query, requested subarray is $[1234, 2, 3, 3, 2, 1]$ , and it's obvious that the number of occurrence of $1$ isn't divisible by $k = 2$ . So the answer is "NO".

In the third query, requested subarray is $[1, 2, 3, 3, 2, 1]$ , and it can be seen that the number of occurrence of every integer in this sub array is divisible by $k = 2$ . So the answer is "YES".

In the sixth query, requested subarray is $[1, 2, 3, 3, 2, 1, 1, 2, 3]$ , and it can be seen that the number of occurrence of every integer in this sub array is divisible by $k = 3$ . So the answer is "YES".