Given an array of n integers, your task is to process q queries of the following types:

1. update the value at position k to u
2. check if every value in range [a, b] is distinct

Input

The first line has two integers n and q: the number of values and queries.

The second line has n integers x_1, x_2,\dots, x_n: the array values.

Finally, there are q lines describing the queries. Each line has three integers: either "1 k u" or "2 a b".

Output

For each query of type 2, print YES if every value in the range is distinct and NO otherwise.

Constraints

• 1 \le n, q \le 2 \cdot 10^5
• 1 \le x_i, u \le 10^9
• 1 \le k \le n
• 1 \le a \le b \le n

Example

Input:

5 4
3 2 7 2 8
2 3 5
2 2 5
1 2 9
2 2 5

Output:

YES
NO
YES