Contiguous Range Query and Update

You are given a sequence a of length n. You need to perform q operations, which are of two types:

1. Update: Change the value at position x to y.
2. Query: Check whether the subsequence in the interval [l, r] can be rearranged to form a contiguous segment of distinct integers.

A subsequence can be rearranged to form a contiguous segment if and only if all the numbers are distinct and if max - min = r - l (using 1-indexed positions), where max and min denote the maximum and minimum values in the interval, respectively. For example, the segment 1 2 2 3 is invalid due to duplicate numbers, while 4 2 3 1 is valid because when rearranged it becomes 1 2 3 4, which is a contiguous range.

Input and Output Formats are described below.

inputFormat

The first line contains two integers n and q (1 ≤ n, q ≤ 10^5 in general, though the constraints for this problem may be smaller).

The second line contains n integers, representing the initial sequence a (1-indexed).

Each of the next q lines describes an operation in one of the following formats:

• 1 x y — update the value at position x to y.
• 2 l r — query whether the subarray from l to r (inclusive) can be rearranged to form a contiguous segment of integers.

outputFormat

For each query operation (operation of type 2), output a single line containing Yes if the segment can be rearranged into a contiguous range, or No otherwise.

sample

5 5
4 2 1 3 9
2 1 4
2 2 5
1 5 5
2 2 5
2 1 5

Yes
No
No
Yes