You are given an array $A$ of size $N$. You must perform $Q$ queries on it. There are two types of queries:

• Change pos val: In this operation, you are required to change the value of $A[pos]$ to $val$.
• Poly L R: You must answer whether there exists a polynomial $P$ such that $P(A[k]) = k$ for every $k$ between $L$ and $R$ $(L \le k \le R)$.

Input format

• The first line of the input contains two integers $N$ and $Q$.
• The next line contains $N$ integers describing the initial array.
• The next $Q$ lines describe a query each. A change operation is denoted by 0 pos val and a question is denoted by 1 L R.
  Note: The array is 1-indexed.

Output format

For each query of the second type, print a line containing Yes or No.

Constraints 

$N,\ Q \le 4 \times 10^5$

For a test set worth 30 points, it holds that $N,\ Q \le 10^3$.

All the numbers initially and after each update, are between 1 and $4\times 10^5$.