Problem Statement

You will participate in $N$ contests, numbered $1$ to $N$ in chronological order. A participant in each contest will be given a value called performance for that contest. Let $P_i$ be the performance for contest $i$. Additionally, you have a value called rating, which changes according to the performances in contests. The initial rating is $0$, and the rating after contest $n$ is $\frac{1}{n} \left(\sum_{i=1}^n P_i \right)$. However, once your rating is $B$ or higher, later contests will not affect your rating.

Before the contests, you have decided to estimate your performance in each contest. Let $a_i$ be the initial estimate of your performance in contest $i$. Process $Q$ queries in the order they are given.

In each query, you are given two integers $c$ and $x$. First, change the estimate of your performance in contest $c$ to $x$. (This change is persistent.) Then, assuming that you get the estimated performances in all $N$ contests, print your final rating after the contests.

Constraints

• $1 \leq N \leq 5 \times 10^5$
• $1 \leq B \leq 10^9$
• $1 \leq Q \leq 10^5$
• $0 \leq a_i \leq 10^9$
• $1 \leq c \leq N$
• $0 \leq x \leq 10^9$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format, where $c_i$ and $x_i$ are the $c$ and $x$ for the $i$-th query:

N B Q
a_1 a_2 \dots a_N
c_1 x_1
c_2 x_2
\vdots
c_Q x_Q

Output

Print $Q$ lines. The $i$-th line should contain the answer to the $i$-th query. Your output is considered correct if the absolute or relative error from the true answer is at most $10^{-9}$.