Best Performances

AtCoder

IDabc306_e

Time6000ms

Memory256MB

Difficulty—

We have a sequence $A=(A_1,A_2,\dots,A_N)$ of length $N$. Initially, all the terms are $0$. Using an integer $K$ given in the input, we define a function $f(A)$ as follows: * Let $B$ be the sequence obtained by sorting $A$ in descending order (so that it becomes monotonically non-increasing). * Then, let $f(A)=B_1 + B_2 + \dots + B_K$. We consider applying $Q$ updates on this sequence. Apply the following operation on the sequence $A$ for $i=1,2,\dots,Q$ in this order, and print the value $f(A)$ at that point after each update. * Change $A_{X_i}$ to $Y_i$. ## Constraints * All input values are integers. * $1 \le K \le N \le 5 \times 10^5$ * $1 \le Q \le 5 \times 10^5$ * $1 \le X_i \le N$ * $0 \le Y_i \le 10^9$ ## Input The input is given from Standard Input in the following format: $N$ $K$ $Q$ $X_1$ $Y_1$ $X_2$ $Y_2$ $\vdots$ $X_Q$ $Y_Q$ [samples]

Samples

Input #1

Output #1

5
6
8
8
15
13
13
11
1
0

In this input, $N=4$ and $K=2$. $Q=10$ updates are applied.

*   The $1$\-st update makes $A=(5, 0,0,0)$. Now, $f(A)=5$.
*   The $2$\-nd update makes $A=(5, 1,0,0)$. Now, $f(A)=6$.
*   The $3$\-rd update makes $A=(5, 1,3,0)$. Now, $f(A)=8$.
*   The $4$\-th update makes $A=(5, 1,3,2)$. Now, $f(A)=8$.
*   The $5$\-th update makes $A=(5,10,3,2)$. Now, $f(A)=15$.
*   The $6$\-th update makes $A=(0,10,3,2)$. Now, $f(A)=13$.
*   The $7$\-th update makes $A=(0,10,3,0)$. Now, $f(A)=13$.
*   The $8$\-th update makes $A=(0,10,1,0)$. Now, $f(A)=11$.
*   The $9$\-th update makes $A=(0, 0,1,0)$. Now, $f(A)=1$.
*   The $10$\-th update makes $A=(0, 0,0,0)$. Now, $f(A)=0$.

API Response (JSON)

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  "problem": {
    "name": "Best Performances",
    "description": {
      "content": "We have a sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$. Initially, all the terms are $0$.   Using an integer $K$ given in the input, we define a function $f(A)$ as follows: *   Let $B$ be the seque",
      "description_type": "Markdown"
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    "limit": {
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      "memory_limit": 262144
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    "difficulty": "None",
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    "sign": "abc306_e"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$. Initially, all the terms are $0$.  \nUsing an integer $K$ given in the input, we define a function $f(A)$ as follows:\n\n*   Let $B$ be the seque...",
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      "language": "English"
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