Reversible Cards 2

AtCoder

IDabc269_g

Time3000ms

Memory256MB

Difficulty—

We have $N$ cards numbered $1$ to $N$. Card $i$ has an integer $A_i$ written on the front and an integer $B_i$ written on the back. Here, $\sum_{i=1}^N (A_i + B_i) = M$. For each $k=0,1,2,...,M$, solve the following problem. > The $N$ cards are arranged so that their front sides are visible. You may choose between $0$ and $N$ cards (inclusive) and flip them. > To make the sum of the visible numbers equal to $k$, at least how many cards must be flipped? Print this number of cards. > If there is no way to flip cards to make the sum of the visible numbers equal to $k$, print $-1$ instead. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $0 \leq M \leq 2 \times 10^5$ * $0 \leq A_i, B_i \leq M$ * $\sum_{i=1}^N (A_i + B_i) = M$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_N$ $B_N$ [samples]

Samples

Input #1

Output #1

1
0
2
1
1
3
2

For $k=0$, for instance, flipping just card $2$ makes the sum of the visible numbers $0+0+0=0$. This choice is optimal.  
For $k=5$, flipping all cards makes the sum of the visible numbers $2+0+3=5$. This choice is optimal.

Input #2

2 3
1 1
0 1

Output #2

\-1
0
1
-1

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Reversible Cards 2",
    "description": {
      "content": "We have $N$ cards numbered $1$ to $N$.   Card $i$ has an integer $A_i$ written on the front and an integer $B_i$ written on the back. Here, $\\sum_{i=1}^N (A_i + B_i) = M$.   For each $k=0,1,2,...,M$, ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc269_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ cards numbered $1$ to $N$.  \nCard $i$ has an integer $A_i$ written on the front and an integer $B_i$ written on the back. Here, $\\sum_{i=1}^N (A_i + B_i) = M$.  \nFor each $k=0,1,2,...,M$, ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments