Festival

AtCoder

IDabc322_c

Time2000ms

Memory256MB

Difficulty—

The AtCoder Kingdom holds a festival for $N$ days. On $M$ of these days, namely on the $A_1$\-th, $A_2$\-th, $\dots$, $A_M$\-th days, fireworks will be launched. It is guaranteed that fireworks will be launched on the last day of the festival. (In other words, $A_M=N$ is guaranteed.) For each $i=1,2,\dots,N$, solve the following problem. * How many days later from the $i$\-th day will fireworks be launched for the first time on or after the $i$\-th day? If fireworks are launched on the $i$\-th day, it is considered to be $0$ days later. ## Constraints * $1 \le M \le N \le 2 \times 10^5$ * $1 \le A_1 < A_2 < \dots < A_M = N$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $\dots$ $A_M$ [samples]

Samples

Input #1

3 2
2 3

Output #1

1
0
0

The kingdom holds a festival for $3$ days, and fireworks are launched on the $2$\-nd and $3$\-rd days.

*   From the $1$\-st day, the first time fireworks are launched is the $2$\-nd day of the festival, which is $1$ day later.
*   From the $2$\-nd day, the first time fireworks are launched is the $2$\-nd day of the festival, which is $0$ days later.
*   From the $3$\-rd day, the first time fireworks are launched is the $3$\-rd day of the festival, which is $0$ days later.

Input #2

8 5
1 3 4 7 8

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Festival",
    "description": {
      "content": "The AtCoder Kingdom holds a festival for $N$ days. On $M$ of these days, namely on the $A_1$\\-th, $A_2$\\-th, $\\dots$, $A_M$\\-th days, fireworks will be launched. It is guaranteed that fireworks will b",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc322_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The AtCoder Kingdom holds a festival for $N$ days. On $M$ of these days, namely on the $A_1$\\-th, $A_2$\\-th, $\\dots$, $A_M$\\-th days, fireworks will be launched. It is guaranteed that fireworks will b...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments