Inverse Prefix Sum

AtCoder

IDabc280_b

Time2000ms

Memory256MB

Difficulty—

You are given an integer $N$ and a sequence $S=(S_1,\ldots,S_N)$ of length $N$. Find a sequence $A=(A_1,\ldots,A_N)$ of length $N$ that satisfies the following condition for all $k=1,\ldots,N$: * $A_1+A_2+\ldots+A_k = S_k$. Such a sequence $A$ always exists and is unique. ## Constraints * $1 \leq N \leq 10$ * $-10^9\leq S_i \leq 10^9$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $S_1$ $\ldots$ $S_N$ [samples]

Samples

Input #1

3
3 4 8

Output #1

3 1 4

The sequence in the output actually satisfies all the conditions:

*   $A_1=3=S_1$;
*   $A_1+A_2=3+1=4=S_2$;
*   $A_1+A_2+A_3=3+1+4=8=S_3$.

Input #2

10
314159265 358979323 846264338 -327950288 419716939 -937510582 97494459 230781640 628620899 -862803482

Output #2

314159265 44820058 487285015 -1174214626 747667227 -1357227521 1035005041 133287181 397839259 -1491424381

API Response (JSON)

{
  "problem": {
    "name": "Inverse Prefix Sum",
    "description": {
      "content": "You are given an integer $N$ and a sequence $S=(S_1,\\ldots,S_N)$ of length $N$. Find a sequence $A=(A_1,\\ldots,A_N)$ of length $N$ that satisfies the following condition for all $k=1,\\ldots,N$: *   $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc280_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer $N$ and a sequence $S=(S_1,\\ldots,S_N)$ of length $N$.\nFind a sequence $A=(A_1,\\ldots,A_N)$ of length $N$ that satisfies the following condition for all $k=1,\\ldots,N$:\n\n*   $...",
      "is_translate": false,
      "language": "English"
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}

Full JSON Raw Segments