Sum of Three Terms

AtCoder

IDarc135_b

Time2000ms

Memory256MB

Difficulty—

You are given a sequence of $N$ integers $S = (S_1, \ldots, S_N)$. Determine whether there is a sequence of $N+2$ integers $A = (A_1, \ldots, A_{N+2})$ that satisfies the conditions below. * $0\leq A_i$ for every $i$ ($1\leq i\leq N+2$). * $S_i = A_{i} + A_{i+1} + A_{i+2}$ for every $i$ ($1\leq i\leq N$). If it exists, print one such sequence. ## Constraints * $1\leq N\leq 3\times 10^5$ * $0\leq S_i\leq 10^9$ ## Input Input is given from Standard Input from the following format: $N$ $S_1$ $\ldots$ $S_N$ [samples]

Samples

Input #1

5
6 9 6 6 5

Output #1

Yes
0 4 2 3 1 2 2

We can verify that $S_i = A_i + A_{i+1} + A_{i+2}$ for every $i$ ($1\leq i\leq N$), as follows.

*   $6 = 0 + 4 + 2$.
*   $9 = 4 + 2 + 3$.
*   $6 = 2 + 3 + 1$.
*   $6 = 3 + 1 + 2$.
*   $5 = 1 + 2 + 2$.

Input #2

5
0 1 2 1 0

Output #2

No

Input #3

1
10

Output #3

Yes
0 0 10

API Response (JSON)

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      "content": "You are given a sequence of $N$ integers $S = (S_1, \\ldots, S_N)$. Determine whether there is a sequence of $N+2$ integers $A = (A_1, \\ldots, A_{N+2})$ that satisfies the conditions below.\n\n*   $0\\leq...",
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