201351: [AtCoder]ARC135 B - Sum of Three Terms
Memory Limit:1024 MB
Time Limit:2 S
Judge Style:Text Compare
Creator:
Submit:0
Solved:0
Description
Score : $500$ points
Problem Statement
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:
$N$ $S_1$ $\ldots$ $S_N$
Output
If there is a sequence $A$ that satisfies the conditions, print Yes
; otherwise, print No
.
In the case of Yes
, print an additional line containing the elements of such a sequence $A$, separated by spaces.
$A_1$ $\ldots$ $A_{N+2}$
If there are multiple sequences satisfying the conditions, you may print any of them.
Sample Input 1
5 6 9 6 6 5
Sample 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.
- $6 = 0 + 4 + 2$.
- $9 = 4 + 2 + 3$.
- $6 = 2 + 3 + 1$.
- $6 = 3 + 1 + 2$.
- $5 = 1 + 2 + 2$.
Sample Input 2
5 0 1 2 1 0
Sample Output 2
No
Sample Input 3
1 10
Sample Output 3
Yes 0 0 10