atcoder#ABC280B. [ABC280B] Inverse Prefix Sum

[ABC280B] Inverse Prefix Sum

Score : 200200 points

Problem Statement

You are given an integer NN and a sequence S=(S1,,SN)S=(S_1,\ldots,S_N) of length NN.

Find a sequence A=(A1,,AN)A=(A_1,\ldots,A_N) of length NN that satisfies the following condition for all k=1,,Nk=1,\ldots,N:

  • A1+A2++Ak=SkA_1+A_2+\ldots+A_k = S_k.

Such a sequence AA always exists and is unique.

Constraints

  • 1N101 \leq N \leq 10
  • 109Si109-10^9\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:

NN

S1S_1 \ldots SNS_N

Output

Print the elements of a sequence A=(A1,,AN)A=(A_1,\ldots,A_N) that satisfies all the conditions in order, separated by spaces.

3
3 4 8
3 1 4

The sequence in the output actually satisfies all the conditions:

  • A1=3=S1A_1=3=S_1;
  • A1+A2=3+1=4=S2A_1+A_2=3+1=4=S_2;
  • A1+A2+A3=3+1+4=8=S3A_1+A_2+A_3=3+1+4=8=S_3.
10
314159265 358979323 846264338 -327950288 419716939 -937510582 97494459 230781640 628620899 -862803482
314159265 44820058 487285015 -1174214626 747667227 -1357227521 1035005041 133287181 397839259 -1491424381