19658번 - Labels 다국어

Today is the first day of work for Charles the Courier. He has been tasked with delivering N packages where each package has a (not necessarily unique) label number between 1 and N inclusive. At the end of each day, he is required to report a sequence A of N integers A₁, . . . , A_N where A_i is the label number of the i^th delivered package.

A mathematician at heart, Charles decides to use delta encoding to save on memory space and records a sequence D of N − 1 integers D₁, . . . , D_N−1 instead, where D_i = A_i+1 − A_i.

After delivering all the packages, Charles realises that he does not know how to recover A from D. Your task today is to help him, or state that it is not possible to uniquely recover A.

Your program must read from standard input.

The first line contains a single integer N, the total number of packages.

The second line contains N − 1 space-separated integers, D₁, . . . , D_N−1. D_i represents the difference between the label numbers of the (i + 1)^th and i^th delivered package.

Your program must print to standard output.

If it is possible to uniquely recover A from D, your output should contain N space-separated integers, the sequence A.

Otherwise, your output should contain a single integer on a single line, the integer -1.

• 2 ≤ N ≤ 3 × 10⁵
• 1 ≤ A_i ≤ N
• −N < D_i < N