Reconstruct Array from Prefix-Skip Sum

pref[i] equals the sum of all elements of the original array except the i-th one. Recover the original array. This site guarantees that an integer solution exists and that N is at least 2; N=1 cannot be determined uniquely, so it is not part of this protocol.

This site uses a standard input/output protocol.

输入格式

The first line contains N, and the second line contains N values pref. This site uses 2≤N≤100000 and −10⁹≤pref[i]≤10⁹, and an integer solution is guaranteed to exist.

输出格式

Output N integers in original index order.

样例 1

输入：

3
2 6 4

输出：

4 0 2

样例 2

输入：

3
11 9 8

输出：

3 5 6

样例 3

输入：

2
-3 5

输出：

5 -3

样例说明

Example 1: the total is 6, and the answer is 4, 0, 2. Example 2: the total is 14, and the answer is 3, 5, 6. Example 3: with two elements, each pref is the other element, so the answer is 5, −3.