A Range Update Problem

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Points: 7
Time limit: 2.0s
Memory limit: 64M

Problem type

You are given an array a of length N. There are Q updates of the form l r v, which means to add v to all elements in the subarray [l, r].

You would like to know the array after these updates.

Input Specification

The first line will contain two integers, N, Q (1 \le N, Q \le 10^5).

The second line will contain N integers, a_1, a_2, \ldots, a_N (0 \le a_i \le 10^9), the initial array.

The next Q lines will each contain an update of the form described above. It is guaranteed 1 \le l \le r and 1 \le v \le 10^9.

Output Specification

Output the array after these updates on a single line.


Subtask [20%]

N, Q \le 100

Subtask [80%]

No further constraints.

Sample Input

5 4
1 2 3 0 2
1 3 2
1 5 1
3 4 10
2 2 1

Sample Output

4 6 16 11 3


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