Marisa planted n apple trees in a row. There are q rainy days. On each day i, a certain amount of rainwater, denoted as wi liters, was received by each tree within the range [li,ri].
Each tree, denoted as the ith tree, requires a specific amount of water, denoted as Ai liters, in order to undergo mutation. Marisa seeks to determine the day on which each tree mutates.
### Input
- The first line contains two integers n,q.
- The second line contains n integer Ai.
- The next q lines, each line three integers li,ri,wi.
### Output
- Print n integers, the ith one is the day on which tree i mutates. Or print −1 if it won't mutate.
### Constraints
- 1≤n,q≤105
- 1≤li≤ri≤n.
- 1≤wi,Ai≤109.
### Example
Input:
5337216153232353
Output:
1−1113