Scheduler

In the multitasking operating system <> there are $N$ processes running. Each process has a priority $p_i$, which affects how often the process runs. The system has only one core on one processor to run things, so it has to distribute CPU time among these processes while taking their priorities into account.

The algorithm that decides which process runs at each moment works as follows. Besides the priority $p_i$, each process also has a counter $t_i$. Initially all $t_i$ equal 0. Then every second:

1. The processes with the maximum value of $p_i + t_i$ are chosen.
2. Among those processes, the process with the smallest number $i$ is chosen.
3. The chosen process $i$ runs for one second.
4. For the chosen process $i$, the value of $t_i$ is set to 0.
5. For all other processes, the value of $t_i$ is increased by 1.

Model the work of the operating system for $T$ seconds and calculate how many seconds each process ran. All calculations and switches between processes are instant, so the running time of each process is an integer number of seconds.

The first line contains two space-separated integers $N$ and $T$: the number of processes in the operating system ($1 \le N \le 10^5$) and the number of seconds to be modeled ($1 \le T \le 10^6$).

The second line contains $N$ space-separated integers $p_i$: the process priorities ($0 \le p_i \le 10^5$).

In the only line of the output, print $N$ space-separated integers: how many seconds each of the processes ran.