Score : $400$ points
There is an online game with $N$ registered players.
Today, which is the $10^{100}$-th day since its launch, the developer Takahashi examined the users' login history. It turned out that the $i$-th player logged in for $B_i$ consecutive days from Day $A_i$, where Day $1$ is the launch day, and did not log in for the other days.
In other words, the $i$-th player logged in on Day $A_i$, $A_i+1$, $\ldots$, $A_i+B_i-1$, and only on those days.
For each integer $k$ such that $1\leq k\leq N$, find the number of days on which exactly $k$ players logged in.
Input is given from Standard Input in the following format:
$N$ $A_1$ $B_1$ $A_2$ $B_2$ $:$ $A_N$ $B_N$
Print $N$ integers with spaces in between, as follows:
$D_1$ $D_2$ $\cdots$ $D_N$
Here, $D_i$ denotes the number of days on which exactly $k$ players logged in.
3 1 2 2 3 3 1
2 2 0
The first player logged in on Day $1$, $2$, the second player logged in on Day $2$, $3$, $4$, and the third player logged in on Day $3$ only.
Thus, we can see that Day $1$, $4$ had $1$ player logged in, Day $2$, $3$ had $2$ players logged in, and the other days had no players logged in.
The answer is: there were $2$ days with exactly $1$ player logged in, $2$ days with exactly $2$ players logged in, and $0$ days with exactly $3$ players logged in.
2 1000000000 1000000000 1000000000 1000000000
0 1000000000
There may be two or more players who logged in during the same period.