[Solution] Narrow road Codeforces Solution VK Cup

A. Narrow road

test time limit

2 seconds

memory limit per test

512 megabytes

input

standard input

conclusion

standard output

Column from𝑛$n$scooter rides on a narrow one-way road to point B. The scooters are numbered from1$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1</span></span>}$to𝑛$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">n</span></span>}$. For every scooter𝑖$i$it is known that the current distance from it to point B is equal to𝑎𝑖$a_{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">i</span></span>}}$meters. Wherein𝑎1<𝑎2<…<𝑎𝑛${\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">a</span></span>}}_{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1</span></span>}}<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><</span></span>{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">a</span></span>}}_{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</span></span>}}<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><</span></span>\dots <span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><</span></span>{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">a</span></span>}}_{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">n</span></span>}}$in particular scooter1$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1</span></span>}$is closest to point B, and the scooter𝑛$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">n</span></span>}$ - farthest.

Scooter with number𝑖$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">i</span></span>}$moves towards point B with a speed𝑖$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">i</span></span>}$meters per second (that is, the closer the scooter in the convoy is to point B, the slower it goes). Since the road is narrow, the scooters cannot overtake each other. Moreover, neighboring scooters in a column must keep a distance of at least1$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1</span></span>}$meter. Therefore, when a faster scooter catches up with a slower one, the faster one has to go further at the speed of the slower one, and at a distance of1$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1</span></span>}$meter from him.

Determine how far each scooter will be to point B in exactly one second.

Input data

The first line contains one integer𝑛$n$ (1≤𝑛≤100$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1</span></span>}\le \mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">n</span></span>}<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">\le </span></span>100$) is the number of scooters in the column.

AT𝑖$i$th of the following𝑛$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">n</span></span>}$rows given one integer𝑎𝑖$a_{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">i</span></span>}}$(1≤𝑎𝑖≤1000$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1</span></span>}<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">\le </span></span>{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">a</span></span>}}_{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">i</span></span>}}<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">\le </span></span>1000$; 𝑎1<𝑎2<…<𝑎𝑛${\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">a</span></span>}}_{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1</span></span>}}<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><</span></span>{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">a</span></span>}}_{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</span></span>}}<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><</span></span>\dots <span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><</span></span>{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">a</span></span>}}_{\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">n</span></span>}}$) — current distance from the scooter𝑖$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">i</span></span>}$to point B in meters.

Output

Bring out𝑛$n$integers — distances from scooters1,2,…,𝑛$1,2<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">,</span></span>\dots <span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">,</span></span>\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">n</span></span>}$to point B in meters in one second.

Note

In the first test, the scooters do not interfere with each other so far, so each scooter𝑖$i$advances on𝑖$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">i</span></span>}$meters towards point B.

In the second test, the scooters have already lined up in a column at a distance1$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1</span></span>}$meter apart and forced to ride at the speed of the slowest scooter with the number1$\mathrm{<span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><span\; style="transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1</span></span>}$.