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Multiplying By Rotation

About Multiplying By Rotation

ณดํ†ต ž—ฐˆ˜˜ …ˆ€ ณตžกํ•œ —ฐ‚ฐด‹ค. –ด–คฒฝšฐ—„œŠ” —ฐ‚ฐฒฐ€ งˆ€ง‰ ˆซž •žœกœ ˜ฎธฐŠ” ฒƒ— ˜ํ•ด„œ –ป„ ˆ˜ žˆ‹ค.

{{| 179487 * 4 = 717948 |}}

ก  ดŸฌํ•œ †„€ ‚ฌšฉํ•˜Š” ˆ˜ฒด„— ”ฐ ‹คฅด‹ค. œ„˜ ˜ˆ œ—„œŠ” 10„ˆ˜ ‚ฌšฉํ–ˆ‹ค. 9„ˆ˜—„œ˜ —Š” ‹คŒ ฐ™‹ค.
{{|
17 * 4 = 71(base 9)
(9 * 1 + 7) * 4 = 7 * 9 + 1
|}}

ฌธ œ˜ ชจ“  ˆซžŠ” 10„ˆ˜€ •„‹ˆ‹ค..!!!

ž… ฅ€ ํ…ŠคํŠธํŒŒด‹ค. „ˆ˜,ฒซฒˆงธ ˆซž˜ งˆ€ง‰ ˆซž(the least significant digit of the first factor)™€ ‘ฒˆงธ ˆซž(second factor)กœ ตฌ„œ 3ฐœ˜ ˆ˜˜€ ํ•œ„”ฉ ž… ฅœ‹ค. ฐ ˆ˜˜Š” ณตœกœ ตฌ„œ‹ค. ‘ฒˆงธ ˆซžŠ” ํ•ด‹ „ˆ˜ณด‹ค  € ˆซžด‹ค. ž… ฅํŒŒ€ EOFกœ ‚œ‹ค.

ํ”„กœทธžจ€ ด™ …ˆ†„„ ฐ–Š” ˆซžค‘ €žฅ ž‘€ ฒซ ฒˆงธ ˆซž˜ žฆฌ ฐœˆ˜ ถœ ฅํ•œ‹ค.ถœ ฅ ํŒŒ„ ํ…ŠคํŠธํŒŒกœ ํ•œ‹ค. ž… ฅ˜Š” ฐดํ„ˆœ„œ— งžถ”–ด ฒฐ ํ•œ „”ฉ ถœ ฅํ•œ‹ค.

Input

10 7 4
9 7 4
17 14 12

output

6
2
4


ํ’€ด

ž‘„ž ‚ฌšฉ–ธ–ด ฐœฐœ‹œ„ ฝ”“œ
€ํšŒ˜ c++ ? MultiplyingByRotation/€ํšŒ˜
ฌธณดฐฝ c++ ? MultiplyingByRotation/ฌธณดฐฝ
ณฝ„ธํ™˜ c++ ? MultiplyingByRotation/ณฝ„ธํ™˜

“ฐ ˆ“œ

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