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Multiplying By Rotation

About Multiplying By Rotation

๋ณด†ต ž—ฐˆ˜˜ ๊ณ…ˆ€ ๋ณตžก•œ —ฐ‚ฐด๋‹ค. –ด๋–ค๊ฒฝšฐ—„œ๋Š” —ฐ‚ฐ๊ฒฐ๊ณผ๊ฐ€ ๋งˆง€๋ง‰ ˆž๋ฅผ •žœผ๋กœ ˜ฎ๊ธฐ๋Š” ๊ฒƒ— ˜•ด„œ –ป„ ˆ˜ žˆ๋‹ค.

{{| 179487 * 4 = 717948 |}}

๋ฌผ๋ก  ด๋Ÿฌ•œ †„€ ‚ฌšฉ•˜๋Š” ˆ˜ฒด๊ณ„— ๋”ฐ๋ผ ๋‹ค๋ฅด๋‹ค. œ„˜ ˜ˆ œ—„œ๋Š” 10„ˆ˜๋ฅผ ‚ฌšฉ–ˆ๋‹ค. 9„ˆ˜—„œ˜ —๋Š” ๋‹คŒ๊ณผ ๊ฐ™๋‹ค.
{{|
17 * 4 = 71(base 9)
(9 * 1 + 7) * 4 = 7 * 9 + 1
|}}

๋ฌธ œ˜ ๋ชจ๋“  ˆž๋Š” 10„ˆ˜๊ฐ€ •„๋‹ˆ๋‹ค..!!!

ž…๋ ฅ€ …ŠคŠธŒŒผด๋‹ค. „ˆ˜,ฒซ๋ฒˆงธ ˆž˜ ๋งˆง€๋ง‰ ˆž(the least significant digit of the first factor)™€ ๋‘๋ฒˆงธ ˆž(second factor)๋กœ ๊ตฌ„๋œ 3๊ฐœ˜ ˆ˜น˜๊ฐ€ •œ„”ฉ ž…๋ ฅ๋œ๋‹ค. ๊ฐ ˆ˜น˜๋Š” ๊ณต๋ฐœผ๋กœ ๊ตฌ๋ถ„๋œ๋‹ค. ๋‘๋ฒˆงธ ˆž๋Š” •ด๋‹น „ˆ˜๋ณด๋‹ค  € ˆžด๋‹ค. ž…๋ ฅŒŒผ€ EOF๋กœ ๋๋‚œ๋‹ค.

”„๋กœ๊ทธ๋žจ€ ด๋™ ๊ณ…ˆ†„„ ๊ฐ–๋Š” ˆžค‘ ๊ฐ€žฅ ž‘€ ฒซ ๋ฒˆงธ ˆž˜ ž๋ฆฌ ๊ฐœˆ˜๋ฅผ ถœ๋ ฅ•œ๋‹ค.ถœ๋ ฅ ŒŒผ๋„ …ŠคŠธŒŒผ๋กœ •œ๋‹ค. ž…๋ ฅ๋˜๋Š” ๋ฐด„ˆœ„œ— ๋งžถ”–ด ๊ฒฐ๊ณผ๋ฅผ •œ „”ฉ ถœ๋ ฅ•œ๋‹ค.

Input

10 7 4
9 7 4
17 14 12

output

6
2
4


’€ด

ž‘„ž ‚ฌšฉ–ธ–ด ๊ฐœ๋ฐœ‹œ๊ฐ„ ฝ”๋“œ
๊น€šŒ˜ c++ ? MultiplyingByRotation/๊น€šŒ˜
๋ฌธ๋ณดฐฝ c++ ? MultiplyingByRotation/๋ฌธ๋ณดฐฝ
๊ณฝ„™˜ c++ ? MultiplyingByRotation/๊ณฝ„™˜

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