145. Star Wars

Codeforces

IDCF10269145

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

You've traveled across a galaxy far, far away, and you land on a planet with two different alien species. Each alien species counts numbers in a different base. Aliens of the first species count numbers using base $a$, and aliens of the second species count numbers using base $b$. The base used by most humans is decimal, base 10. The two alien species are about to start a war, because they cannot properly communicate in numbers. Your task is to convert a number from the first alien species, in base $a$, into base $b$, in order to avert the impending alien war. The first line of input contains two integers $a$ and $b$ less than or equal to 10: the number base used by the first alien species, and the number base used by the second alien species, respectively. The second line of input contains a single integer $n$ in base $a$. Output $m$: the given integer, converted from base $a$ to base $b$. ## Input The first line of input contains two integers $a$ and $b$ less than or equal to 10: the number base used by the first alien species, and the number base used by the second alien species, respectively.The second line of input contains a single integer $n$ in base $a$. ## Output Output $m$: the given integer, converted from base $a$ to base $b$. [samples]

**Definitions** Let $ a, b \in \mathbb{Z} $ with $ 2 \leq a, b \leq 10 $ be the source and target bases, respectively. Let $ n $ be a non-negative integer represented in base $ a $ as a string of digits $ d_k d_{k-1} \dots d_0 $, where each $ d_i \in \{0, 1, \dots, a-1\} $. **Constraints** 1. $ 2 \leq a \leq 10 $ 2. $ 2 \leq b \leq 10 $ 3. $ n $ is a valid base-$ a $ numeral (no leading zeros unless $ n = 0 $) **Objective** Convert $ n $ from base $ a $ to base $ b $: Let $ N = \sum_{i=0}^{k} d_i \cdot a^i $ be the decimal value of $ n $. Output the base-$ b $ representation of $ N $ as a string of digits $ m = e_\ell e_{\ell-1} \dots e_0 $, where $ N = \sum_{j=0}^{\ell} e_j \cdot b^j $ and each $ e_j \in \{0, 1, \dots, b-1\} $.

API Response (JSON)

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