G. Next Number

Codeforces

IDCF10219G

Time2000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

You are given a number with n digits written in base b. For example, our monetary system is written in base 10 (i.e. 926 JOD) and a binary number is written in base 2 (i.e. 10101110). Your task is to find the next greater number that consists of distinct digits (no digit is repeated twice). It is *guaranteed* that there is an answer for the given number. The first line of input contains two integers n and b (1 ≤ n ≤ 3 × 105) (2 ≤ b ≤ 3 × 105), the number of digits of the number and the base it is written in. The second line of input contains n integers ai (0 ≤ ai < b), where ai is the ith digit in the number. It is *guaranteed* that the number has no leading zeros. Output a single line with the next greater number that consists of distinct digits. Separate the digits by a single space. ## Input The first line of input contains two integers n and b (1 ≤ n ≤ 3 × 105) (2 ≤ b ≤ 3 × 105), the number of digits of the number and the base it is written in.The second line of input contains n integers ai (0 ≤ ai < b), where ai is the ith digit in the number. It is *guaranteed* that the number has no leading zeros. ## Output Output a single line with the next greater number that consists of distinct digits. Separate the digits by a single space. [samples]

**Definitions** Let $ n, b \in \mathbb{Z} $ with $ 1 \leq n \leq 3 \times 10^5 $ and $ 2 \leq b \leq 3 \times 10^5 $. Let $ A = (a_1, a_2, \dots, a_n) $ be a sequence of digits with $ a_i \in \{0, 1, \dots, b-1\} $, $ a_1 \neq 0 $, representing a number in base $ b $. **Constraints** 1. All digits in $ A $ may not be distinct initially. 2. The number has no leading zeros: $ a_1 \neq 0 $. 3. There exists at least one number greater than $ A $ in base $ b $ with exactly $ n $ digits and all distinct digits. **Objective** Find the lexicographically smallest sequence $ B = (b_1, b_2, \dots, b_n) $ such that: - $ B > A $ (as base-$ b $ numbers), - $ b_i \in \{0, 1, \dots, b-1\} $ for all $ i $, - $ b_1 \neq 0 $, - All digits in $ B $ are distinct: $ b_i \neq b_j $ for $ i \neq j $. Output $ B $ as $ b_1, b_2, \dots, b_n $ separated by spaces.

API Response (JSON)

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