D. Coins and Queries

Codeforces

IDCF1003D

Time2000ms

Memory256MB

Difficulty—

greedy

English · Original

Chinese · Translation

Formal · Original

Polycarp has $n$ coins, the value of the $i$\-th coin is $a_i$. It is guaranteed that all the values are integer powers of $2$ (i.e. $a_i = 2^d$ for some **non-negative** integer number $d$). Polycarp wants to know answers on $q$ queries. The $j$\-th query is described as integer number $b_j$. The answer to the query is the minimum number of coins that is necessary to obtain the value $b_j$ using some subset of coins (Polycarp can use only coins he has). If Polycarp can't obtain the value $b_j$, the answer to the $j$\-th query is _\-1_. The queries are independent (the answer on the query doesn't affect Polycarp's coins). ## Input The first line of the input contains two integers $n$ and $q$ ($1 \le n, q \le 2 \cdot 10^5$) — the number of coins and the number of queries. The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ — values of coins ($1 \le a_i \le 2 \cdot 10^9$). It is guaranteed that all $a_i$ are integer powers of $2$ (i.e. $a_i = 2^d$ for some **non-negative** integer number $d$). The next $q$ lines contain one integer each. The $j$\-th line contains one integer $b_j$ — the value of the $j$\-th query ($1 \le b_j \le 10^9$). ## Output Print $q$ integers $ans_j$. The $j$\-th integer must be equal to the answer on the $j$\-th query. If Polycarp can't obtain the value $b_j$ the answer to the $j$\-th query is _\-1_. [samples]

Polycarp 有 $n$ 枚硬币，第 $i$ 枚硬币的面值为 $a_i$。保证所有面值均为 $2$ 的整数次幂（即 $a_i = 2^d$，其中 $d$ 为某个非负整数）。 Polycarp 需要回答 $q$ 个查询。第 $j$ 个查询由一个整数 $b_j$ 描述。该查询的答案是：使用他拥有的某些硬币子集来凑出面值 $b_j$ 所需的最少硬币数量。如果 Polycarp 无法凑出面值 $b_j$，则第 $j$ 个查询的答案为 _-1_。各个查询相互独立（一个查询的答案不会影响 Polycarp 的硬币）。输入的第一行包含两个整数 $n$ 和 $q$（$1 lt.eq n, q lt.eq 2 dot.op 10^5$），分别表示硬币数量和查询数量。第二行包含 $n$ 个整数 $a_1, a_2, dots.h, a_n$，表示硬币的面值（$1 lt.eq a_i lt.eq 2 dot.op 10^9$）。保证所有 $a_i$ 均为 $2$ 的整数次幂（即 $a_i = 2^d$，其中 $d$ 为某个非负整数）。接下来的 $q$ 行，每行包含一个整数。第 $j$ 行包含一个整数 $b_j$，表示第 $j$ 个查询的面值（$1 lt.eq b_j lt.eq 10^9$）。请输出 $q$ 个整数 $a n s_j$。第 $j$ 个整数必须等于第 $j$ 个查询的答案。如果 Polycarp 无法凑出面值 $b_j$，则该查询的答案为 _-1_。 ## Input 输入的第一行包含两个整数 $n$ 和 $q$（$1 lt.eq n, q lt.eq 2 dot.op 10^5$），分别表示硬币数量和查询数量。第二行包含 $n$ 个整数 $a_1, a_2, dots.h, a_n$，表示硬币的面值（$1 lt.eq a_i lt.eq 2 dot.op 10^9$）。保证所有 $a_i$ 均为 $2$ 的整数次幂（即 $a_i = 2^d$，其中 $d$ 为某个非负整数）。接下来的 $q$ 行，每行包含一个整数。第 $j$ 行包含一个整数 $b_j$，表示第 $j$ 个查询的面值（$1 lt.eq b_j lt.eq 10^9$）。 ## Output 请输出 $q$ 个整数 $a n s_j$。第 $j$ 个整数必须等于第 $j$ 个查询的答案。如果 Polycarp 无法凑出面值 $b_j$，则该查询的答案为 _-1_。 [samples]

**Definitions** Let $ n, q \in \mathbb{Z}^+ $ denote the number of coins and queries, respectively. Let $ A = (a_1, a_2, \dots, a_n) $ be a sequence of coin values, where each $ a_i = 2^{d_i} $ for some $ d_i \in \mathbb{Z}_{\ge 0} $. Let $ B = (b_1, b_2, \dots, b_q) $ be a sequence of query values, where each $ b_j \in \mathbb{Z}^+ $. **Constraints** 1. $ 1 \le n, q \le 2 \cdot 10^5 $ 2. $ 1 \le a_i \le 2 \cdot 10^9 $ and $ a_i = 2^{d_i} $ for some $ d_i \in \mathbb{Z}_{\ge 0} $ 3. $ 1 \le b_j \le 10^9 $ **Objective** For each query $ b_j $, find the minimum number of coins from $ A $ whose sum equals $ b_j $, i.e., find the smallest $ k \in \mathbb{Z}_{\ge 0} $ such that there exists a multiset $ S \subseteq A $ with $ |S| = k $ and $ \sum_{x \in S} x = b_j $. If no such subset exists, output $ -1 $.

Samples

Input #1

Output #1

API Response (JSON)

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