The Values You Can Make

题意翻译

##### 题目描述 Pari想向Arya买一块昂贵的巧克力。她有n个硬币，第i个硬币的价值是ci。巧克力的价格是k，所以Pari需要把总价值为k的硬币给Arya。现在Pari想要知道所有的值x，使得存在总和为k的硬币，其中某些硬币的总价值为x。 #### 输入输出格式 ###### 输入格式 第一行包含两个整数n和k（1<=n，k<=500），分别为硬币数量和巧克力价格。 第二行包含n个整数c1，c2，...，cn（1<=ci<=500），表示每个硬币的价值。 保证存在某些硬币的总价值为k。 ###### 输出格式 输出的第一行包含一个整数q，表示x的个数。然后按升序输出整数x，相邻两数用空格隔开。

题目描述

Pari wants to buy an expensive chocolate from Arya. She has $ n $ coins, the value of the $ i $ -th coin is $ c_{i} $ . The price of the chocolate is $ k $ , so Pari will take a subset of her coins with sum equal to $ k $ and give it to Arya. Looking at her coins, a question came to her mind: after giving the coins to Arya, what values does Arya can make with them? She is jealous and she doesn't want Arya to make a lot of values. So she wants to know all the values $ x $ , such that Arya will be able to make $ x $ using some subset of coins with the sum $ k $ . Formally, Pari wants to know the values $ x $ such that there exists a subset of coins with the sum $ k $ such that some subset of this subset has the sum $ x $ , i.e. there is exists some way to pay for the chocolate, such that Arya will be able to make the sum $ x $ using these coins.

输入输出格式

输入格式

The first line contains two integers $ n $ and $ k $ ( $ 1<=n,k<=500 $ ) — the number of coins and the price of the chocolate, respectively. Next line will contain $ n $ integers $ c_{1},c_{2},...,c_{n} $ ( $ 1<=c_{i}<=500 $ ) — the values of Pari's coins. It's guaranteed that one can make value $ k $ using these coins.

输出格式

First line of the output must contain a single integer $ q $ — the number of suitable values $ x $ . Then print $ q $ integers in ascending order — the values that Arya can make for some subset of coins of Pari that pays for the chocolate.

输入输出样例

输入样例 #1

6 18
5 6 1 10 12 2

输出样例 #1

16
0 1 2 3 5 6 7 8 10 11 12 13 15 16 17 18 

输入样例 #2

3 50
25 25 50

输出样例 #2

3
0 25 50