Knapsack

题意翻译

您有 $n$ $(1≤n≤200$ $000)$ 个物品，第 $i$ 个物品的重量为 $w_i$ $(1≤w_i≤10^9)$。同时您还有一个容量为 $W$ $(1≤W≤10^{18})$的背包。 我们希望将一些物品加入背包中，使其总重量超过 $W$ 的一半，但不超过 $W$ 。 如果有，请输出物品的个数以及物品的编号；如果没有，输出 "-1" （不必输出双引号）。 **注意：如果存在多个满足条件的物品列表，输出其中任意一个**

题目描述

You have a knapsack with the capacity of $ W $ . There are also $ n $ items, the $ i $ -th one has weight $ w_i $ . You want to put some of these items into the knapsack in such a way that their total weight $ C $ is at least half of its size, but (obviously) does not exceed it. Formally, $ C $ should satisfy: $ \lceil \frac{W}{2}\rceil \le C \le W $ . Output the list of items you will put into the knapsack or determine that fulfilling the conditions is impossible. If there are several possible lists of items satisfying the conditions, you can output any. Note that you don't have to maximize the sum of weights of items in the knapsack.

输入输出格式

输入格式

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). Description of the test cases follows. The first line of each test case contains integers $ n $ and $ W $ ( $ 1 \le n \le 200\,000 $ , $ 1\le W \le 10^{18} $ ). The second line of each test case contains $ n $ integers $ w_1, w_2, \dots, w_n $ ( $ 1 \le w_i \le 10^9 $ ) — weights of the items. The sum of $ n $ over all test cases does not exceed $ 200\,000 $ .

输出格式

For each test case, if there is no solution, print a single integer $ -1 $ . If there exists a solution consisting of $ m $ items, print $ m $ in the first line of the output and $ m $ integers $ j_1 $ , $ j_2 $ , ..., $ j_m $ ( $ 1 \le j_i \le n $ , all $ j_i $ are distinct) in the second line of the output — indices of the items you would like to pack into the knapsack. If there are several possible lists of items satisfying the conditions, you can output any. Note that you don't have to maximize the sum of weights items in the knapsack.

输入输出样例

输入样例 #1

3
1 3
3
6 2
19 8 19 69 9 4
7 12
1 1 1 17 1 1 1

输出样例 #1

1
1
-1
6
1 2 3 5 6 7

说明

In the first test case, you can take the item of weight $ 3 $ and fill the knapsack just right. In the second test case, all the items are larger than the knapsack's capacity. Therefore, the answer is $ -1 $ . In the third test case, you fill the knapsack exactly in half.