310559: CF1851E. Nastya and Potions

E. Nastya and Potionstime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

Alchemist Nastya loves mixing potions. There are a total of $n$ types of potions, and one potion of type $i$ can be bought for $c_i$ coins.

Any kind of potions can be obtained in no more than one way, by mixing from several others. The potions used in the mixing process will be consumed. Moreover, no potion can be obtained from itself through one or more mixing processes.

As an experienced alchemist, Nastya has an unlimited supply of $k$ types of potions $p_1, p_2, \dots, p_k$, but she doesn't know which one she wants to obtain next. To decide, she asks you to find, for each $1 \le i \le n$, the minimum number of coins she needs to spend to obtain a potion of type $i$ next.

Input

The first line of each test contains an integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

Each test case is described as follows:

The first line contains two integers $n$ and $k$ ($1 \le k < n \le 2 \cdot 10^5$) — the total number of potion types and the number of potion types Nastya already has.

The second line contains $n$ integers $c_1, c_2, \dots, c_n$ ($1 \le c_i \le 10^9$) — the costs of buying the potions.

The third line contains $k$ distinct integers $p_1, p_2, \dots, p_k$ ($1 \le p_i \le n$) — the indices of potions Nastya already has an unlimited supply of.

This is followed by $n$ lines describing ways to obtain potions by mixing.

Each line starts with the integer $m_i$ ($0 \le m_i < n$) — the number of potions required to mix a potion of the type $i$ ($1 \le i \le n$).

Then line contains $m_i$ distinct integers $e_1, e_2, \dots, e_{m_i}$ ($1 \le e_j \le n$, $e_j \ne i$) — the indices of potions needed to mix a potion of the type $i$. If this list is empty, then a potion of the type $i$ can only be bought.

It is guaranteed that no potion can be obtained from itself through one or more mixing processes.

It is guaranteed that the sum of all $n$ values across all test cases does not exceed $2 \cdot 10^5$. Similarly, it is guaranteed that the sum of all $m_i$ values across all test cases does not exceed $2 \cdot 10^5$.

Output

For each test case, output $n$ integers — the minimum number of coins Nastya needs to spend to obtain a potion of each type.

ExamplesInput

4
5 1
30 8 3 5 10
3
3 2 4 5
0 
0 
2 3 5
0 
3 2
5 143 3
1 3
1 2
0 
2 1 2
5 1
5 4 1 3 4
2
2 4 5
3 3 5 4
2 1 4
1 5
0 
4 2
1 1 5 4
2 4
3 2 4 3
0 
2 2 4
1 2

Output

23 8 0 5 10 
0 143 0 
5 0 1 3 4 
0 0 0 0 

Input

3
6 3
5 5 4 5 2 2
3 4 5
2 2 5
1 5
3 4 1 6
4 2 6 1 5
0 
0 
6 2
1 4 4 1 5 2
3 6
4 6 3 4 5
4 6 5 3 4
0 
1 5
1 6
0 
2 1
4 3
1
0 
1 1

Output

0 0 0 0 0 2 
0 0 0 0 0 0 
0 0 

Note

In the first test case of the first sample, it is optimal:

• Get a potion of the first type by buying and mixing $2$, $4$ and $5$;
• a potion of the second type can only be obtained by purchasing it;
• Nastya already has an unlimited number of potions of the third type;
• a potion of the fourth type is more profitable to buy than to buy and mix other potions;
• a potion of the fifth type can only be obtained by purchasing it.

题目大意：
Nastya是一个炼金术士，她喜欢混合药剂。总共有n种药剂，每种药剂i可以花费c_i金币购买。任何药剂只能通过混合其他一种药剂得到，并且用于混合的药剂将被消耗。Nastya有无限供应的k种药剂p_1, p_2, ..., p_k，但她不知道接下来想获得哪种药剂。为了决定，她请你帮她找出对于每个1 ≤ i ≤ n，获得一种类型为i的药剂所需花费的最少金币数。

输入数据格式：
第一行包含一个整数t（1 ≤ t ≤ 10^4）——测试用例的数量。
每个测试用例的描述如下：
第一行包含两个整数n和k（1 ≤ k < n ≤ 2 * 10^5）——药剂的种类总数和Nastya已经拥有的药剂种类数。
第二行包含n个整数c_1, c_2, ..., c_n（1 ≤ c_i ≤ 10^9）——购买药剂的费用。
第三行包含k个不同的整数p_1, p_2, ..., p_k（1 ≤ p_i ≤ n）——Nastya已经拥有的无限供应的药剂索引。
接下来n行描述通过混合获得药剂的方式。
每行开始于一个整数m_i（0 ≤ m_i < n）——混合类型为i的药剂所需的药剂数量（1 ≤ i ≤ n）。
然后是该行包含m_i个不同的整数e_1, e_2, ..., e_{m_i}（1 ≤ e_j ≤ n，e_j ≠ i）——混合类型为i的药剂所需的药剂索引。如果这个列表为空，那么药剂i只能通过购买获得。
保证没有任何药剂可以通过一个或多个混合过程从自身获得。
保证所有测试用例的n值总和不超过2 * 10^5。同样，保证所有测试用例的m_i值总和也不超过2 * 10^5。

输出数据格式：
对于每个测试用例，输出n个整数——Nastya获得每种类型药剂所需花费的最少金币数。题目大意： Nastya是一个炼金术士，她喜欢混合药剂。总共有n种药剂，每种药剂i可以花费c_i金币购买。任何药剂只能通过混合其他一种药剂得到，并且用于混合的药剂将被消耗。Nastya有无限供应的k种药剂p_1, p_2, ..., p_k，但她不知道接下来想获得哪种药剂。为了决定，她请你帮她找出对于每个1 ≤ i ≤ n，获得一种类型为i的药剂所需花费的最少金币数。 输入数据格式： 第一行包含一个整数t（1 ≤ t ≤ 10^4）——测试用例的数量。 每个测试用例的描述如下： 第一行包含两个整数n和k（1 ≤ k < n ≤ 2 * 10^5）——药剂的种类总数和Nastya已经拥有的药剂种类数。 第二行包含n个整数c_1, c_2, ..., c_n（1 ≤ c_i ≤ 10^9）——购买药剂的费用。 第三行包含k个不同的整数p_1, p_2, ..., p_k（1 ≤ p_i ≤ n）——Nastya已经拥有的无限供应的药剂索引。 接下来n行描述通过混合获得药剂的方式。 每行开始于一个整数m_i（0 ≤ m_i < n）——混合类型为i的药剂所需的药剂数量（1 ≤ i ≤ n）。 然后是该行包含m_i个不同的整数e_1, e_2, ..., e_{m_i}（1 ≤ e_j ≤ n，e_j ≠ i）——混合类型为i的药剂所需的药剂索引。如果这个列表为空，那么药剂i只能通过购买获得。 保证没有任何药剂可以通过一个或多个混合过程从自身获得。 保证所有测试用例的n值总和不超过2 * 10^5。同样，保证所有测试用例的m_i值总和也不超过2 * 10^5。 输出数据格式： 对于每个测试用例，输出n个整数——Nastya获得每种类型药剂所需花费的最少金币数。