## Problem #

Source: [PAT 1053]

### Description #

Given a non-empty tree with root R, and with weight W_{i} assigned to each tree node T_{i}. The weight of a path from R to L is defined to be the sum of the weights of all the nodes along the path from R to any leaf node L.

Now given any weighted tree, you are supposed to find all the paths with their weights equal to a given number. For example, let’s consider the tree showed in the following figure: for each node, the upper number is the node ID which is a two-digit number, and the lower number is the weight of that node. Suppose that the given number is 24, then there exists 4 different paths which have the same given weight: {10 5 2 7}, {10 4 10}, {10 3 3 6 2} and {10 3 3 6 2}, which correspond to the red edges in the figure.

### Input Specification: #

Each input file contains one test case. Each case starts with a line containing 0<N≤100, the number of nodes in a tree, M (<N), the number of non-leaf nodes, and 0<S<2_{30}, the given weight number. The next line contains N positive numbers where W_{i} (<1000) corresponds to the tree node T_{i}. Then M lines follow, each in the format:

`ID K ID[1] ID[2] ... ID[K]`

where ID is a two-digit number representing a given non-leaf node, K is the number of its children, followed by a sequence of two-digit ID’s of its children. For the sake of simplicity, let us fix the root ID to be 00.

### Output Specification: #

For each test case, print all the paths with weight S in non-increasing order. Each path occupies a line with printed weights from the root to the leaf in order. All the numbers must be separated by a space with no extra space at the end of the line.

Note: sequence {A_{1},A_{2},⋯,A_{n}} is said to be greater than sequence {B_{1},B_{2},⋯,B_{m}} if there exists 1≤k<min{n,m} such that A_{i} =B_{i} for i=1,⋯,k, and A_{k+1}>B_{k+1}.

### Sample Input: #

```
20 9 24
10 2 4 3 5 10 2 18 9 7 2 2 1 3 12 1 8 6 2 2
00 4 01 02 03 04
02 1 05
04 2 06 07
03 3 11 12 13
06 1 09
07 2 08 10
16 1 15
13 3 14 16 17
17 2 18 19
```

### Sample Output: #

```
10 5 2 7
10 4 10
10 3 3 6 2
10 3 3 6 2
```