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 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 {A1 ,A2 ,⋯,An } is said to be greater than sequence {B1 ,B2 ,⋯,Bm } if there exists 1≤kBk+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

#include
#include
#include
const int MAXN =110;
using namespace std;
struct node{
    int weight;
    vector<int> child;
}Node[MAXN];
bool cmp(int a,int b){
    return Node[a].weight>Node[b].weight;
}
int n,m,s;
int path[MAXN];
void DFS(int index,int numNode,int sum){
    if(sum>s) return ;
    if(sum==s){
        if(Node[index].child.size()!=0)return ;
        for(int i=0;i<numNode;i++){
            cout<<Node[path[i]].weight;
            if(i<numNode-1) cout<<" ";
            else cout<<endl;
        }
        return;
    }
    for(int i=0;i<Node[index].child.size();i++){
        int child=Node[index].child[i];
        path[numNode]=child;
        DFS(child,numNode+1,sum+Node[child].weight);
    }
}
int main(){
    cin>>n>>m>>s;
    for(int i=0;i<n;i++){
        cin>>Node[i].weight;
    }
    int id,k,child;
    for(int i=0;i<m;i++){
        cin>>id>>k;
        for(int j=0;j<k;j++){
            cin>>child;
            Node[id].child.push_back(child);
        }
        sort(Node[id].child.begin(),Node[id].child.end(),cmp);
    }
    path[0]=0;
    DFS(0,1,Node[0].weight);
    return 0;

}
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