write a go solution for D. D/D/Dtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputOf course, a problem with the letter D is sponsored by Declan Akaba.You are given a simple, connected, undirected graph with n vertices and m edges. The graph contains no self-loops or multiple edges. You are also given a multiset A consisting of ell elements:  A = \{A_1, A_2, \ldots, A_\ell\} Starting from vertex 1, you may perform the following move any number of times, as long as the multiset A is not empty:   Select an element kinA and remove it from the multiset . You must remove exactly one occurrence of k from A.  Traverse any walk^∗ of exactly k edges to reach some vertex (possibly the same one you started from). For each i (1<=i<=n), determine whether there exists a sequence of such moves that starts at vertex 1 and ends at vertex i, using the original multiset A. Note that the check for each vertex i is independent — you restart from vertex 1 and use the original multiset A for each case.^∗A walk of length k is a sequence of vertices v_0,v_1,ldots,v_k-1,v_k such that each consecutive pair of vertices (v_i,v_i+1) is connected by an edge in the graph. The sequence may include repeated vertices.InputEach test contains multiple test cases. The first line contains the number of test cases t (1<=t<=10^4). The description of the test cases follows. The first line of each test case contains three integers n, m, and ell (2<=n<=2*10^5, n-1<=m<=4*10^5, 1<=ell<=2*10^5) — the number of vertices, the number of edges, and the size of the multiset, respectively.The second line of each test case contains ell integers A_1,A_2,ldots,A_ell (1<=A_i<=10^4) — the elements of the multiset.Each of the following m lines contains two integers u and v (1<=u<v<=n) — the endpoints of an edge in the graph. It is guaranteed that the edges form a simple, connected graph without self-loops or multiple edges.It is guaranteed that the sum of n, the sum of m, and the sum of ell over all test cases does not exceed 2*10^5, 4*10^5, and 2*10^5, respectively.OutputFor each test case, output a binary string of length n, where the i-th character is mathtt1 if there exists a sequence of moves ending at vertex i, and mathtt0 otherwise.ExampleInput36 5 22 31 22 33 44 55 65 5 151 22 33 44 53 55 4 3100 200 3001 21 31 42 5Output111101
11111
10001
NoteIn the first test case:   Vertex 1 is reachable without making any moves.  Vertex 2 is reachable by selecting element 3inA; one possible walk is [1arrow2arrow1arrow2].  Vertex 3 can be reached by selecting element 2inA and taking the walk [1arrow2arrow3].  Vertex 4 is reachable by selecting element 3inA and following the walk [1arrow2arrow3arrow4].  Vertex 5 is not reachable by any valid sequence of moves.  Vertex 6 is reachable by first selecting element 2inA and taking the walk [1arrow2arrow3], followed by selecting element 3inA and taking the walk [3arrow4arrow5arrow6].. Output only the code with no comments, explanation, or additional text.