B'Doremy has a rooted tree of size n whose root is vertex r . Initially there is a number w_i written on vertex i . Doremy can use her power to perform this operation at most k times: Doremy wants to know what is the lexicographically smallest ^ dagger array w after performing all the operations. Can you help her? If there are multiple answers, you may output any one. ^ dagger For arrays a and b both of length n , a is lexicographically smaller than b if and only if there exist an index i ( 1 <= q i <= n ) such that a_i < b_i and for all indices j such that j<i , a_j=b_j is satisfied. The input consists of multiple test cases. The first line contains a single integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The description of the test cases follows. The first line contains three integers n , r , k ( 2 <= n <= 5000 , 1 <= r <= n , 0 <= k <= min(500,n) ). The second line contains n integers w_1,w_2, ldots,w_n ( 1 <= w_i <= 10^6 ). Each of the next n-1 lines contains two integers u_i , v_i ( 1 <= q u_i, v_i <= q n ), representing an edge between u_i and v_i . It is guaranteed that the given edges form a tree. It is guaranteed that the sum of n does not exceed 50 ,000 . For each test case, In the first line, output a single integer cnt ( 0 <= cnt <= k ) -- the number of operations you perform. Then, in the second line output cnt integers p_1,p_2, ldots,p_{cnt} -- x is chosen to be p_i for i -th operation. If there are multiple answers, you may output any one. In the first test case: At first w=[1,9,2,6,1,8] . You can choose some vertex x to perform at most one operation. w is lexicographically smallest when x=2 . '...