Cows have assembled from around the world for a massive gathering. There are N
cows, and N-1 pairs of cows who are friends with each other. Every cow knows
every other cow through some chain of friendships.
They had great fun, but the time has come for them to leave, one by one. They want to leave in some order such that as long as there are still at least two cows left, every remaining cow has a remaining friend. Furthermore, due to issues with luggage storage, there are M pairs of cows (ai, bi) such that cow ai must leave before cow bi. Note that the cows ai and bi may or may not be friends.
Help the cows figure out, for each cow, whether she could be the last cow to leave. It may be that there is no way for the cows to leave satisfying the above constraints.
Line 1 contains two space-separated integers N and M.
Lines 2 ≤ i ≤ N each contain two integers xi and yi with 1 ≤ xi, yi ≤ N and xi yi indicating that cows xi and yi are friends.
Lines N+1 ≤ i ≤ N+M each contain two integers ai and bi with 1 ≤ ai, bi ≤ N and ai ≠ bi indicating that cow ai must leave the gathering before cow bi.
It is guaranteed that 1 ≤ N, M ≤ 105. In test cases worth 20\% of the points, it is further guaranteed that N, M ≤ 3000.