Valera has n counters numbered from 1 to n . Some of them are connected by wires, and each of the counters has a special button. Initially, all the counters contain number 0 . When you press a button on a certain counter, the value it has increases by one. Also, the values recorded in all the counters, directly connected to it by a wire, increase by one. Valera and Ignat started having a dispute, the dispute is as follows. Ignat thought of a sequence of n integers a 1 , a 2 , ..., a n . Valera should choose some set of distinct counters and press buttons on each of them exactly once (on other counters the buttons won't be pressed). If after that there is a counter with the number i , which has value a i , then Valera loses the dispute, otherwise he wins the dispute. Help Valera to determine on which counters he needs to press a button to win the dispute. The first line contains two space-separated integers n and m (1 ≤ n , m ≤ 10 5 ) , that denote the number of counters Valera has and the number of pairs of counters connected by wires. Each of the following m lines contains two space-separated integers u i and v i (1 ≤ u i , v i ≤ n , u i ≠ v i ) , that mean that counters with numbers u i and v i are connected by a wire. It is guaranteed that each pair of connected counters occurs exactly once in the input. The last line contains n space-separated integers a 1 , a 2 , ..., a n (0 ≤ a i ≤ 10 5 ) , where a i is the value that Ignat choose for the i -th counter. If Valera can't win the dispute print in the first line -1. Otherwise, print in the first line integer k (0 ≤ k ≤ n ) . In the second line print k distinct space-separated integers — the numbers of the counters, where Valera should push buttons to win the dispute, in arbitrary order. If there exists multiple answers, you are allowed to print any of them.