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 a₁, a₂, ..., 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 ≤ 10⁵), 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 a₁, a₂, ..., a_n (0 ≤ a_i ≤ 10⁵), 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.