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.

Input

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.

Output

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.