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*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub>. 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*<sub class="lower-index">*i*</sub>, 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<sup class="upper-index">5</sup>), 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*<sub class="lower-index">*i*</sub> and *v*<sub class="lower-index">*i*</sub> (1 ≤ *u*<sub class="lower-index">*i*</sub>, *v*<sub class="lower-index">*i*</sub> ≤ *n*, *u*<sub class="lower-index">*i*</sub> ≠ *v*<sub class="lower-index">*i*</sub>), that mean that counters with numbers *u*<sub class="lower-index">*i*</sub> and *v*<sub class="lower-index">*i*</sub> 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*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub> (0 ≤ *a*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">5</sup>), where *a*<sub class="lower-index">*i*</sub> is the value that Ignat choose for the *i*-th counter.
from queue import Queue
n,m = map(int,input().split())
e = [[]for i in range(n+1)]
b = [0]*n
for i in range(m):
    u,v = map(int,input().split())
    e[u-1].append(v-1)
    e[v-1].append(u-1)
ans = 0
q = Queue()
a = input().split()
ai = [-1]*n
c=0
mask = [False]*n
for i in a:
    inti = int(i)
    ai[c] = inti
    if inti == 0:
        q.put(c)
        b[c]=1
    c+=1
T=[]
while not q.empty():
    i = q._get()
    ans+=1
    T.append(i+1)
    for j in e[i]:
        b[j]+=1
        if b[j]== ai[j]:
            q.put(j)

print(ans)
print(T)

