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, ..., an. 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 ai, 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 ≤ 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 ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi), that mean that counters with numbers ui and vi 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, ..., an (0 ≤ ai ≤ 105), where ai 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.

Examples

Input

5 5
2 3
4 1
1 5
5 3
2 1
1 1 2 0 2


Output

2
1 2


Input

4 2
1 2
3 4
0 0 0 0


Output

3
1 3 4
py2 = round(0.5)

if py2:
    from future_builtins import ascii, filter, hex, map, oct, zip
    range = xrange
    from cStringIO import StringIO as BytesIO
else:
    from io import BytesIO
    from builtins import str as __str__
    str = lambda x=b'': x if type(x) is bytes else __str__(x).encode()

import os, sys
from io import IOBase

# FastIO for PyPy2 and PyPy3 (works with interactive) by Pajenegod
class FastI(object):
    def __init__(self, fd=0, buffersize=2**14):
        self.stream = stream = BytesIO(); self.bufendl = 0
        def read2buffer():
            s = os.read(fd, buffersize + os.fstat(fd).st_size); pos = stream.tell()
            stream.seek(0,2); stream.write(s); stream.seek(pos); return s
        self.read2buffer = read2buffer
    
    # Read entire input
    def read(self):
        while self.read2buffer(): pass
        return self.stream.read() if self.stream.tell() else self.stream.getvalue()
    
    def readline(self):
        while self.bufendl == 0: s = self.read2buffer(); self.bufendl += s.count(b"\n") + (not s)
        self.bufendl -= 1; return self.stream.readline()
    
    def input(self): return self.readline().rstrip(b'\r\n')
    
    # Read all remaining integers, type is given by optional argument, this is fast
    def readnumbers(self, zero=0):
        conv = ord if py2 else lambda x:x
        A = []; numb = zero; sign = 1; i = 0; s = self.read()
        try:
            while True:
                if s[i] >= b'0' [0]:
                    numb = 10 * numb + conv(s[i]) - 48
                elif s[i] == b'-' [0]: sign = -1
                elif s[i] != b'\r' [0]:
                    A.append(sign*numb)
                    numb = 0; sign = 1
                i += 1
        except:pass
        if s and s[-1] >= b'0' [0]:
            A.append(sign*numb)
        return A

class FastO(IOBase):
    def __init__(self, fd=1):
        stream = BytesIO()
        self.flush = lambda: os.write(1, stream.getvalue()) and not stream.truncate(0) and stream.seek(0)
        self.write = stream.write if py2 else lambda s: stream.write(s.encode())

sys.stdin, sys.stdout = FastI(), FastO()
input = sys.stdin.input

import sys
class ostream:
    def __lshift__(self,a):
        sys.stdout.write(str(a))
        return self
    def tie(self, val):pass
    def flush(self):sys.stdout.flush()
cout = ostream()
endl = b'\n'

class istream:
    inp = None
    def __rlshift__(a,b):
        if type(b)==tuple or type(b)==list:
            return type(b)(type(c)(a.get()) for c in b)
        return type(b)(a.get())
    def get(a):
        while not a.inp:
            a.inp = sys.stdin.readline().split(); a.inp.reverse()
        return a.inp.pop()
cin = istream()


n,m = [int(x) for x in input().split()]

coupl = [[] for _ in range(n)]
for _ in range(m):
    u,v = [int(x)-1 for x in input().split()]
    coupl[u].append(v)
    coupl[v].append(u)

A = [int(x) for x in input().split()]
val = [0]*n
pressed = [False]*n

updater = [node for node in range(n) if A[node]==val[node]]
for node in updater:
    if val[node] == A[node]:
        val[node] += 1
        pressed[node] = True
        for nei in coupl[node]:
            val[nei] += 1
            if val[nei] == A[nei]:
                updater.append(nei)

out = [node for node in range(n) if pressed[node]]
cout << len(out) << '\n';
for node in out:
    cout << node+1 << " ";
cout << '\n';
