242_D. Dispute_18666
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
#include <bits/stdc++.h>
using namespace std;
const double PI = acos(-1);
const double eps = 1e-10;
const int inf = 2000000000;
const long long int MOD = 1000000007;
int MOD1 = 1000000007;
int MOD2 = 1000000009;
inline bool checkBit(long long int n, long long int i) {
  return n & (1LL << i);
}
inline long long int setBit(long long int n, long long int i) {
  return n | (1LL << i);
  ;
}
inline long long int resetBit(long long int n, long long int i) {
  return n & (~(1LL << i));
}
int dx[] = {0, 0, +1, -1};
int dy[] = {+1, -1, 0, 0};
inline bool EQ(double a, double b) { return fabs(a - b) < 1e-9; }
inline bool isLeapYear(long long int year) {
  return (year % 400 == 0) || (year % 4 == 0 && year % 100 != 0);
}
inline void normal(long long int &a) {
  a %= MOD;
  (a < 0) && (a += MOD);
}
inline long long int modMul(long long int a, long long int b) {
  a %= MOD, b %= MOD;
  normal(a), normal(b);
  return (a * b) % MOD;
}
inline long long int modAdd(long long int a, long long int b) {
  a %= MOD, b %= MOD;
  normal(a), normal(b);
  return (a + b) % MOD;
}
inline long long int modSub(long long int a, long long int b) {
  a %= MOD, b %= MOD;
  normal(a), normal(b);
  a -= b;
  normal(a);
  return a;
}
inline long long int modPow(long long int b, long long int p) {
  long long int r = 1LL;
  while (p) {
    if (p & 1) r = modMul(r, b);
    b = modMul(b, b);
    p >>= 1LL;
  }
  return r;
}
inline long long int modDiv(long long int a, long long int b) {
  return modMul(a, modPow(b, MOD - 2));
}
bool comp(const pair<long long int, pair<long long int, long long int> > &p1,
          const pair<long long int, pair<long long int, long long int> > &p2) {
  return p1.first > p2.first;
}
long long int converter(string a) {
  long long int i, mul = 1, r, t, ans = 0LL;
  if (a.length() == 0) return 0;
  for (i = a.length() - 1; i >= 0; i--) {
    t = a[i] - '0';
    r = t % 10;
    ans += (mul * r);
    mul = mul * 10;
  }
  return ans;
}
int a[200005], id[200005], vis[200005];
vector<int> adj[200005];
vector<int> virus;
vector<int> anss;
void dfs(int u) {
  vis[u] = true;
  id[u]++;
  for (auto it : adj[u]) {
    id[it]++;
    if (id[it] == a[it]) dfs(it);
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  int n, m, i, x, y;
  cin >> n >> m;
  for (i = 1; i <= m; ++i) {
    cin >> x >> y;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
  for (i = 1; i <= n; ++i) {
    cin >> a[i];
    if (a[i] == 0) virus.push_back(i);
  }
  for (auto it : virus) {
    if (id[it] == 0) {
      dfs(it);
    }
  }
  for (i = 1; i <= n; ++i) {
    if (id[i] == a[i]) {
      cout << "-1" << '\n';
      return 0;
    }
    if (vis[i]) anss.push_back(i);
  }
  cout << anss.size() << '\n';
  for (auto it : anss) cout << it << " ";
  return 0;
}
