Problem: You are given a connected undirected graph with n vertices and m edges. The vertices are enumerated from 1 to n. 

You are given n integers c1, c2, ..., cn, each of them is between  - n and n, inclusive. It is also guaranteed that the parity of cv equals the parity of degree of vertex v. The degree of a vertex is the number of edges connected to it.

You are to write a weight between  - 2·n2 and 2·n2 (inclusive) on each edge in such a way, that for each vertex v the sum of weights on edges connected to this vertex is equal to cv, or determine that this is impossible.

Input

The first line contains two integers n and m (2 ≤ n ≤ 105, n - 1 ≤ m ≤ 105) — the number of vertices and the number of edges.

The next line contains n integers c1, c2, ..., cn ( - n ≤ ci ≤ n), where ci is the required sum of weights of edges connected to vertex i. It is guaranteed that the parity of ci equals the parity of degree of vertex i.

The next m lines describe edges of the graph. The i-th of these lines contains two integers ai and bi (1 ≤ ai, bi ≤ n; ai ≠ bi), meaning that the i-th edge connects vertices ai and bi.

It is guaranteed that the given graph is connected and does not contain loops and multiple edges.

Output

If there is no solution, print "NO".

Otherwise print "YES" and then m lines, the i-th of them is the weight of the i-th edge wi ( - 2·n2 ≤ wi ≤ 2·n2).

Examples

Input

3 3
2 2 2
1 2
2 3
1 3


Output

YES
1
1
1


Input

4 3
-1 0 2 1
1 2
2 3
3 4


Output

YES
-1
1
1


Input

6 6
3 5 5 5 1 5
1 4
3 2
4 3
4 5
3 5
5 6


Output

YES
3
5
3
-1
-3
5


Input

4 4
4 4 2 4
1 2
2 3
3 4
4 1


Output

NO

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <class T>
inline void gmin(T &x, const T &y) {
  if (x > y) x = y;
}
template <class T>
inline void gmax(T &x, const T &y) {
  if (x < y) x = y;
}
const int BufferSize = 1 << 16;
char buffer[BufferSize], *Bufferhead, *Buffertail;
bool Terminal;
inline char Getchar() {
  if (Bufferhead == Buffertail) {
    int l = fread(buffer, 1, BufferSize, stdin);
    if (!l) {
      Terminal = 1;
      return 0;
    }
    Buffertail = (Bufferhead = buffer) + l;
  }
  return *Bufferhead++;
}
template <class T>
inline bool read(T &x) {
  x = 0;
  char c = Getchar(), rev = 0;
  while (c < '0' || c > '9') {
    rev |= c == '-';
    c = Getchar();
    if (Terminal) return 0;
  }
  while (c >= '0' && c <= '9') x = x * 10 + c - '0', c = Getchar();
  if (c == '.') {
    c = Getchar();
    double t = 0.1;
    while (c >= '0' && c <= '9')
      x = x + (c - '0') * t, c = Getchar(), t = t / 10;
  }
  x = rev ? -x : x;
  return 1;
}
template <class T1, class T2>
inline bool read(T1 &x, T2 &y) {
  return read(x) & read(y);
}
template <class T1, class T2, class T3>
inline bool read(T1 &x, T2 &y, T3 &z) {
  return read(x) & read(y) & read(z);
}
template <class T1, class T2, class T3, class T4>
inline bool read(T1 &x, T2 &y, T3 &z, T4 &w) {
  return read(x) & read(y) & read(z) & read(w);
}
inline bool reads(char *x) {
  char c = Getchar();
  while (c < 33 || c > 126) {
    c = Getchar();
    if (Terminal) return 0;
  }
  while (c >= 33 && c <= 126) (*x++) = c, c = Getchar();
  *x = 0;
  return 1;
}
template <class T>
inline void print(T x, const char c = '\n') {
  if (!x) {
    putchar('0');
    putchar(c);
    return;
  }
  if (x < 0) putchar('-'), x = -x;
  int m = 0, a[20];
  while (x) a[m++] = x % 10, x /= 10;
  while (m--) putchar(a[m] + '0');
  putchar(c);
}
const int inf = 0x3f3f3f3f;
const int N = 200005, M = 100005, mod = 1e9 + 7;
template <class T, class S>
inline void ch(T &x, const S y) {
  x = (x + y) % mod;
}
inline int exp(int x, int y, const int mod = ::mod) {
  int ans = 1;
  while (y) {
    if (y & 1) ans = (long long)ans * x % mod;
    x = (long long)x * x % mod;
    y >>= 1;
  }
  return ans;
}
int n, m, tot, fa[N], from[N], dep[N], c[N], cir[N], edg[N];
vector<pair<int, int> > g[N], f[N];
long long res[N], val[N];
bool vis[N];
inline void add(vector<pair<int, int> > *g, int x, int y, int z) {
  g[x].push_back(make_pair(y, z));
  g[y].push_back(make_pair(x, z));
}
inline void findcir(int x) {
  vis[x] = 1;
  for (auto i : g[x]) {
    int y = i.first;
    if (vis[i.first]) {
      if (!tot && dep[y] > dep[x] && !(dep[y] - dep[x] & 1)) {
        cir[++tot] = y, edg[tot] = i.second;
        while (y != x) edg[++tot] = from[y], y = fa[y], cir[tot] = y;
        add(f, x, y, i.second);
      }
      continue;
    }
    add(f, x, y, i.second);
    dep[y] = dep[x] + 1;
    fa[y] = x;
    from[y] = i.second;
    findcir(y);
  }
}
inline long long dfs(int x) {
  long long ret = c[x];
  vis[x] = 1;
  for (auto i : f[x]) {
    int y = i.first;
    if (vis[y]) continue;
    ret -= (res[i.second] = dfs(y));
  }
  return ret;
}
int main() {
  read(n, m);
  for (int i = 1; i <= n; i++) read(c[i]);
  for (int i = 1; i <= m; i++) {
    int x, y;
    read(x, y);
    add(g, x, y, i);
  }
  findcir(1);
  memset(vis, 0, sizeof(vis));
  if (!tot) {
    if (dfs(1)) {
      puts("NO");
      return 0;
    }
    puts("YES");
    for (int i = 1; i <= m; i++) printf("%lld\n", res[i]);
    return 0;
  }
  puts("YES");
  for (int i = 1; i <= tot; i++) vis[cir[i]] = 1;
  long long b = 0;
  for (int i = 1; i <= tot; i++) {
    val[i] = dfs(cir[i]);
    b = val[i] - b;
  }
  res[edg[1]] = b / 2;
  for (int i = 1; i < tot; i++) res[edg[i + 1]] = val[i] - res[edg[i]];
  for (int i = 1; i <= m; i++) printf("%lld\n", res[i]);
  return 0;
}