Problem: We have a connected undirected graph with N vertices and M edges. Edge i in this graph (1 \leq i \leq M) connects Vertex U_i and Vertex V_i bidirectionally. We are additionally given N integers D_1, D_2, ..., D_N.

Determine whether the conditions below can be satisfied by assigning a color - white or black - to each vertex and an integer weight between 1 and 10^9 (inclusive) to each edge in this graph. If the answer is yes, find one such assignment of colors and integers, too.

* There is at least one vertex assigned white and at least one vertex assigned black.
* For each vertex v (1 \leq v \leq N), the following holds.
* The minimum cost to travel from Vertex v to a vertex whose color assigned is different from that of Vertex v by traversing the edges is equal to D_v.



Here, the cost of traversing the edges is the sum of the weights of the edges traversed.

Constraints

* 2 \leq N \leq 100,000
* 1 \leq M \leq 200,000
* 1 \leq D_i \leq 10^9
* 1 \leq U_i, V_i \leq N
* The given graph is connected and has no self-loops or multiple edges.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M
D_1 D_2 ... D_N
U_1 V_1
U_2 V_2
\vdots
U_M V_M


Output

If there is no assignment satisfying the conditions, print a single line containing `-1`.

If such an assignment exists, print one such assignment in the following format:


S
C_1
C_2
\vdots
C_M


Here,

* the first line should contain the string S of length N. Its i-th character (1 \leq i \leq N) should be `W` if Vertex i is assigned white and `B` if it is assigned black.
* The (i + 1)-th line (1 \leq i \leq M) should contain the integer weight C_i assigned to Edge i.

Examples

Input

5 5
3 4 3 5 7
1 2
1 3
3 2
4 2
4 5


Output

BWWBB
4
3
1
5
2


Input

5 7
1 2 3 4 5
1 2
1 3
1 4
2 3
2 5
3 5
4 5


Output

-1


Input

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


Output

BBBW
1
1
1
2
1
1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define ld double
#define ull unsigned long long
#define ll long long
#define pii pair <int, int>
#define iiii pair <int, pii >
#define mp make_pair
#define INF 1000000000
#define rep(i, x) for(int (i) = 0; (i) < (x); (i)++)
inline int getint() {
  int x = 0, p = 1; char c = getchar();
  while (c <= 32) c = getchar();
  if (c == 45) p = -p, c = getchar();
  while (c > 32) x = x * 10 + c - 48, c = getchar();
  return x * p;
}
using namespace std;
const int mod = 1e9 + 7;
inline void reduce(int &x) { x += x >> 31 & mod; }
inline int mul(int x, int y) { return 1ll * x * y % mod; }
//ruogu_alter
const int N = 2e5 + 5;
int n, m, len[N], vis[N], d[N];
vector<pii> v, g[N];
//
int main() {
  n = getint(); m = getint();
  rep(i, n) v.emplace_back(d[i] = getint(), i);
  sort(v.begin(), v.end());
  rep(i, m) {
    int x = getint() - 1, y = getint() - 1;
    g[x].emplace_back(y, i);
    g[y].emplace_back(x, i);
  }
  rep(i, m) len[i] = INF;
  for (auto &u : v) {
    int s = u.second, l = u.first;
    if (vis[s]) continue;
    bool fg = false;
    for (auto &to : g[s]) if (vis[to.first]) {
      fg = true;
      vis[s] = 3 - vis[to.first];
      len[to.second] = l;
      break;
    }
    if (fg) continue;
    for (auto &to : g[s]) if (d[to.first] == l) {
      fg = true;
      vis[s] = 1; vis[to.first] = 2;
      len[to.second] = l;
      break;
    }
    if (!fg) return !printf("%d\n", -1);
  }
  rep(i, n) putchar(vis[i] == 1 ? 'W' : 'B');
  putchar('\n');
  rep(i, m) printf("%d\n", len[i]);
  return 0;
}