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 <cstdio>
#include <iostream>
#include <cassert>
#include <string>
#include <algorithm>
#include <cstring>
#include <utility>
#include <vector>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <cmath>
#include <deque>
#include <unordered_map>
#define IOS ios_base::sync_with_stdio(0); cin.tie(0)
using namespace std;
typedef long long LL;
typedef pair<int, int> pii;
typedef pair<LL, LL> pll;
const int MAXN = 123456;
vector<pii> G[MAXN];
int D[MAXN], color[MAXN];
int ans[2 * MAXN];

int main() {
    int N, M;
    scanf("%d %d", &N, &M);
    vector<pii> V;
    for (int i = 1; i <= N; i++) {
        scanf("%d", &D[i]);
        V.push_back(make_pair(D[i], i));
    }
    for (int i = 0; i < M; i++) {
        int a, b;
        scanf("%d %d", &a, &b);
        G[a].push_back(make_pair(i, b));
        G[b].push_back(make_pair(i, a));
    }
    sort(V.begin(), V.end());
    for (int i = 0; i < N; i++) {
        int cur = V[i].second;
        bool OK = false;
        for (auto j : G[cur]) {
            int to = j.second;
            if (D[to] <= D[cur]) OK = true;
        }
        if (!OK) return !printf("-1\n");
    }
    for (int i = 0; i < N; i++) {
        int cur = V[i].second;
        if (color[cur]) continue;
        for (auto j : G[cur]) {
            int to = j.second, idx = j.first;
            if (D[to] > D[cur]) continue;
            if (!color[to]) {
                color[to] = 1;
                color[cur] = 2;
            } else if (color[to] == 1) {
                color[cur] = 2;
            } else {
                color[cur] = 1;
            }
            ans[idx] = D[cur];
            break;
        }
    }
    for (int i = 1; i <= N; i++) {
        if (!color[i]) assert(false);
        if (color[i] == 1) printf("B");
        else printf("W");
    }
    puts("");
    for (int i = 0; i < M; i++) {
        if (!ans[i]) ans[i] = (int)1e9;
        printf("%d\n", ans[i]);
    }
    return 0;
}