Problem:
Score : 900 points

Problem Statement

You are given an undirected graph consisting of N vertices and M edges.
The vertices are numbered 1 to N, and the edges are numbered 1 to M.
In addition, each vertex has a label, A or B. The label of Vertex i is s_i.
Edge i bidirectionally connects vertex a_i and b_i.

The phantom thief Nusook likes to choose some vertex as the startpoint and traverse an edge zero or more times.
Today, he will make a string after traveling as above, by placing the labels of the visited vertices in the order visited, beginning from the startpoint.

For example, in a graph where Vertex 1 has the label A and Vertex 2 has the label B, if Nusook travels along the path 1 \rightarrow 2 \rightarrow 1 \rightarrow 2 \rightarrow 2, the resulting string is ABABB.

Determine if Nusook can make all strings consisting of A and B.

Constraints

2 \leq N \leq 2 \times 10^{5}

1 \leq M \leq 2 \times 10^{5}

|s| = N

s_i is A or B.

1 \leq a_i, b_i \leq N

The given graph may NOT be simple or connected.

Input

Input is given from Standard Input in the following format:

N M
s
a_1 b_1
:
a_{M} b_{M}

Output

If Nusook can make all strings consisting of A and B, print Yes; otherwise, print No.

Sample Input 1

2 3
AB
1 1
1 2
2 2

Sample Output 1

Yes

Since Nusook can visit Vertex 1 and Vertex 2 in any way he likes, he can make all strings consisting of A and B.

Sample Input 2

4 3
ABAB
1 2
2 3
3 1

Sample Output 2

No

For example, Nusook cannot make BB.

The given graph may not be connected.

Sample Input 3

13 23
ABAAAABBBBAAB
7 1
10 6
1 11
2 10
2 8
2 11
11 12
8 3
7 12
11 2
13 13
11 9
4 1
9 7
9 6
8 13
8 6
4 10
8 7
4 3
2 1
8 12
6 9

Sample Output 3

Yes

Sample Input 4

13 17
BBABBBAABABBA
7 1
7 9
11 12
3 9
11 9
2 1
11 5
12 11
10 8
1 11
1 8
7 7
9 10
8 8
8 12
6 2
13 11

Sample Output 4

No

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

// package agc.agc027;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    static long __startTime = System.currentTimeMillis();

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        int m = in.nextInt();
        char[] s = in.nextToken().toCharArray();
        int[] ab = new int[n];
        for (int i = 0; i < s.length; i++) {
            ab[i] = s[i] == 'A' ? 0 : 1;
        }

        List<Integer>[] graph = new List[n];
        for (int i = 0; i < n ; i++) {
            graph[i] = new ArrayList<>();
        }
        for (int i = 0; i < m ; i++) {
            int a = in.nextInt()-1;
            int b = in.nextInt()-1;
            if (a != b) {
                graph[a].add(b);
                graph[b].add(a);
            } else {
                graph[a].add(a);
            }
        }

        boolean isOK = false;
        boolean[] visited = new boolean[n];
        int[] que = new int[32*n*3];
        int[][][] dp = new int[2][16][n];
        for (int i = 0; i < n ; i++) {
            int nt = 0;
            if (!visited[i] && ab[i] == 0) {
                visited[i] = true;
                dp[0][nt][i] = 1;
                int qh = 0;
                int qt = 0;
                que[qh++] = 0;
                que[qh++] = nt;
                que[qh++] = i;
                while (qt < qh) {
                    int par = que[qt++];
                    int flg = que[qt++];
                    int now = que[qt++];
                    visited[now] = true;
                    for (int to : graph[now]) {
                        if (ab[to] != ab[now]) {
                            if (par == 1) {
                                int tp = 0;
                                int tf = 0;
                                if (ab[to] == 0 && dp[0][0][to] == 1) {
                                    isOK = true;
                                }
                                if (dp[tp][tf][to] == 0) {
                                    dp[tp][tf][to] = 1;
                                    que[qh++] = tp;
                                    que[qh++] = tf;
                                    que[qh++] = to;
                                }
                            }
                        } else {
                            if (par == 0) {
                                int tp = par ^ 1;
                                int tf = 0;
                                if (dp[tp][tf][to] == 0) {
                                    dp[tp][tf][to] = 1;
                                    que[qh++] = tp;
                                    que[qh++] = tf;
                                    que[qh++] = to;
                                }
                            }
                        }
                    }
                }
            }
        }


        out.println(isOK ? "Yes" : "No");
        out.flush();
    }

    private static void printTime(String label) {
        debug(label, System.currentTimeMillis() - __startTime);
    }

    private static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }

    public static class InputReader {
        private static final int BUFFER_LENGTH = 1 << 12;
        private InputStream stream;
        private byte[] buf = new byte[BUFFER_LENGTH];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int next() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            return (char) skipWhileSpace();
        }

        public String nextToken() {
            int c = skipWhileSpace();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            return (int) nextLong();
        }

        public long nextLong() {
            int c = skipWhileSpace();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        int skipWhileSpace() {
            int c = next();
            while (isSpaceChar(c)) {
                c = next();
            }
            return c;
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}