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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Globalization;
using System.Diagnostics;



class Myon
{
    public Myon() { }
    public static int Main()
    {
        new Myon().calc();
        return 0;
    }
    
    Scanner cin;

    int N, M;
    string s;
    List<int>[] es;

    Queue<long> q;
    long[] hash;
    XRand rnd;

    Dictionary<long, bool[]> dic;
    bool ok;

    void calc()
    {
        cin = new Scanner();
        N = cin.nextInt();
        M = cin.nextInt();
        s = cin.next();
        es = new List<int>[N];
        for (int i = 0; i < N; i++)
        {
            es[i] = new List<int>();
        }

        for (int i = 0; i < M; i++)
        {
            int a = cin.nextInt() - 1;
            int b = cin.nextInt() - 1;
            es[a].Add(b);
            es[b].Add(a);
        }

        ok = true;
        rnd = new XRand();
        bool[] first = new bool[N];
        hash = new long[N];
        for (int i = 0; i < N; i++)
        {
            first[i] = true;
            hash[i] = ((long)rnd.nextInt(1 << 30) << 30) + rnd.nextInt(1 << 30);
        }
        q = new Queue<long>();
        dic = new Dictionary<long, bool[]>();
        addQueue(first);
        int cnt = 10;
        while(q.Count != 0)
        {
            bool[] br = dic[q.Dequeue()];
            bool[] next = new bool[N];
            for (int i = 0; i < N; i++)
            {
                if (!br[i]) continue;
                foreach (var j in es[i])
                {
                    next[j] = true;
                }
            }
            addQueue(next);
            if (cnt > 10) break;
        }

        if (ok) Console.WriteLine("Yes");
        else Console.WriteLine("No");
    }
    
    void addQueue(bool[] ar)
    {
        bool[] a = new bool[N];
        bool[] b = new bool[N];
        for (int i = 0; i < N; i++)
        {
            if (!ar[i]) continue;
            if (s[i] == 'A') a[i] = true;
            else b[i] = true;
        }
        long ah = getHash(a);
        long bh = getHash(b);

        if (!dic.ContainsKey(ah))
        {
            dic[ah] = a;
            q.Enqueue(ah);
        }

        if (!dic.ContainsKey(bh))
        {
            dic[bh] = b;
            q.Enqueue(bh);
        }

    }

    long getHash(bool[] ar)
    {
        long ans = 0;
        for (int i = 0; i < N; i++)
        {
            if (!ar[i]) continue;
            ans ^= hash[i];
        }
        if (ans == 0) ok = false;
        return ans;
    }
}






class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}



class XRand
{
    uint x, y, z, w;


    public XRand()
    {
        init();
    }

    public XRand(uint s)
    {
        init();
        init_xor128(s);
    }

    void init()
    {
        x = 314159265; y = 358979323; z = 846264338; w = 327950288;

    }

    public void init_xor128(uint s)
    {
        z ^= s;
        z ^= z >> 21; z ^= z << 35; z ^= z >> 4;
        z *= 736338717;
    }

    uint next()
    {
        uint t = x ^ x << 11; x = y; y = z; z = w; return w = w ^ w >> 19 ^ t ^ t >> 8;
    }

    public long nextLong(long m)
    {
        return (long)((((ulong)next() << 32) + next()) % (ulong)m);
    }

    public int nextInt(int m)
    {
        return (int)(next() % m);
    }

    public int nextIntP(int a)
    {
        return (int)Math.Pow(a, nextDouble());
    }

    public int nextInt(int min, int max)
    {
        return min + nextInt(max - min + 1);
    }


    public double nextDouble()
    {
        return (double)next() / uint.MaxValue;
    }

    public double nextDoubleP(double a)
    {
        return Math.Pow(a, nextDouble());
    }
}