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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace agc027_c
{
	class Program
	{
		static bool ret;
		static bool[,] canab;
		static HashSet<int>[] edge;
		static string s;
		static void dfs(int start, int x, string move)
		{
			move += s[x];
			if (move.Length == 4)
			{
				if (edge[x].Contains(start) && "AABBAABB".Contains(move)) ret = true;
				return;
			}
			foreach (var item in edge[x])
			{
				if (canab[item, 0] && canab[item, 1]) dfs(start, item, move);
			}
		}
		static void Main(string[] args)
		{
			int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
			s = Console.ReadLine();
			edge = new HashSet<int>[x[0]];
			for (int i = 0; i < x[0]; i++) edge[i] = new HashSet<int>();
			canab = new bool[x[0], 2];
			for (int i = 0; i < x[1]; i++)
			{
				int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray(); a[0]--; a[1]--;
				edge[a[0]].Add(a[1]); edge[a[1]].Add(a[0]);
				canab[a[0], s[a[1]] == 'A' ? 0 : 1] = true;
				canab[a[1], s[a[0]] == 'A' ? 0 : 1] = true;
			}
			for (int i = 0; i < x[0]; i++)
			{
				if (canab[i, 0] && canab[i, 1]) dfs(i, i, "");
			}
			Console.WriteLine(ret ? "Yes" : "No");
		}
	}
}