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.Generic;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		int N = int.Parse(str[0]);
		int M = int.Parse(str[1]);
		string s = Console.ReadLine();
		int[] B = new int[N];
		List<int>[] D = new List<int>[N];
		var E = new List<int>();
		for(var i=0;i<N;i++){
			D[i] = new List<int>();
			E.Add(i);
			if(s.Substring(i,1) == "B"){
				B[i] = 1;
			}
		}
		int[,] A = new int[M,2];
		int[,] C = new int[N,2];
		for(var i=0;i<M;i++){
			string[] str2 = Console.ReadLine().Split();
			int a = int.Parse(str2[0]);
			int b = int.Parse(str2[1]);
			if(a>b){
				A[i,0] = b;
				A[i,1] = a;
			} else {
				A[i,0] = a;
				A[i,1] = b;
			}
			if(!D[A[i,0]-1].Contains(A[i,1]-1)){
				D[A[i,0]-1].Add(A[i,1]-1);
				if(B[A[i,1]-1] == 1){
					C[A[i,0]-1,1] += 1;
				} else {
					C[A[i,0]-1,0] += 1;
				}
			}
			if(!D[A[i,1]-1].Contains(A[i,0]-1)){
				D[A[i,1]-1].Add(A[i,0]-1);
				if(B[A[i,0]-1] == 1){
					C[A[i,1]-1,1] += 1;
				} else {
					C[A[i,1]-1,0] += 1;
				}
			}
		}
		E.Sort((x,y) =>C[y,0]+C[y,1]-C[x,0]-C[x,1]);
		int ct = N;
		string ans = "No";
		while(true){
			int ct2 = 0;
			var d1 = new List<int>();
			foreach(var i in E){
				if(C[i,0]==0 || C[i,1]==0){
					var d2 = new List<int>();
					foreach(var j in D[i]){
						d2.Add(j);
					}
					foreach(var j in d2){
						D[j].Remove(i);
						C[j,B[i]] -= 1;
					}
					d1.Add(i);
				}
			}
			foreach(var i in d1){
				E.Remove(i);
				ct -= 1;
				ct2 += 1;
			}
			if(ct==0){
				break;
			}
			if(ct2 == 0){
				ans = "Yes";
				break;
			}
		}
		Console.WriteLine(ans);
	}
}