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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<vector>
#include<string>
using namespace std;
vector<int> G[200000];
bool avai[200000];
bool mark[200000];

bool hasHeiro(vector<int> G[],bool avai[],bool mark[],int v){
    if(!avai[v]) return false;
    mark[v]=true;
    for (int i = 0; i < (int)G[v].size(); ++i) {
	    if(mark[G[v][i]])
		return true;
	    else
		return hasHeiro(G,avai,mark,G[v][i]);
	
    }
    return false;
}

int main(){
    int n,m;
    cin>>n>>m;
    string s;
    cin>>s;
    for (int i = 0; i < m; ++i) {
        int p,q;
	cin>>p>>q;
	G[p-1].push_back(q-1);
	G[q-1].push_back(p-1);
    }
    for (int i = 0; i < n; ++i) {
	int flag=0;
        for(int j=0;j<(int)G[i].size();j++){
	if(s[G[i][j]]=='A'
	&&flag!=1&&flag!=3)
	    flag+=1;
	else if(s[G[i][j]]=='B'
	&&flag!=2&&flag!=3)
	    flag+=2;
	}
	if(flag==3) avai[i]=true;
    }
    bool ans=false;
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
	    mark[j]=false;
        }
	if(hasHeiro(G,avai,mark,i)){
	    ans=true;
	    break;
	}
    }
    if(ans) cout<<"Yes"<<endl;
    else cout<<"No"<<endl;

}