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<bits/stdc++.h>
using namespace std;
long long int n,m;
string s;
long long int a[300000],b[300000],po[300000];
vector<vector<long long int > >ma;
vector<long long int>row;
map<char,long long int>aho;

int ssA(int x){
    int alf=0;
    for(int i=0;i<ma[x].size();i++){
        if(s[ma[x][i]]=='B')alf++;
    }
    if(alf>0)return 5;
    else return 0;
}

int ssB(int x){
    int alf=0;
    for(int i=0;i<ma[x].size();i++){
        if(s[ma[x][i]]=='A')alf++;
    }
    if(alf>0)return 4;
    else return 0;
}

int chc(int x){
    for(int i=0;i<ma[x].size();i++){
        if(po[ma[x][i]]==5)aho['A']++;
        if(po[ma[x][i]]==4)aho['B']++;
    }
    aho[s[x]]--;
    if(aho['A']==aho['B'])return 1;
    else return 0;
}

int saikiA(int x){

    int xz=0,xy=0;
    for(int i=0;i<ma[x].size();i++){
        if(s[ma[x][i]]=='A')xz=ssA(ma[x][i]);
    }
    int alf=0;
    for(int i=0;i<ma[x].size();i++){
        if(s[ma[x][i]]=='B')alf++;
    }
    if(alf>0)xy=5;
    else xy=0;

    return min(xy,xz);

}

int saikiB(int x){
    int xz=0,xy=0;
    for(int i=0;i<ma[x].size();i++){
        if(s[ma[x][i]]=='B')xz=ssB(ma[x][i]);
    }
    int alf=0;
    for(int i=0;i<ma[x].size();i++){
        if(s[ma[x][i]]=='A')alf++;
    }
    if(alf>0)xy=4;
    else xy=0;

    return min(xy,xz);
}



int main(){
    cin>>n>>m;
    cin>>s;
    for(int i=0;i<n;i++){
        ma.push_back(row);
    }
    for(int i=0;i<m;i++){
        cin>>a[i]>>b[i];
        ma[a[i]-1].push_back(b[i]-1);
        ma[b[i]-1].push_back(a[i]-1);
    }
    for(int i=0;i<n;i++){
        if(s[i]=='A')po[i]=saikiA(i);
        if(s[i]=='B')po[i]=saikiB(i);
    }




    for(int i=0;i<n;i++){
        if(po[i]==5||po[i]==4){
            if(chc(i)){
                cout<<"Yes"<<endl;
                return 0;
            }
        }
    }
    cout<<"No"<<endl;



}