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 <algorithm>
#include <queue>

using namespace std;

template<typename T>
ostream& operator<<(ostream& out, const vector<T> &v) {
    for(auto it=v.begin();it != v.end();it++) {
        cout << *it << " ";
    }
    cout << endl;
    return out;
}

int main() {
    int n,m;
    string s;
    cin >> n >> m;
    cin >> s;
    vector<vector<int>> v(n);
    vector<int> aok(n);
    vector<int> bok(n);
    fill(aok.begin(), aok.end(), 0);
    fill(bok.begin(), bok.end(), 0);
    for(int i=0;i<m;i++) {
        int a, b;
        cin >> a >> b;
        if (s[a-1] == 'A') {
            aok[a-1]++;
        } else {
            bok[b-1]++;
        }
        v[a-1].push_back(b-1);
        if (a == b) {
            continue;
        }
        if (s[b-1] == 'A') {
            aok[a-1]++;
        } else {
            bok[a-1]++;
        }
        v[b-1].push_back(a-1);
    }
    queue<int> q;
    for(int i=0;i<n;i++) {
        if (aok[i] == 0 || bok[i] == 0) {
            q.push(i);
        }
    }
    while(q.size() > 0) {
        int t = q.front();
        q.pop();
        //cout << t << endl;
        for(auto it = v[t].begin();it != v[t].end();it++) {
            if (aok[(*it)] == 0 || bok[(*it)] == 0) {
                continue;
            }
            if (s[t] == 'A') {
                aok[(*it)]--;
            } else {
                bok[(*it)]--;
            }
            if (aok[(*it)] == 0 || bok[(*it)] == 0) {
                q.push(*it);
            }
        }
    }
    //cout << aok << bok;
    if (aok[0] == 0 || bok[0] == 0) {
        cout << "NO" << endl;
    } else {
        cout << "Yes" << endl;
    }
    return 0;
}