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 Rust (1.15.1) (judge verdict: Time Limit Exceeded)

use std::io::*;
use std::str::FromStr;

fn main() {
    let (n, m): (usize, usize) = (read(), read());
    let s: Vec<char> = read::<String>().chars().collect();
    let mut graph: Vec<Vec<usize>> = vec![Vec::new(); n];
    let mut count: Vec<(i32, i32)> = vec![(0, 0); n];
    for _ in 0..m {
        let (a, b) = (read::<usize>() - 1, read::<usize>() - 1);
        graph[b].push(a);
        if s[a] == 'A' {
            count[b].0 += 1;
        } else {
            count[b].1 += 1;
        }
        if a == b {
            continue;
        }
        graph[a].push(b);
        if s[b] == 'A' {
            count[a].0 += 1;
        } else {
            count[a].1 += 1;
        }
    }
    let mut changed = true;
    let mut list: Vec<usize> = (0..n).collect();
    while changed {
        changed = false;
        let mut next: Vec<usize> = Vec::new();
        for i in &list {
            if count[*i].0 <= 0 || count[*i].1 <= 0 {
                changed = true;
                for j in &graph[*i] {
                    if s[*i] == 'A' {
                        count[*j].0 -= 1;
                    } else {
                        count[*j].1 -= 1;
                    }
                }
            } else {
                next.push(*i);
            }
        }
        list = next;
    }
    let mut ok = false;
    for i in 0..n {
        if count[i].0 > 0 && count[i].1 > 0 {
            ok = true;
        }
    }
    println!("{}", if ok { "Yes" } else { "No" });
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}