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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun main(args:Array<String>){
    val line1 = readLine()!!.trim().split(' ').map(String::toInt)
    val str = readLine()!!.trim()
    val n = line1[0]//頂点の個数
    val m = line1[1]//辺の本数
    val aList = arrayListOf<Int>()
    val aOK = hashSetOf<Int>()
    val bOK = hashSetOf<Int>()
    for(i in 1..n){
        if(str.get(i-1).equals('A'))aList.add(i)
    }
    for(i in 1..m){
        val list = readLine()!!.trim().split(' ').map(String::toInt)
        val x = list[0]
        val y = list[1]
        if(aList.contains(x)) aOK.add(y) else bOK.add(y)
        if(aList.contains(y)) aOK.add(x) else bOK.add(x)
        if(i%5==0){
            var calc = 0
            for(z in aOK){
                if(bOK.contains(z))calc++
            }
            if(calc>=2){
                println("YES")
                return
            }
        }
    }
    var calc = 0
    for(z in aOK){
        if(bOK.contains(z))calc++
    }
    if(calc>=2){
        println("YES")
        return
    }
    println("NO")
}