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 Scala (2.11.7) (judge verdict: Accepted)

object Main {
  def main(args: Array[String]): Unit = {
    val s = new Main()
    s.solve()
    s.out.flush()
  }
}

class Main {
  import java.io._
  import java.util.StringTokenizer

  import scala.collection.mutable
  import scala.util.Sorting
  import math.{abs, max, min}
  import mutable.{ArrayBuffer, ListBuffer}
  import scala.reflect.ClassTag

  val MOD = 1000000007
  val out = new PrintWriter(System.out)

  def solve(): Unit = {
    val N, M = ni()
    val S = ns(N)
    val tpe = Array.ofDim[Int](N)
    rep(N) { i =>
      tpe(i) = if (S(i) == 'A') 0 else 1
    }

    val From, To = Array.ofDim[Int](2 * M)
    rep(M) { i =>
      val v, u = ni() - 1

      if (tpe(v) == tpe(u)) {
        // 0 -> 1
        From(i * 2) = v
        To(i * 2) = u + N
        From(i * 2 + 1) = u
        To(i * 2 + 1) = v + N
      } else {
        // A0 <-> B0
        From(i * 2) = v + N
        To(i * 2) = u
        From(i * 2 + 1) = u + N
        To(i * 2 + 1) = v
      }
    }
    val g = packDGraph(2 * N, From, To)
    val cycle = findCycle(2 * N, g)
    val ans = if (cycle.isDefined) "Yes" else "No"
    out.println(ans)
  }

  def packDGraph(n: Int, from: Array[Int], to: Array[Int]): Array[Array[Int]] = {
    val t = new Array[Array[Int]](n)
    val p = new Array[Int](n)
    val m = from.length
    rep(m)(i => p(from(i)) += 1)
    rep(n)(i => t(i) = new Array(p(i)))
    rep(m) { i =>
      p(from(i)) -= 1
      t(from(i))(p(from(i))) = to(i)
    }
    t
  }

  def findCycle(n: Int, g: Array[Array[Int]]): Option[Array[Int]] = {
    val flag = Array.ofDim[Int](n)
    val ix = Array.ofDim[Int](n)
    val q = Array.ofDim[Int](n)

    def dfs(i: Int): Option[Array[Int]] = {
      var last = 0
      q(0) = i
      while(last >= 0) {
        val v = q(last)

        flag(v) match {
          case 2 =>
            last -= 1

          case 0 | 1 =>
            flag(v) = 1
            if (g(v).length == ix(v)) {
              last -= 1
              flag(v) = 2
            } else {
              val u = g(v)(ix(v))
              if (flag(u) == 0) {
                last += 1
                q(last) = u
              } else if (flag(u) == 1) {
                val found = q.indexOf(u)
                return Some(java.util.Arrays.copyOfRange(q, found, last + 1))
              }
              ix(v) += 1
            }
        }
      }
      None
    }

    rep(n) { i =>
      if (flag(i) == 0) {
        val res = dfs(i)
        if (res.isDefined) return res
      }
    }

    None
  }

  class InputReader(val stream: InputStream) {
    private val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private var tokenizer: StringTokenizer = _

    def next(): String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = next().toInt
    def nextLong(): Long = next().toLong
    def nextChar(): Char = next().charAt(0)
  }
  val sc = new InputReader(System.in)
  def ni(): Int = sc.nextInt()
  def nl(): Long = sc.nextLong()
  def nc(): Char = sc.nextChar()
  def ns(): String = sc.next()
  def ns(n: Int): Array[Char] = ns().toCharArray
  def na(n: Int): Array[Int] = map(n)(_ => ni())
  def nal(n: Int): Array[Long] = map(n)(_ => nl())
  def nm(n: Int, m: Int): Array[Array[Char]] = map(n) (_ => ns(m))
  def rep(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = offset
    val N = n + offset
    while(i < N) { f(i); i += 1 }
  }
  def rep_r(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = n - 1 + offset
    while(i >= offset) { f(i); i -= 1 }
  }

  def map[@specialized A: ClassTag](n: Int)(f: Int => A): Array[A] = {
    val res = Array.ofDim[A](n)
    rep(n)(i => res(i) = f(i))
    res
  }

  def sumL(as: Array[Int]): Long = {
    var s = 0L
    rep(as.length)(i => s += as(i))
    s
  }
}