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: Accepted)

import java.util.*

// Reads multiple ints in a line, separate by a space.
// It works even if the actual number of ints is smaller than n.
// WARNING: This function does not work for -2^31.
// NOTE: This function does not handle error cases.
fun fastReadInts(n: Int): IntArray {
  val xs = IntArray(n)
  val s = readLine()!!
  var currentValue = 0
  var isNegative = false
  var currentIndex = 0
  for (c in s) {
    if (c == ' ') {
      xs[currentIndex] = currentValue * if (isNegative) -1 else 1
      currentValue = 0
      isNegative = false
      currentIndex++
    } else if (c == '-') {
      isNegative = true
    } else {
      currentValue *= 10
      currentValue += c - '0'
    }
  }
  xs[currentIndex] = currentValue * if (isNegative) -1 else 1
  return xs
}

fun main(args: Array<String>) {
  val (n, m) = fastReadInts(2)
  val label = readLine()!!
  val graph = Array(n, { mutableListOf<Int>() })
  repeat(m) {
    val (v1Input, v2Input) = fastReadInts(2)
    val v1 = v1Input - 1
    val v2 = v2Input - 1
    if (v1 != v2) {
      graph[v1].add(v2)
      graph[v2].add(v1)
    } else {
      graph[v1].add(v1)
    }
  }

  val aCount = IntArray(n)
  val bCount = IntArray(n)
  for (v in 0 until n) {
    for (u in graph[v]) {
      if (label[u] == 'A') {
        aCount[v]++
      } else {
        bCount[v]++
      }
    }
  }

  val q = Stack<Int>()
  for (v in 0 until n) {
    q.push(v)
  }

  val isBad = BooleanArray(n)
  while (q.isNotEmpty()) {
    val v = q.pop()
    if (isBad[v]) continue
    if (aCount[v] == 0 || bCount[v] == 0) {
      isBad[v] = true
      for (u in graph[v]) {
        if (u != v && !isBad[u]) {
          q.push(u)
          if (label[v] == 'A') {
            aCount[u]--
          } else {
            bCount[u]--
          }
        }
      }
    }
  }

  if (isBad.all { it }) {
    println("No")
  } else {
    println("Yes")
  }
}