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Contest: Task: Related: TaskB TaskD

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.
77e96cf8e213d606ddd8f3c3f8315d32.png

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.
1ab1411cb9d6ee023d14ca4e77c4b584.png

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